Search

Regarding the design optimization of the heat exchanger, the traditional method of changing the size of the macroscopic structure can no longer meet the increasing demand for heat exchange performance. The superhydrophobic surface can significantly reduce the flow resistance, which is expected to be a new method for the optimal design of heat exchanger. However, when the superhydrophobic effect is applied to a specific type of heat exchanger, its flow and heat transfer performance is not clear. In this paper, the flow and heat transfer model of the traversing superhydrophobic tube bundle is studied. Combined with the FLUENT 18.0 software, the slip boundary conditions of the superhydrophobic surface are deduced, and the flow and heat transfer characteristics of the superhydrophobic tube bundle surface and the wake are numerically analyzed, the influence mechanisms of slip effect on flow and heat transfer characteristics were obtained. Overall, as Ls increases, the comprehensive Nu, also known as heat transfer performance, on the cylindrical surface gradually increases, while the comprehensive Cf, also known as frictional resistance, on the cylindrical surface gradually decreases, indicating that superhydrophobic performance is expected to achieve heat transfer enhancement. The above conclusions can provide a theoretical basis for the optimal design of high-efficiency compact heat exchanger, and have important engineering application significance. [ABSTRACT FROM AUTHOR]

Ternary hybrid nanofluids are crucial to be modeled and researched before their commercial application as a heat transfer fluid. This study investigates the stagnation point flow of a ternary hybrid nanofluid past a stretching/shrinking sheet, focusing on the influence of the melting parameter and second-order velocity slip. The governing partial differential equations (PDEs) are initially formulated and subsequently reduced to ordinary differential equations (ODEs). These ODEs are further transformed into first-order form and numerically solved using the bvp4c solver in MATLAB. Stability analysis is conducted due to the existence of two potential solutions, of which only one proves stable upon analysis. The numerical results indicate significant enhancements in heat transfer performance under conditions of elevated melting and enhanced velocity slip. Reducing the melting parameter and second-order velocity slip may expand the solution range, leading to a delay in boundary layer separation. The stable numerical solution for the heat transfer rate is then validated with the use of a logic mining model namely Permutation 2 Satisfiability Reverse Analysis (P2SATRA). The most accurate induced logic, chosen to illustrate the overall relationship between the selected parameters is achieved in the third fold of a 10-fold cross-validation, yielding an accuracy of 0.81818. [ABSTRACT FROM AUTHOR]

This paper is on the motion of a neutrally buoyant but circular slip particle in a clockwise double-lid-driven square cavity. The slip flow at the particle surface is implemented by the lattice Boltzmann method with corrected slip boundary schemes. The effects of slip length (Ls), initial particle position, Reynolds number (Re), and particle size (D) are studied on the migration of the slip particle. The motion of the circular slip particle is dominated by the centrifugal and boundary-repulsion forces. The results show that the cavity center is the unique fixed point, and once the slip particle initially deviates from the cavity center, it is always stabilized at the same limit cycle. With the increase in slip length, the limit cycle of the circular slip particle is closer to the cavity boundaries, which brings a stronger centrifugal force to balance the increased boundary-confinement effect. As the slip length, Ls, exceeds 0.02D, the limit cycle forms more quickly than the circular no-slip particle. When Re increases to within 1000, the limit cycle is squashed along the leading diagonal of the cavity and pushed toward the boundaries; however, when Re increases beyond 1000, two developing secondary vortices confine the limit cycle to shrink toward the cavity center. With the increase in particle size, the enhanced boundary confinements lead to the shrinkage of the limit cycle toward the cavity center. [ABSTRACT FROM AUTHOR]

The influence of thermal radiation, multiple slip boundary conditions, and binary chemical reaction on the three‐dimensional circulation of unsteady magnetohydrodynamic (MHD) natural convection Carreau hybrid nanofluid (MoS2+SiO2/H2O${\mathrm{MoS}}_2 + {\mathrm{SiO}}_2/{{\mathrm{H}}}_2{\mathrm{O}}$) across a stretching sheet comprised of heat source/sink (H‐SS) and variable thermal conductivity are investigated. Runge‐Kutta‐Fehlberg 4th‐5th order (RKF‐45), in conjunction with the shooting approach, is utilized for numerical computation. Computed solutions indicate that the volume fraction of silicon dioxide and velocity slip parameters tends to retard the velocity profile. It is inferred from the graphs that temperature profile upsurges with enhancing the magnitude of thermal Grashof number, H‐SS parameter, mass Grashof number, variable conductivity parameter, and radiative parameter, whereas converse effects for thermal slip parameter. The chemical reaction parameter and solutal slip constraint tend to decrease the concentration profile. Furthermore, the heat transfer phenomenon uplifts with the consideration of radiative effects, while the mass transfer rate diminishes with enhancing the magnitude of magnetic parameters and activation energy. [ABSTRACT FROM AUTHOR]

The article "Unveiling the mystery of effective slip" published in the Journal of Fluid Mechanics explores the concept of boundary layers in fluid flows, tracing back to Leonardo da Vinci's observations of pipe flow. It discusses the historical development of slip length theories and the applicability of the no-slip boundary condition at fluid-solid interfaces. Lauga & Stone (2003) proposed an effective slip model to bridge microscopic wall conditions to macroscopic slip lengths, impacting fluid dynamics research and surface design applications. The model provides insights into slip boundary conditions over complex boundaries and offers a framework for understanding fluid behaviors near fluid-solid interfaces. [Extracted from the article]

We consider the optimal control of unsteady natural convective flow of reactive viscous fluid with heat transfer. It is assumed that Newton's law governs the heat transfer within an exothermic reaction under Arrhenius kinetics and Navier slip condition on the lower surface of the channel. The flow is examined in a vertical channel formed by two infinite vertical parallel plates, with a distance (H) between them. Time-dependent natural convective slip flow of reactive viscous fluid and heat transfer equations are solved in a unit interval using the Galerkin-Finite Element Method (FEM) with quadratic finite elements in space and the implicit Euler method in time. The direct solutions are obtained for testing various values of the problem parameters: the Biot number, the Frank Kamenetskii parameter, the Navier slip parameter, and the computation of the skin friction and the Nusselt number (Nu). The optimal control problem is designed for the momentum and energy equations to derive the fluid-prescribed velocity and temperature profiles by defining controls on the boundary of the domain in two ways: (a) controls are formulated as parameters in the boundary conditions, such as slip length and Biot number; (b) controls are assigned as time-dependent functions in the boundary conditions, representing the slip velocity and the heat transfer rate. Following a discretize-then-optimize approach to the control problem, optimization is performed by the SLSQP (Sequential Least Squares Programming) algorithm, a subroutine of SciPy. Numerically simulated results show that the proposed approach successfully drives the flow to prescribed velocity and temperature profiles. [ABSTRACT FROM AUTHOR]

The present study unveils research that examines the laminar motion of water-infused nanofluid comprised of nanoparticles of TiO2 (titanium dioxide), Ag (silver), and Cu (copper) over a stretching sheet. The flow undergoes a novel slip condition based on Thomson and Troian to model complex fluid behavior near solid walls and incorporate the Darcy-Forchheimer model to comprehensively analyze the influence of a porous medium on flow behavior. Moreover, a heat source/sink and radiation are included to ensure the outcome of the energy equation will resemble most actual-world applications. Partial differential equations (PDEs) of higher order, originally used to describe the system are then reformulated into higher-order non-linear ordinary differential equations (ODEs) by taking symmetry variables that are chosen thoughtfully. The resulting boundary layer equations are then turned into a set of ODEs by implementing relevant similarity transformations, which can be solved using the MATLAB function bvp4c. Through graphs, the variations in the velocity, Nusselt number, temperature, and skin friction coefficient were displayed. The outcome showed that the incorporation of silver nanoparticles (0.01-0.03) enhanced the skin friction coefficient by = 1.68% and the Nusselt number reduced up to = 5%. The Forchheimer number also reported a 6.5% enhancement and 1.5% reduction in the skin friction coefficient and the Nusselt number, respectively. The velocity slip parameter γ1 correlates with an upswing in temperature and skin friction coefficient for the ternary nanofluid while observing a decline in the velocity and Nusselt number. [ABSTRACT FROM AUTHOR]

This primary goal of this analysis is to investigate how several slips affect the flow, heat, and mass performance of Darcy–Forchheimer unstable behavior beyond a stretching sheet using a numerical analysis of the Soret effect. The novel constitutive model Cattaneo–Christov is illustrated to analyze the features of thermal relaxation time. The Cattaneo–Christov method is used to predict heat and mass transport. A surface that slanders and has varying thicknesses propels the flow. Through the use of local similarity transformations, the governing nonlinear partial differential equations reduce to the coupled ordinary differential equations and include the momentum, energy, and concentration equations. The altered ODEs are calculated numerically using the Runge–Kutta Fehlberg scheme and an efficient shooting procedure. The physical properties of the temperature, concentration, and fluid velocity profiles are shown visually and shed light on the change of several governing parameters. For example, in comparison to the classical Fourier's heat model, our result suggests that the Cattaneo–Christov heat flux constitution has lower temperature and thermal boundary layer thickness. In the meantime, a high wall thickness parameter greatly upgrades the rate of heat transfer, and thermal relaxation has the opposite effect. Discussion is held regarding the effects of various miscellaneous variables on temperature, concentration, and velocity. [ABSTRACT FROM AUTHOR]

This study investigates the fluid flow, heat, and mass transfer phenomena within a vertical channel containing two immiscible fluids, with a particular focus on slip effects. These effects include no slip, velocity slip, thermal slip, and multiple slips, each analyzed with appropriate boundary conditions. The study thoroughly examines key characteristics, such as variations in thermal conductivity and viscosity. Using a sixth‐order Runge–Kutta numerical method implemented using Mathematica, the study achieves precise solutions for complex scenarios. The detailed results show how the various slip mechanisms and relevant parameters interact with each other in complex ways. These findings are useful for both theoretical understanding and application in real‐life engineering situations. This study also gives important information about how fluid flow, heat transfer, and mass transfer change under different slip effects. It looks at these effects and shows how they change visually. It also carefully calculates and analyzes engineering parameters like the Nusselt number, shear stress, and Sherwood number using bar charts, showing how they affect and behave. The study resulted in velocity slip having a minimal impact on temperature, whereas thermal slip resulted in higher temperatures. Both velocity and thermal slip conditions simultaneously result in the lowest temperatures. [ABSTRACT FROM AUTHOR]

This paper investigates magnetohydrodynamic (MHD) boundary layer slip flow with heat transfer over a bullet shaped object. The study addresses a significant problem in fluid dynamics and heat transport with applications in various engineering and industrial domains, including aerospace, material processing, and energy systems. The governing equations are resolved using the bvp4c, an inbuilt MATLAB tool, and the arithmetic computation for the momentum and thermotic equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted with the aid of velocity and temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The heat transfer processes and fluid flow are remarkably influenced by means of the ratio of surface thickness and stretching potential. The results obtained designated that the Mixed convection parameter λ increases momentum BL thickness, whereas the temperature profile diminishes. Furthermore, momentum and temperature profile improve for surface thickness parameter s $s$. The current investigation highlights the potential utility of heat transport rate and friction factor in the industrial divisions for regulating cooling rates and enhancing the quality of end products. [ABSTRACT FROM AUTHOR]

The performances of the heat transfer due to dissipative heat likely magnetic dissipation is a challenging field of research because of it's diversifies applications in industries and engineering. Particularly, nowadays, in biomedical field of research the implementation of dissipation along with thermal radiation is vital. Based upon the current scenario, the present investigation leading to the role of magnetic dissipation vis‐à‐vis thermal radiation on the water‐based hybrid nanofluid past an electro‐magnetized elongating surface associated with melting boundary conditions. The adaptation of the transformed rule particularly, similarity rules are useful to convert the proposed set of problems in to ordinary. Further, shooting‐based numerical technique is proposed to handle the governing equations. The interesting and novel approach in this topic is the use of robust statistical technique, that is, response surface methodology for the optimizing Nusselt number for the use of various factors. Moreover, the validation is obtained by conducting a hypothetical testing using analysis of variance (ANOVA) which conforms a best output model for appropriate response. Further, the major outcomes of the study are depicted as; the unsteadiness parameter decelerates the velocity profile of the hybrid nanofluid for the interaction. However, the increasing particle concentration favours in enhancing the heat transport phenomenon. [ABSTRACT FROM AUTHOR]

Purpose: The current work investigates an unsteady squeezed flow of hybrid-nanofluid between two parallel plates in occurrence with a uniform transverse magnetic field. Water is used as base fluid mixed with Graphene Oxide (GO) and Copper (Cu) nanoparticles. The flow considered here is under slip boundary conditions. Design/methodology/approach: The governing PDEs are transmuted into ODEs by applying an appropriate similarity transformation and then solved numerically using the 4th order R-K method with shooting technique. Graphical illustrations for velocity, temperature, entropy generation (NG), Bejan number (Be), streamline etc. are presented and discussed in detail from the physical point of view. The nature of the Nusselt number is also studied numerically through contour plots for different flow parameters. Findings: There is no funding obtained for the research work. Social implications: This kind of study may be used in various fields including polymer processing, lubrication apparatus, compression including hydrodynamical machines compression, food processing etc. Originality/value: It is observed that very little investigation has yet been made about the movement of hybrid nanofluid between two analogous plates. [ABSTRACT FROM AUTHOR]

The article "Harnessing wall slip towards tunable microswimming in Poiseuille flow" delves into the movement of microswimmers in confined Poiseuille flow with slippery walls. Through an analytical-numerical approach, the study examines how slip length impacts microswimmer dynamics, leading to changes in propulsion mechanisms and swimming states for pullers and pushers. The research sheds light on specific motion behaviors, offering valuable insights for the development of microfluidic drug delivery systems and the prevention of biofilm deposition in biomedical devices. The study emphasizes the intricate relationship between slip effects and external flow patterns in shaping the locomotion strategy of microswimmers in narrow channels. [Extracted from the article]

Reiner–Philippoff (RP) fluid flow above a heated sheet concluded the model of Cattaneo–Christov heat flux for Darcy-Forchheimer is implemented in this work. The influences of thermal radiation, heat source/sink, velocity, and thermal slip boundary conditions are also deliberated. The transformations are used to convert obtained partial differential equations into a set of ordinary differential equations, and they are solved numerically using the shooting method (RK-4) solver with the help of the computational software MATLAB. The dimensionless temperature and velocity numbers are further developed. More engineering curiosity of local Nusselt and Skin frictions are tabulated, depicted, and interpreted. The study presents graphical and tabular illustrations depicting flow parameters, velocity profiles, and temperature profiles. Key conclusions drawn include, When the inertia coefficient F r increases, the velocity field f ′ (η) decreases. Analytical calculations are performed for the flow of a Reiner-Philippoff fluid over a shrinking sheet, considering influences such as thermal radiation, velocity slip, and temperature fluctuations. Increased heat absorption correlates with higher Nusselt numbers, whereas temperature generation lowers wall temperatures. The skin friction magnitude gradually increases in the order of dilatant, viscous, and pseudo-plastic fluids, respectively. [ABSTRACT FROM AUTHOR]

The present study explores the dynamics of a two-dimensional, incompressible nanofluid flow through a stretching curved sheet within a highly porous medium. The mathematical model is formulated by including external forces such as viscous dissipation, thermal radiation, Ohmic heating, chemical reactions, and activation energy by utilizing a curvilinear coordinate system. The viscosity and thermal conductivity of the nanofluids are examined using the Koo–Kleinstreuer–Li model. The choice of |$Al_{2}O_{3}$| and |$CuO$| nanoparticles in this model stems from their distinct thermal properties and widespread industrial applicability. By non-dimensionalizing the governing partial differential equations, the physical model is simplified into ordinary differential equations. BVP-5C solver in MATLAB is utilized to numerically solve the obtained coupled non-linear ordinary differential equation. Graphical results are presented to investigate the velocity, temperature, and concentration profiles with entropy generation optimization under the influence of several flow parameters. The artificial neural network backpropagated with Levenberg–Marquardt method (ANN-BLMM) used to study the model. The performance is validated using regression analysis, mean square error and error histogram plots. The outcome illustrates that the velocity and temperature profiles increase with increasing the Forchhiemer parameter. Also, the velocity profile increases with increasing curvature parameter, while, reverse effect is observed for temperature profile. This research augments our comprehension of nanofluid dynamics over curved surfaces, which has implications for engineering applications. The insights gained have the potential to significantly contribute to the advancement of energy-efficient and environmentally sustainable cooling systems in industrial processes. [ABSTRACT FROM AUTHOR]

In the existing investigation, impacts of slip and chemical reactions on mass and heat exchange on an incompressible and electrically conducting micropolar fluid past a porous wedge within the sight of Hall and ion slip are examined. By employing similarity conversion, the relevant highly nonlinear PDEs are reformed into a collection of nonlinear linked ODEs. The equations framed in this manner have been resolved by using the bvp5c, the in-build MATLAB. Examination of magneto-hydrodynamic micropolar fluid on stagnation point flow is significant due to its uses in the production of plastic substances, polymer extrusion, lubricants, etc. The influence of the magnetic field, heat generation, microrotation, along with Hall and ion slip on the liquid flow is analyzed. Examination with prior published research papers is performed and the outcomes are compared with each other. Numerical simulations for shear stress coefficients, Sherwood and Nusselt numbers are provided in tabular form, and in addition, the variations in axial and microrotation velocities, temperature and solutal profiles are evaluated visually for various parameters in detail. The ion slip and slip velocity both slow down the shear rate, whereas the elevated values of the Hall and magnetic parameters show an opposite trend. The profile shows thinning of the bounding surface and offers its greatest magnitude in the case of a Newtonian liquid. [ABSTRACT FROM AUTHOR]

The present study analyzes the mixed convection with magnetohydrodynamic (MHD) flow, Joule heating, and heat transfer in hybrid nanofluids on exponentially stretching or shrinking sheets. The study aims to optimize heat transfer and fluid dynamics properties in engineering and industrial applications. The governing partial differential equations are converted into ordinary differential equations by employing appropriate similarity transformations and then solved using the BVP4C MATLAB tool. In this study, the effects of silver volume fraction, velocity slip, thermal slip, magnetic field, heat generation, Eckert number, and thermal radiation on the skin friction coefficient, Nusselt number, velocity profile, and temperature profile are examined and graphically discussed. The base fluid water contained 2% silver (Ag) and 0.1% titanium oxide (TiO2) nano-particles in this hybrid model. The dual solution was present for a shrinking sheet ($\lambda \lt 0$λ<0) when $\lambda \ge {\lambda _c}$λ≥λc. The skin friction coefficient values decreased by approximately 37%, while the local Nusselt number increased by approximately 3.1% when the velocity slip increased in the first solution. The Nusselt number increased by approximately 0.28% and 12% when the Eckert number and radiative parameter increased, respectively, but decreased by approximately 7.5% and 0.20% when the thermal slip and heat generation increased, respectively. [ABSTRACT FROM AUTHOR]

The receptivity phase located upstream from the neutral point might be significantly affected by local rarefaction effects (especially surface slip effects) in terms of the boundary-layer transition of near-space hypersonic vehicles. In this paper, the receptivity of a supersonic flat-plate boundary layer to freestream acoustic waves in no-slip and slip flows is analyzed using direct numerical simulations and linear stability theory. The Maxwell–Smoluchowski velocity-slip and temperature-jump boundary conditions are adopted at the wall to account for surface slip effects. A Mach 4.5 flow at different wall-cooling degrees is mainly analyzed, and another Mach-6 case is presented, both with freestream unit Reynolds number on the order of 1 × 10 6 /m. The main goal is to clarify the qualitative and quantitative influence of surface slip effects on the receptivity phase under different conditions. The results show that the receptivity mechanism in the slip flow is similar to that in the no-slip flow. That is, the mode S or F is excited near the leading edge due to synchronization with slow or fast acoustic waves, and the Mack second mode is excited further downstream after synchronization between modes S and F. However, the slip effects lead to distinctly quantitative differences in receptivity. The slip effects have little influence on the excitation of mode S or F near the leading edge but largely affect the evolution (intermodal exchange) of modes S and F as propagating downstream. Consequently, as for the receptivity to slow acoustic waves, the slip effects play a stabilizing role in receptivity when mode S is stable while a destabilizing role when mode S converts to the first mode in the upstream. As for receptivity to fast acoustic waves, as slip degree increases, the slip effects initially stabilize and then destabilize the receptivity, where the receptivity coefficient of the tested slip case can increase by 25% compared with the no-slip case. [ABSTRACT FROM AUTHOR]

The primary purpose of this study is to provide more information on the stable and incompressible stream of a hybrid nanofluid over a poignant tiny needle in two dimensions under slip boundary conditions. In the hybrid nanofluid flow, Al2O3 and Fe3O4 are nanoparticles, water and ethylene glycol (50:50) are considered as the base fluids. Furthermore, the impacts of Joule heating and inclined magnetic fields are considered. The PDE's governing equations are converted into ODEs by using similarity transformations and solved by a numerical technique based on Runge–Kutta fourth-order method. The results illustrate that the crucial parameters such as the magnetic parameter, Eckert number, nanoparticles of solid volume fractions, inclined angle parameter, and Prandtl numbers significantly affect the momentum and thermal profiles. The heat transfer rate and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in a table. These analyses manifest that raising the magnetic parameter results in a decrease in the hybrid nanofluid velocity under slip and no-slip circumstances. The Nusselt number has also grown as a result of the volumetric fractions of nanoparticles and the intensification of the angle parameter. This analysis might include areas such as microfluidics, biomedical devices, heat exchangers, and other engineering applications where precise control over fluid behavior and temperature distribution is important. [ABSTRACT FROM AUTHOR]

The focus of present study is to incorporate the variable viscosity and temperature slip impact on heating rate and induced magnetic gradient along the moving non-conducting wedge under magnetic field. In industrial and engineering procedures, the impact of induced magnetization improves the efficiency of thermal systems to main the heating rates. The similarity transformations and stream functions are applied to reduce the governing equations into ordinary form. During this transformation, the pertinent parameters such as wedge parameter, moving parameter, Prandtl factor, viscosity parameter and temperature-slip parameter is obtained. These parameters play a prominent role on the physical values of fluid velocity, induced magnetic field and temperature distributions. The skin friction, Nusselt coefficient and induced magnetic gradient are incorporated through these parameters. The numerical values are executed by using the Keller box analysis with Newton–Raphson technique. It is depicted that the maximum slip in fluid velocity and temperature distribution is obtained for each values of thermal-slip parameter. It is noticed that maximum magnitude in induced magnetic field is reported for each wedge factor. The maximum velocity slip and temperature slip is observed for each choice of moving parameter. It is reported that the maximum variation in heating rate and induced magnetic gradient is obtained for magnetic force and viscosity parameter. The enhancing behavior of skin friction is observed for maximum values of Prandtl number. [ABSTRACT FROM AUTHOR]

An unsteady two-dimensional nanofluid flow across a permeable stretched sheet is examined in terms of thermodynamic analysis. Water is utilized as the basic fluid, together with four distinct types of nanoparticles: copper (Cu), copper oxide (CuO), aluminum oxide (Al2O3), and titanium dioxide (TiO2). An external source is used to describe the heat transfer phenomena. The effects of heat generation and absorption are also taken into account. The nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via a similarity transformation. The spectral quasi-linearization approach is then used to numerically integrate the altered equations. Except when otherwise noted, the findings are provided for copper nanoparticle situations. A visual and detailed explanation of the effects of several physical factors on the profiles of dimensionless velocity, temperature, average entropy generation function, skin friction, and the Nusselt number are discussed. As exceptional circumstances of the current findings, there is a strong agreement between the current conclusion and the findings of the other researchers. The average entropy generation number, temperature, and velocity profiles are shown to be strongly influenced by regulating factors. It is concluded that the average entropy generation decreased in the presence of a temperature- and space-dependent heat source/sink, but it improves with enhanced viscosity parameter. The significance of the present study has frequent applications in the major area of heat transfer enhancement in renewable energy systems, industrial thermal management, and also materials processing. [ABSTRACT FROM AUTHOR]

This article recognizes the time-dependent axisymmetric flow of a non-Newtonian Williamson fluid caused by a radially stretching surface in the presence of nanoparticles in the porous medium. The combined impacts of Joule heating and viscous dissipation on the flow profiles are also discussed. Chemical reaction at the surface is implemented. The convective heat transfer model and Brownian motion are also studied for the electrically conducting nanofluid flow. The Williamson nanofluid flow has been modeled using a set of partial differential equations based on the fundamental conservation laws of mechanics. By using nondimensional quantities, these equations are first transformed into ordinary differential equations. The Galerkin weighted residual method is performed to resolve these equations numerically. Visual displays and detailed descriptions of the impacts of relevant variables on the thermal performance, concentration field, and velocity field are provided. It is noticed that the thermal profile enhances as the values of the Brownian motion parameter and temperature ratio parameter increase while declining when the values of the velocity slip parameter increase. The Biot number, activation energy, and unsteadiness parameters have proportional effects on the concentration profile, but the reaction parameter has inversely proportional effects on the concentration profile. Heat transfer rate increases with increasing the Weissenberg number and velocity slip parameter, drops with increasing the thermophoresis and unsteadiness parameters, and the Arrhenius activation energy. Finally, a comparison of the obtained numerical solution for the porous and nonporous medium are also done graphically and discussed in details. [ABSTRACT FROM AUTHOR]

Nanofluids are emerging as a revolutionary replacement for traditional cooling agents. In addition to this, the motile microorganism helps to stabilize the nanofluid. In this direction, the present investigation addressed Casson fluid flow immersed with gyrotactic microorganisms due to an inclined surface. This flow is controlled by incorporating magnetic forces and restricted to passing through porous media. The influence of the chemical activities and heat convection is examined to complete the mathematical description of the flow situation. The total energy involvement is obtained by the addition of resistive heating and viscous dissipation terms in the energy equation. The current flow situation of equations of said physical condition is renovated into the ordinary differential equations (ODEs) with the implementation of proper similarity variables. The numerical solution is developed with the Runge-Kutta scheme. Graphical illustration for respective physical parameters is obtained via MATLAB. The numerical discussion of the present work is validated with previously published literature. The flow motion is controlled by strengthening the magnetic strength. Boost in the Schmidt number and bioconvection Schmidt number reduces the boundary layer thickness. [ABSTRACT FROM AUTHOR]

The flow of ethylene glycol-based titania nanoliquid passing through a vertical plate induced by significant buoyancy forces (nonlinear convection) is analyzed with quadratic thermal radiation and considering the aggregation kinematics of the nanoparticles. The nanoliquid is modeled accounting for thermo-migration, Brownian motion, and the effectual thermophysical properties. The realistic zero mass flux and thermal slip conditions are considered on the surface of the plate. In addition, the mechanisms of exponential space-related heat source (ESHS) and thermal-based heat source (THS) are incorporated. The finite-difference technique-based bvp5c routine is used to obtain the numerical solution of thenonlinear system of equations. The effects of the parameters are examined on the dimensionless profiles of velocity, temperature, heat transport rate, the volume fraction of nanoparticles, and streamlines. It was found that the aggregation of nanoparticles significantly advances the temperature field while the velocity field is reduced. The ESHS and THS modulations improve the thickness of the thermal boundary layer. The quadratic thermal convection aspect improves the velocity of nanoliquid. Furthermore, the effects of quadratic thermal radiation assist the growth of the thermal boundary layer. The present results are relevant to various thermal systems including flat plate solar collectors, heat exchangers, and nuclear reactors. [ABSTRACT FROM AUTHOR]

This research stands out due to its utilization of a Casson ternary hybrid nanofluid (THNF) consisting of SiC, SWCNTs and MWCNTs , and H 2 O as the base fluid. Additionally, the introduction of slip flow, convective heat transfer boundary, and applied magnetic field are the objectives to elucidate the heat transfer behavior on fluid flow and energy profile. The article emphasizes the analysis of heat transfer properties in a 2D flow of magnetohydrodynamic Casson ternary nanofluid past a stretching sheet. The effect of non-uniform heat absorption/generation is considered in the study to better understand the heat transfer phenomena. By operating suitable similarity variables, the governing equations are transmuted into a dimensionless form. The numerical outcomes are obtained through the Runge–Kutta-based shooting scheme. The uniqueness of this paper stems from employing a Casson THNF with partial velocity jump and convective boundary. The highlight of the study is that an increment in the Casson parameter enhances fluid yield stress, reducing momentum and thermal boundary layer thickness. Elevated suction reduces boundary layer thickness, while magnetic fields influence fluid thermal conductivity, leading to higher Nusselt numbers and enhanced convective heat transfer. The findings derived from this study offer valuable insights applicable to a range of engineering and industrial processes. [ABSTRACT FROM AUTHOR]

In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al2O3, for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/Dh), and volume fraction of Al2O3 nanoparticles (ϕ) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or ϕ would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/Dh ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and ϕ = 0.1 (Pr = 0.729). Finally, Nuavg, Nux, U/Um, and ReCf were corelated with Kn, Pr, Re, and x/Dh with proper coefficient of determination (R2) values. [ABSTRACT FROM AUTHOR]

It observers that an object is submerged in a liquid, more pressure is applied to its bottom surface than its top surface, as a result pressure rises within depth of fluids. A buoyancy force is generated due to the pressure difference. In the current investigation, the mathematical formulation of bio-convective stagnation point flow of a radiative Maxwell fluid with multiple slip effect on an exponentially porous stretching surface is analyzed thoroughly. The buoyancy assisting and opposing conditions with magnetic field are discussed in the current investigation. Moreover, the energy and concertation equations are formulated by the utilization of Cattaneo–Christov theory and non-uniform heat source/sink. The flow model is developed in the form of partial derivatives, then use the similarity variables to convert the physical system into nonlinear ordinary derivative. The nonlinear system is tackled numerically with the help of Bvp4c approach on the MATLAB. The graphical upshots for various emerging parameter are observed with two aspects: buoyancy assisting λ > 0 and buoyancy opposing λ < 0 . The observation shows that the greater values of mixed convection parameter improves the fluid velocity for assisting flow λ > 0 , while declining trend is noticing for opposing flow situation λ > 0 . Further, it is worth noticing that stronger inputs of thermal and concentration relaxation parameter yield lesser thermal and concentration diffusivity, which reduces the temperature and nanoparticles concentration. [ABSTRACT FROM AUTHOR]

Riga plate is known to create a crossing electric and magnetic field to generate a wall-parallel Lorentz force. The significance of Casson nanofluid flow past a Riga plate is observed in the sphere of engineering, such as polymer extrusion, food manufacturing, plastic films, oil reserves and geothermal manufacturing. Researchers are interested in this model because of its potential use in biological rheological models. As Casson nanofluid flows are of great interest, this study aims to investigate the three-dimensional magnetohydrodynamics (MHD) flow with heat and mass transport of Casson nanofluid over a flat Riga plate. As a novelty, this study also includes the effectiveness of wall velocity slip, activation energy, nonlinear radiation, and temperature and space-dependent heat source/sink. Suitable similarity transformations have been employed to generate the dimensionless ordinary differential equations (ODEs) from the partial differential equations (PDEs) regulating the fluid flow problem. The transformed nonlinear boundary value problem is then solved numerically using the in-built routine "bvp4c" in MATLAB. The visual demonstrations are provided for the effects of various significant physical factors on the flow, heat and mass distributions. On the other hand, wall shear stress and rates of heat and mass transport at the surface are measured and displayed numerically in tabular form. The findings indicate that the fluid velocity in both directions slows as the velocity slip parameter increases. However, the velocity profile is escalated with the boost of modified Hartmann number. An increase in heat source parameters leads to decrease the heat transmission rate at the wall. The higher values of the radiation parameter result in a better wall heat transmission rate. Further, the rate of mass transport drops when the activation energy parameter is hiked. [ABSTRACT FROM AUTHOR]

This paper investigates the flow and heat transfer attributes of Bödewadt flow in nanofluid, accounting for velocity slip, thermal slip, and a radially stretching permeable disk. The von Kármán similarity variables have been applied to simplify the governing partial differential equations into nonlinear ordinary differential equations, which are subsequently solved numerically using Python's solve_bvp module. The results indicate that an adequate amount of stretching rate is required for the heat transfer equation's similarity solution to be present in the case of a no-slip stretching disk in order to satisfy the boundary conditions. The momentum and thermal boundary layer thickness are affected by the presence of velocity slip and thermal slip, along with stretching parameter. Additionally, variation of the local skin friction coefficient and local Nusselt number shows that heat transfer enhancement occurs in optimal situations when the slip value is minimal, a higher volume fraction of nanoparticles is used, and larger stretching parameters are applied. [ABSTRACT FROM AUTHOR]

Modern energy systems are finding new applications for magnetohydrodynamic rheological bio-inspired pumping systems. The incorporation of the electrically conductive qualities of flowing liquids into the biological geometries, rheological behavior, and propulsion processes of these systems was a significant effort. Additional enhancements to transport properties are possible with the use of nanofluids. Due to their several applications in physiology and industry, including urine dynamics, chyme migration in the gastrointestinal system, and the hemodynamics of tiny blood arteries. Peristaltic processes also move spermatozoa in the human reproductive system and embryos in the uterus. The present research examines heat transport in a two-dimensional deformable channel containing magnetic viscoelastic nanofluids by considering all of these factors concurrently, which is vulnerable to peristaltic waves and hall current under ion slip and other situations. Nanofluid rheology makes use of the Sutterby fluid model, while nanoscale effects are modeled using the Buongiorno model. The current study introduces an innovative numerical computing solver utilizing a Multilayer Perceptron feed-forward back-propagation artificial neural network (ANN) with the Levenberg–Marquardt algorithm. Data were collected for testing, certifying, and training the ANN model. In order to make the dimensional PDEs dimensionless, the non-similar variables are employed and calculated by the Homotopy perturbation technique. The effects of developing parameters such as Sutterby fluid parameter, Froude number, thermophoresis, ion-slip parameter, Brownian motion, radiation, Eckert number, and Hall parameter on velocity, temperature, and concentration are demonstrated. The machine learning model chooses data, builds and trains a network, and subsequently assesses its performance using the mean square error metric. Current results declare that the improving Reynolds number tends to increase the pressure rise. Improving the Hall parameter is shown to result in a decrease in velocity. When raising a fluid's parameter, the temperature profile rises. [ABSTRACT FROM AUTHOR]

A nanofluid refers to a suspension of nanoparticles in a conventional fluid, which finds unique applications in diverse sectors, including engineering, technology, and medicine. When multiple nanoparticles are suspended, it creates a hybrid nanofluid. In this study, we aim to investigate an unsteady flow of hybrid nanofluid over a permeable shrinking inclined rotating disk subjected to heat radiation, magnetohydrodynamics and slip effects. The chosen nanoparticles for this study are alumina (Al2O3) and copper (Cu), incorporated into a base fluid of water (H2O) to create the hybrid nanofluid. An appropriate method of similarity transformation is executed along a set of partial differential equations that were reduced to a system of nonlinear ordinary differential equations, where numerical outcomes were then obtained via bvp4c in MATLAB software, with the influence of various parameters such as unsteadiness parameter, nanoparticle volume fraction, shrinking, radiation, magnetic and velocity slip parameters, shown in tables and figures. Multiple solutions (including dual, upper, and lower branch solutions) are identified for the governing similarity equations. Through the conducted stability analysis, it is determined that the upper branch solutions exhibit stability and physically realizable in practice, while the lower branch solutions are unstable. Our numerical findings showed that dual solutions exist when ε c ≤ ε ≤ - 1 , where ε c < 0 is the critical value of ε for which the boundary value problem poses physical solutions applicable in practice. Yet, the boundary value problem lacks a similarity solution for ε ≤ ε c ≤ 0 , and the complete set of partial differential equations needs to be solved numerically. Improvements in heat transfer rate are observed concerning the radiation parameter, nanoparticle fraction, and shrinking parameter. Furthermore, azimuthal velocity profiles show an increase influenced by velocity slip and magnetic parameters. The non-dimensional physical parameters, including stretching/shrinking, suction, slip, and unsteadiness, are also considered and their effects are presented in figures and tables. [ABSTRACT FROM AUTHOR]

The goal of the current investigation is to ascertain the influence of Soret and Dufour on a magneto‐micropolar fluid past a permeable stretching surface with a nonuniform heat source/sink. Moreover, the investigation considers the influence of melting heat transfer, as well as the implications of velocity, thermal, and solutal slips. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The analysis of our results reveals several important findings. Enhancing the material parameter leads to an upsurge in the velocity profile, whereas the opposite trend exists for the boosting estimations of the magnetic parameter. Enhancing the Soret parameter leads to an improvement in the concentration profile while improving the Dufour factor results in an enhancement in the temperature distribution. These findings are critical for understanding the heat transfer over a stretching sheet, subject to different models and they encompass aspects such as temperature distribution, heat transfer rates, boundary layer characteristics, velocity profiles, and the potential for implementing heat transfer enhancement techniques. The findings of this current investigation are consistent with those that have been previously reported. Fluid dynamics, materials processing, cooling systems, and thermal systems are just a few of the real‐life domains that can benefit from understanding magneto‐micropolar fluid flow over a porous stretching surface with a nonuniform heat source–sink and incorporating Soret and Dufour effects. [ABSTRACT FROM AUTHOR]

This article contains vital information on the internal heat generation effect on mixed convection slip flow past a vertical plate. The partial differential equations were first simplified to ordinary differential equations through similarity transformation. The simplified first‐order differential equations were integrated with Maple Software 2022 after utilizing the shooting technique. One of the most important discoveries is that the internal heat generation acts as a barrier to stop heat from flowing from the left to right plate edge. However, this could be averted by considering strong mixed convection to covet away the heat conducted through the left surface of the plate and the internal heat generated. However, for weak mixed convection, the movement of the fluid from the left to the right surface of the plate is achievable even with minimal internal heat generation. Since the right surface temperature is warmer (higher) than the left surface, the flow properties, in this case, are also affected by the internal heat generation, which also causes the reverse of heat flow from the plate. Particle injection could also be used to avert unwanted reversed flow for various momentum slip conditions considered. There is a marginal reverse flow at the plate surface, which may be related to the flow's mixed convective characteristics. Due to the plate surface's reinforcement, the rise in flow formation caused by the momentum slip parameter is more substantial close to the plate. [ABSTRACT FROM AUTHOR]

In current investigation the optimization of heat transportation rate in a nonlinear radiative buoyancy‐driven hydromagnetic carbon nanotube (CNT) hybrid nanofluid flow is analysed. The proposed catalytic effects and slip condition is accounted for the real‐world complexities of the system. The Hamilton–Crosser (HC) and Yamada–Ota (YO) models are employed to characterize the behaviour of the nanofluid. The primary objective is to enhance the heat transmission rate, which is crucial for various engineering applications such as thermal management, energy systems and so forth. To achieve this, sensitivity analysis is performed to identify the most influential parameters affecting heat transfer in the system. By understanding the sensitivity of these parameters, the performance of the system can be improvised. The study focuses on the interplay between key factors including radiative heat transfer, buoyancy‐driven flow, magnetic field influence, catalytic effects, and slip condition. The presence of CNTs in the nanofluid adds another dimension to the complexity of the system that explores the effects of varying the concentration and size of CNTs on the heat transfer rate. By utilizing advanced mathematical modelling and numerical simulations, the performance of the system under different scenarios and identify the optimal conditions for maximizing heat transfer rate is evaluated. The findings of this research provide valuable insights into the design and optimization of heat transfer systems involving nanofluids with nonlinear radiative and hydromagnetic effects. The observation shows that, irrespective to single wall and multi wall CNT nanoparticles the fluid velocity attenuates significantly whereas it favours in enhancing the fluid temperature. Further, the comparative analysis reveals that the heat transfer augments in the case of HC model than that of YO model. [ABSTRACT FROM AUTHOR]

The present work deals with a study of non-Newtonian Casson and Williamson nanofluids flow models with a linearly porous stretching sheet across convective conditions. The heat transfer phenomenon has been explored under the impacts of heat source, radiation and viscous dissipation. The higher-order chemical reaction and suction/injection are also taken into consideration. The system of nonlinear dimensionally governing PDEs are converted into dimensionless nonlinear ODEs with the use of appropriate similarity transformations. The transformed set of ODEs are numerically solved by using R–K Fehlberg approach based on shooting technique. The graphical representations for physical parameters are plotted using the in-built MATLAB solver bvp5c. Additionally, the numerical tabular values calculated for the skin friction coefficient, heat transfer rate and mass transfer rate. It is noticed that with elevated amounts of magnetic field, Brownian motion parameter, heat generation and thermal radiation, the temperature significantly increases. The velocity increases with increased thermal and mass Grashof numbers, and the reverse phenomenon exists with increasing magnetic field, porous medium and suction. The Williamson nanofluid velocity is less significant than the Casson nanofluid velocity. The concentration drops while enhancing the higher-order chemical reaction and Schmidt number. Moreover, the increment in the radiation and Biot number increases the Nusselt number. [ABSTRACT FROM AUTHOR]

Hybrid nanofluid flow analyses have obtained a lot of attention due to their usefulness as coolants in hybrid electric vehicles, health care, thermal exchange systems, cancer thermo-therapy, nuclear reactors, microfluidics, aerospace, acoustics, naval structures and power generation in power plants, This research investigated the impacts of slip and induced magnetic field effects on tangential hyperbolic hybrid nanofluid over a stretching wedge with non-uniform heat source. The nanoparticles used in this work are aluminum oxide (Al2O3) and copper (Cu) while water is the based fluid. The fluid flow are modelled as partial differential equations (PDEs). These are transformed to their corresponding ordinary forms (ODEs), which are solved by the homotopy analysis technique with the aid of similarity variables. The impact of prominent physical factors on fluid temperature, velocity, induced magnetic field, local Nusselt number and drag coefficient is explored. Tables and graphs are used to display the results which agreed with the existing ones in the literature. [ABSTRACT FROM AUTHOR]

In this article, the impact of Joule heating on the thermal performance of Williamson nanofluid is analyzed under the influence of viscous dissipation along with the Joule heating. Also, the flow is subjected to Thompson and Troian slip conditions that directly influence the velocity of the flow at the boundary. Meanwhile, to achieve the even distribution of nanoparticles in the nanofluid, gyrotactic microorganisms are dispersed whose motion is due to the virtue of density gradient. The heat conduction at the surface is governed by the convective condition which allows the interpretation of the Biot number. The mathematical model is constructed employing these presumptions using partial differential equations, which are then subsequently reduced using similarity transformations to get the ordinary differential equations (ODEs). The RKF-45 numerical approach is used to solve the nonlinear ODE system thus acquired, and the findings are validated by comparing them to the previously published works. The results of this study showed that the higher values of thermophoresis and Brownian motion parameters cause more heat conduction. Also, the rise in the Eckert number that relates to the internal friction enhances the temperature conducted by the nanofluid. Meanwhile, the Lorentz force helps in controlling the flow velocity. [ABSTRACT FROM AUTHOR]

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the effects of thermal radiation and chemical reactions on magnetohydrodynamic hyperbolic tangent liquid, which includes nanoparticles on a stretched surface while taking into account Brownian motion and thermophoresis. The nonlinear partial differential equations governing the system are converted into nonlinear ordinary differential equations through suitable similarity transformations. The focus of the study is to elucidate important engineering concepts such as skin friction, Sherwood number, and heat transfer, as well as to understand the effects of various expressions on the different profiles. The Keller-box approach, a sophisticated numerical tool, is used to get the numerical answers to the current enquiry. The generated findings are extensively tested for correctness and dependability. The findings of this study might have far-reaching ramifications for a variety of technical applications, including heat exchangers, chemical reactors, and thermal management systems.The results show that the rate of mass transfer rises with the increment in the factors of chemical reaction, thermal radiation, nanoparticles volume, and Brownian motion. [ABSTRACT FROM AUTHOR]

This study explores the complex dynamics of magnetohydrodynamic (MHD) flow within a porous medium while considering the impact of thermal radiation. The primary focus of the investigation centers on a cylinder that is vertically elongating, serving as a means to characterize the behavior of a viscous, incompressible fluid. Notably, the analysis introduces an added layer of intricacy by incorporating both second-order momentum slip and first-order thermal slip boundary conditions. By applying well-suited similarity variables, the governing equations encompassing continuity, momentum, and energy are transformed into a set of non-linear ordinary differential equations. The method employed to effectively handle these equations is the finite element method, known for its robustness in numerical approaches. This approach facilitates the exploration of detailed insights into the distribution of velocity and temperature, consequently revealing nuanced patterns and prevailing trends. A thorough examination of diverse physical parameters offers a comprehensive understanding of their respective influences, thus providing a holistic perspective on their roles within the system. The research goes on to present explicit formulations for critical parameters, including the skin-friction coefficient, Nusselt number, fluid velocity, and temperature surrounding the cylinder. These formulations are visually elucidated through informative graphical depictions. Beyond its theoretical contributions, this research carries tangible practical significance across domains such as thermal engineering, fluid dynamics, and energy systems. Its insights have the potential to impact the optimization and design of real-world processes and systems, underscoring its relevance to technological advancements in these fields. [ABSTRACT FROM AUTHOR]

The objective of this article is to study the importance of velocity and thermal slip in the exponentially stretching or shrinking sheet with the megnetohydrodynamic (MHD) hybrid nanofluid flow along with magnetic field, radiative, heat generation effects. This study has practical importance in enhancing heat transfer efficiency, improving energy conversion and optimizing thermal management systems. The findings can also contribute to the development of sustainable energy systems and aid in assessing the stability and safety of nanofluid applications. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformation. The ODEs are solved using bvp4c solver in MATLAB. The dual solutions are achieved for specific range of the stretching or shrinking parameter and mass suction parameter. The first solution is physically significant after considering stability analysis. The hybrid nanofluid has numerous real‐life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical, and drug reduction. The skin‐friction increases but Nusselt number decreases over the stretching sheet whereas the opposite effect shows over shrinking sheet for the both solution with the increasing velocity slip parameter. On the other hand, The Nusselt number decreases over the shrinking or stretching sheet for both solutions with the increasing in the thermal slip parameter. The skin friction increases over shrinking sheet but decreases over stretching sheet for the first solution with increasing silver volume fraction parameter and porosity parameter (K$K$). Enhancing magnetic field parameter leads to the skin friction increases over the shrinking sheet but decreases over stretching sheet but Nusselt number shows opposite trend. The Nusselt number decreases over shrinking sheet but increases over stretching sheet for the first solution with increasing porosity parameter (K$K$). The Nusselt number decreases over shrinking or stretching sheet as the increases heat generation (β$\beta$) and variable thermal conductivity parameter (w$w$) but Nusselt number shows opposite trend as the increases radiative parameter (Rd$Rd$). [ABSTRACT FROM AUTHOR]

This study examines the two-phase nanofluid magnetohydrodynamic (MHD) boundary layer flow model with heat absorption or generation and chemical reaction via porous media due to an exponential stretching sheet using the Haar wavelet collocation method (HWCM). First, the governing nonlinear partial differential equations (PDEs) are transformed into coupled, highly nonlinear, ordinary differential equations (ODEs) using similarity transformations. Then the coupled ODEs are translated from the infinite domain [0, ∞ ) to the finite domain [0, 1] via coordinate transformation because the wavelet plays a crucial role in [0, 1]. The obtained equations are solved using HWCM. The impacts of the physical parameters are discussed using tables and graphs. It was found that the Nusselt number R e x − 1 / 2 N u x is a decreasing function of the magnetic field, porous media parameter, heat generation or absorption parameter, and chemical reaction parameter. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to focus on the transient flow and heat transfer of a non-newtonian fluid (Casson fluid) between parallel disks in the presence of an external magnetic field. The bottom disk is considered to be porous and fixed, whereas the upper disk moves down. Also, the influence of the heat source/sink and viscous dissipation is taken into account. The conservative partial differential equations have been transformed into dimensionless ones and are solved semi-analytically using Least Square Method. Besides, applying a numerical solution, the accuracy of analytical results is verified using the fourth-order Runge–Kutta method. The effects of various physical parameters such as suction/injection, heat source/sink, Prandtl number, magnetic field, slip condition, and Casson fluid parameter on velocity and temperature distribution as well as skin-friction coefficient and Nusselt number are examined and discussed. The results have shown that higher values of the Casson fluid parameter decrease the Nusselt number and shear stress. Also, it is observed that the Hartmann number augmentation decreases the heat transfer rate. What is more, it is shown that the intensity of injection/suction affects how streamlines behave against the central vertical axis. [ABSTRACT FROM AUTHOR]

Rotating-disk generated flows find potential applications in industry such as cooling of electronics, car-breaking system, wind turbine engineering and others. Current article formulates heat transfer in the steady revolving flow of viscoplastic fluid obeying Bingham model over a rotating disk. Simulations are conducted by applying partial slip wall conditions, which are Robbin-type and non-linear in velocity components. Contribution of viscous dissipation, representing the conversion of mechanical energy into thermal energy caused by internal friction, is added in the analysis. Furthermore, the phenomenon of Joule heating due to the consideration of magnetic field affected flow is accounted for. The self-similar problem that arises after implementing Von-Kármán variables is computationally addressed using the MATLAB tool bvp4c. Significance of yield stress on the Von-Kármán flow under slip boundary assumption is elucidated through graphical results. Additionally, the implications of frictional heating and Joule heating on the development of a thermal boundary layer in a Bingham fluid are clarified. As the yield stress τ y increases, the velocity profiles meet their respective far field conditions at smaller vertical distances, and therefore a higher torque is required by the disk. Noticeably, considering the slip effect not only lowers the torque that the disk requires, but it also boosts disk's rate of cooling—a desirable outcome in practical applications. The reliability of the mathematical model is assessed by performing uncertainty analysis of the computational data. [ABSTRACT FROM AUTHOR]

It is vitally critical to understand the dynamics of the non-Newtonian fluids model from an engineering and industrial perspective. Many industrial and technical activities, such as the extrusion of polymer sheets, the manufacturing of paper, and the development of photographic films, require non-Newtonian fluids. Energy transportation has numerous industrial applications, and classical heat and mass transfer laws do not accurately anticipate thermal and solute relaxation times. This study applies the modified Ohm law to heat and mass transport, utilizing Fick's and generalized Fourier concepts. And the primary purpose of this study is to explore the characteristics of heat and mass transport in the magnetohydrodynamics-mixed convective flow involving a micropolar Casson fluid across the vertically inclined starching surface with multiple slip effects. Moreover, the study considers additional factors like thermal radiation, heat generation, chemical reactions, and the influence of thermophoretic to analyze both energy and nanoparticle concentration aspects comprehensively. To simplify the flow analysis, the original flow model is transformed into a couple of ordinary differential equations (ODEs) by employing relevant similarity transformations. These ODEs establish a system that is solved numerically by using the Bvp4c solver through MATLAB. It is worth noticing that a more substantial estimation of the thermal and concentration relaxation parameters decays the fluid temperature and nanoparticle concentration, respectively, and the growth of the material parameter reduces the drag force, which consequently augmenting the fluid velocity. Furthermore, the enhancement occurs in the skin friction due to greater estimation of the micropolar parameter, while the Casson fluid parameter causes the opposite trend. [ABSTRACT FROM AUTHOR]

This article presents an analytical and numerical investigation on the quasi-steady, slow flow generated by the movement of a micropolar fluid drop sphere of at a concentrical position within another immiscible viscous fluid inside a spherical slip cavity. Additionally, the effect of a cavity with slip friction along with the change in the micropolarity parameter on the movement of the fluid sphere is introduced. When Reynolds numbers are low, the droplet moves along a diameter that connects their centres. The governing and constitutive differential equations are reduced to a computationally convenient form using appropriate transformations. By using the resulting linear partial differential equations for the stream functions and using the method of separation variables, we can obtain their solutions. General solutions for velocity fields are found using spherical coordinate systems, which are based on the concentric point of the cavity; this allows to obtain solutions to the Navier-Stokes equations internal and external to the spherical droplet. The vorticity-microrotation boundary condition is used in regard to the micropolar droplet case in a viscous fluid. The normalised drag forces acted upon the micropolar drop are illustrated via graphs and tables for diverse values of the viscosity ratio and drop-to-wall radius ratio, with the change of the spin parameter that attaches the microrotation to vorticity. The correction wall factor is shown to increase with an increase in the drop-to-wall radius ratio, when moving from the gas bubble case to the solid sphere case, with an increase in the micropolarity parameter, and with an increase in the slip frictional resistance. This study is relevant due to its potential uses in a variety of biological, natural, and industrial processes, including the creation of raindrops, the investigation of blood flow, fluid-fluid extraction, the forecasting of weather conditions, the rheology of emulsions, and sedimentation phenomena. [ABSTRACT FROM AUTHOR]

The present study aims to provide a mathematical model of the Williamson fluid flow via a permeable stretching/shrinking sheet in the MHD boundary layer in the presence of a heat source, chemical reaction, and suction. This study is novel because it investigates the physical effects of thermal and solutal stratification on convective heat and mass transport using thermal radiation. The flow's PDEs are numerically solved using the BVP4c approach and the pertinent similarity variables until a stable solution is found. Through visual analysis, the effects of dimensionless factors on temperature, velocity, and concentration profiles are examined. This encompasses the mass transfer rate, the heat transfer rate, and the coefficient of friction. The results of the present analysis are found to be consistent with those of previously published studies. The findings demonstrate that enhanced temperature and concentration profiles cause the Williamson, magnetic, and permeability parameters to rise in conjunction with a drop in the dimensionless velocity. In relation to temperature, the thermal stratification parameter exhibits the opposite tendency. Regarding the solutal stratification parameter, concentration profiles are seen to show the opposite trend. Lastly, the current work will have important implications for the removal of dust and viruses from viscoelastic fluid in bioengineering, the medical sciences, and medical equipment. [ABSTRACT FROM AUTHOR]

This study theoretically investigates the temperature and velocity spatial distributions in the flow of a copper–water nanofluid induced by a rotating rigid disk in a porous medium. Unlike previous work on similar systems, we assume that the disk surface is well polished (coated); therefore, there are velocity and temperature slips between the nanofluid and the disk surface. The importance of considering slip conditions in modeling nanofluids comes from practical applications where rotating parts of machines may be coated. Additionally, this study examines the influence of heat generation on the temperature distribution within the flow. By transforming the original Navier–Stokes partial differential equations (PDEs) into a system of ordinary differential equations (ODEs), numerical solutions are obtained. The boundary conditions for velocity and temperature slips are formulated using the effective viscosity and thermal conductivity of the copper–water nanofluid. The dependence of the velocity and temperature fields in the nanofluid flow on key parameters is investigated. The major findings of the study are that the nanoparticle volume fraction significantly impacts the temperature distribution, particularly in the presence of a heat source. Furthermore, polishing the disk surface enhances velocity slips, reducing stresses at the disk surface, while a pronounced velocity slip leads to distinct changes in the radial, azimuthal, and axial velocity components. The study highlights the influence of slip conditions on fluid velocity as compared to previously considered non-slip conditions. This suggests that accounting for slip conditions for coated rotating disks would yield more accurate predictions in assessing heat transfer, which would be potentially important for the practical design of various devices using nanofluids. [ABSTRACT FROM AUTHOR]

In response to the observed phenomenon of poor fluid mixing within the reactor, this study proposes a novel mixing method to enhance fluid mixing efficiency. In this study, numerical simulation and purification tests were carried out for the purification of zinc sulfate solution. Numerical simulations were conducted to compare the effects of variable-speed stirring and uniform-speed stirring on mixing efficiency, considering both momentum transfer process and mass transfer process. The purification test further demonstrated a significant improvement in the reaction rate under variable-speed stirring, as evidenced by the analysis of purification efficiency and microscopic morphology. It was elaborated that the enhancement mechanism of variable-speed stirring involved disrupting the periodic order structure in the tank, leading to the generation of a multi-scale vortex that increased stirring kinetic energy to form a shear force. This force contributed to reducing the velocity slip between the impurity ions and zinc particles, consequently decreasing reaction time and enhancing purification rate. The results indicated that sinusoidal stirring yielded the most effective mixing. When implemented in practical production settings, it enhanced dimensionless mixing efficiency by 24.83 % compared to the homogeneous stirring system. Additionally, it reduced reaction time by 15.47 % and decreased mixing energy per unit volume by 32.38 %, while simultaneously lowering energy consumption by 24.77 %. [ABSTRACT FROM AUTHOR]