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The objective of this paper is to investigate the heat transfer mechanism while considering the attributes of viscous dissipation, Joule heating, and nonlinear thermal radiations in the three-dimensional steady incompressible flow of Carreau liquid on an extendable rotating disk. By using the similarity transformation, the governed equations were converted into the nonlinear coupled ordinary differential equations. The essential characteristics of various variables like Prandtl number, Lewis number, Carreau liquid parameter, Brownian motion, thermophoresis parameter, radiation parameter, Eckert number and Hartmann number on velocity, thermal, and concentration are discussed through graphs and tables. The presented investigation divulges that the thermal and mass transfer rates enhance when Brownian motion and thermophoresis processes extended and manifest as opposing features on the concentration field. [ABSTRACT FROM AUTHOR]

Exponential space‐based heat source with shear‐thinning/thickening behavior offers innovative insights into the optimization of thermal transport process in complex systems, such as in the cooling of microelectronics, energy storage technologies, and biomedical devices, where accurate thermal control is critical. This study explores the investigation of an exponential space‐based heat source with effects of shear thinning/thickening behavior of a ternary infinite shear rate viscosity‐dependent Carreau water‐based nanofluid [Cu, Fe3O4, SiO2] over a three‐dimensional wedge in a magnetized environment. The interaction between heat transport and magnetic fields is explored through the behavior of the ternary nanofluid by classifying the both shear‐thinning and shear‐thickening effects. The incorporation of physical assumptions in the model gives the set of partial differential equations (PDEs) and similarity transformations are launched to convert them into ordinary differential equations (ODEs). Furthermore, bvp4c scheme is used to fetch the numerical solution. Temperature profile is increasing with exponential‐based source heat parameter due to a reduction in the rate of heat absorption by the fluid. Ternary nanofluids exhibit the highest rate of temperature increment due to the effects of multiple nanoparticles as compared to hybrid or single‐nanoparticle nanofluids. Rate of velocity decrement in ternary nanofluids compared to bi‐hybrid nanofluids and single‐particle nanofluids. [ABSTRACT FROM AUTHOR]

The study of magnetohydrodynamics (MHD) and thermal radiation over‐stretching and shrinking sheets has significant applications in a wide range of fields, from chemical manufacturing to transport engine cooling systems, electronic chip cooling, plasma, the nuclear‐powered sector, saltwater, etc. The present study aims to numerically and theoretically analyze the movement of thermally magnetized Williamson nanofluid owing to an extended/contracting sheet. The regulating flow equations are converted to self‐similar equations through similarity transformation, and then numerically solved by bvp4c using MATLAB software. A comparison of the present numerical study with the published study is quite impressive. The investigation demonstrates that the self‐similar equations disclose the two branches for the limited shrinking factor range. For the stretching case, only one solution exists. As a result, the most fundamentally feasible solution has been determined by the linear assessment of temporal stability. For the aim of stability analysis, the lowest eigenvalue sign indicates the stability or instability of a solution. Through stability analysis, it is witnessed that the first solution (first branch) is stable. Due to the presence of the Lorentz force effect, it is perceived that the velocity curves decline in the whole channel. The point to be noted here is that the velocity of the lower branch compared to the upper branch is higher. The reduced Skin Friction is increased in the first branch and declines in the second branch for the two different values of magnetic factor. [ABSTRACT FROM AUTHOR]

The incorporation of three distinct nanoparticles in blood within the context of cubic autocatalysis holds significant potential for enhancing biomedical applications, particularly in targeted drug delivery and therapeutic interventions. The increased reaction rate improves the efficiency of catalytic processes within the bloodstream. This research investigates the thermal transport characteristics of a trihybrid Carreau nanofluid (blood) containing copper (Cu), titanium dioxide (TiO2), and aluminum oxide (Al2O3), nanoparticles in the context of a wedge‐shaped artery under the influence of autocatalytic cubic autocatalysis. Effects of thermal radiation, and heat generation are used for heat transport analysis, heterogeneous‐homogeneous chemical process included for blood concentration, and an inclined magnetic field is imposed for securitization of blood velocity. Also, the generated PDEs from the physical model are handled through similarity transformations and converted into ODEs. Bvp4c, a numerical technique is used to get the solution and then Levenberg‐Marquardt neural network (LM‐NN), a multilayer neural network scheme is used to train and predict the solution for each parameter. In addition, the numerical values of volumetric friction of coefficients enhance the thermal conductivity, and the heat transport rate is increased. The magnetic parameter, radiation and chemical processes enhance the rate of heat transport while the Weissenberg number reduces the velocity profile. [ABSTRACT FROM AUTHOR]

This study investigates the electrically conducting Maxwell fluid flow over a stretching sheet with the effects of homogeneous‐heterogeneous chemical reactions, thermal radiation, and melting heat. The nanomaterial characteristics are analyzed considering Brownian motion and thermophoresis (Buongiorno's model). Irreversibility analysis is conducted to assess entropy generation. The governing equations of the problem are transformed into dimensionless equations through appropriate similarity transformations. The graphical and tabular numerical solutions are attained through NDSolve via Mathematica. The study examines how various parameters affect the velocity, concentration, temperature, and entropy generation within the flow. This study provides insights into isothermal chemical processes which contribute to the optimization of industrial and engineering applications. It is seen that heterogeneous diffusion parameter increases molecular disorder and rate of irreversible processes, whereas homogeneous diffusion parameter shows opposite trend. [ABSTRACT FROM AUTHOR]

Research Problem: The importance of improving the temperature properties of commonly used fluids in industrial processes is being addressed in this research. Nanofluids, which are composed of extremely small particles dispersed in common liquids such as water or petrol, are the main subject of this area of study. Using a vertically stretchable surface subjected to thermal radiation, the study examines the heat transfer behavior and efficiency of nanofluids.Methodology: Nanofluids that convey heat are studied by applying the fundamental rules of fluid physics to the variables that control their motion. To measure the amount of energy transferred, a nanofluid model is used. Similarity transformations are used to convert the system’s differential equations into ordinary differential equations (ODEs). The subsequent set of nonlinear ODEs is solved using numerical methods. Utilizing graphical analysis, patterns of velocity and temperature may be seen, and their responses to changes in other parameters can be investigated.Implications: This research has important implications for our knowledge of how nanofluids act in heat transfer applications, especially when exposed to thermal radiation and working with vertically stretchy surfaces. The effects of flow direction and thermal conductivity on distributions of velocity and temperature were elucidated, among other important results. More effective heating and cooling systems may be possible as a result of these findings, which have consequences for improving heat transfer processes in industrial environments.Future Work: To better understand how nanofluids behave in heat transfer applications, future studies might investigate more complicated situations and boundary circumstances. It may be possible to optimize nanofluid formulations by studying the impact of various nanoparticle kinds and concentrations on heat transfer efficiency. Research could be more applicable to real-world industrial processes if the numerical results were experimentally validated. [ABSTRACT FROM AUTHOR]

Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow. [ABSTRACT FROM AUTHOR]

In order to keep mechanical processes running smoothly, there is a growing need for effective heat transport. The present study aims to explore the variation of heat on time‐dependent maximum hydrodynamic drag (MHD) second‐grade nanofluids perceiving motile gyrotactic microbe with stretchable sheets. We process the analysis of the thermal energy distribution by using the convective boundary conditions. In addition to this, we take both the chemical reaction and the heat radiation into consideration. The governing nonlinear (PDEs) are converted into (ODEs) by a similarity transformation and then computed BVP4c technique. The multiple results are marked in the range of opposing flows only. Then, the effects of numerous physical variables on temperature, concentration, fluid velocity, and motile microorganisms are scrutinized using different graphical representations. The unsteady parameter and second‐grade fluid also strengthen for higher qualities, while inverse conduct is identified for a magnetic field framework. Finally, the temperature field cultivates a more significant assessment of the Biot number, and reverse behavior is observed for the Prandtl number. The obtained results are found appropriate to the existing literature. [ABSTRACT FROM AUTHOR]

This study aims to discover the application of bioconvection and heat absorption or omission aspect of 2D incompressible MHD Oldroyd-B nanofluid over the stagnation region. Directed by suitable similarity transformations, the system of PDEs is transformed into a system of coupled nonlinear ODEs. The results were made by using Runge–Kutta shooting technique. The Buongiorno model is capitalized while Oldroyd-B model is employed for portraying the viscoelastic behavior of the flow. In order to visualize the impact of relevant parameters on momentum boundary layer, temperature, concentration and microorganism profiles are computed graphically. Numerical outcomes for the local Nusselt number, Sherwood number, microorganism number and local skin friction number are calculated for different parametric situations to provide interesting features of the examination. Furthermore, it has been also observed from statistical point that the correlation coefficient of the local Nusselt number, Sherwood number, microorganism number and local skin friction number with various parametric situations are highly significant at the α = 0. 0 1 level of significance (p < 0. 0 0 0 1 for a two-tailed test). [ABSTRACT FROM AUTHOR]

The current study analyses the entropy of nanofluid flow over three different geometries with thermophoretic particle deposition and thermal radiation. It is essential while considering heat exchangers, transpiration, fiber coating, and other similar processes, to have a solid understanding of the transfer of both heat and mass that occurs during MHD flows across three dissimilar shapes. A mathematical model will be utilized to explore magnetohydrodynamic flows including energy transfer with heat and mass variations. In this model, some of the innovative concepts include thermophoresis, Brownian motion, the Cattaneo–Christov dual flux with the application of an external magnetic field, and the entropy generation effect are considered. By the appropriate similarity transformations, fundamental PDE's converted into ODE's. To solve these ODE's, the Runge–Kutta fourth order is used along with the shooting technique. The results are displayed in graphs and tables. It is observed that the velocity gets decreases with the increase of the porous parameter and magnetic field and gets stronger with the increase of the Grashof number. The temperature increases with an increase in the magnetic field, radiation parameter, Brownian motion parameter, and thermophoresis parameter. Concentration increases with the increase in a magnetic field and Brownian motion parameter but reduces with the increase of other parameters. Entropy generation gets enhanced with an increase in the magnetic field, temperature difference, concentration difference and diffusion parameters. When a flow is directed through geometries the heat and mass transfer rates are both affected by a parameter known as the thermal relaxation parameter. The influence of skin friction, Nusselt number and Sherwood number were analyzed and results were discussed. [ABSTRACT FROM AUTHOR]

The consider work focuses on MHD rotating flow of Maxwell nanofluid affected by non-uniform heat source/sink and thermal radiation. The flow is induced by stretchable surface (linear/exponential) with the implementation of stratification boundary conditions on the surface. The thermal energy and mass concentration equations are discussed with the effect of variable thermal conductivity and variable chemical reaction. The flow model PDEs are converted into the system of nonlinear ODEs with the help of similarity transformation. These nonlinear coupled equations are computed numerically by the utilization of Bvp4c MATLAB technique. The noteworthy impact of different parameters is observed along the velocity, temperature, and concentration distribution. It is examined through graphical discussion that higher estimation of Deborah number and magnetic field parameter retard the fluid motion, as a result the velocity of fluid lower down. Further, higher estimation of rotation parameter causes to Coriolis force, which declines the fluid velocity. The transport of heat and mass for the higher estimation of Deborah number and rotation parameter is reduced consequently. The comparison of current computations is down with the pervious published article, which result shows good agreement. [ABSTRACT FROM AUTHOR]

This article explores the influence of activation energy and microorganisms on the flow of Jeffrey nanofluid over an electrically conducting stretching surface, considering key factors such as Brownian motion, thermophoresis, Joule heating, and thermal radiation. The fluid dynamics entail a stretching surface subjected to prescribed surface temperature and constant wall surface temperature. Through similarity transformations, the governing equations are solved using MATLAB's bvp4c function. Employing a numerical and perturbative approach, the study examines critical parameters' effects on flow distribution, heat transfer, mass transport, and microorganism density. Graphical illustrations and tabulations are utilized to illustrate these effects, including the elucidation of Nusselt, Sherwood, friction coefficient, and motile microbe. The study's findings hold promise for optimizing processes in environmental remediation, bioengineering, and nanotechnology. It is seen that thermophoresis reduced the coefficients of motile density number, Sherwood number, and Nusselt number. Peclet and bio-convective Schmidt numbers enhanced the spread of microorganisms. CWT profile exhibits greater dominance compared to PST profile. • The influence of activation energy and microorganisms on the flow of Jeffrey nanofluid over an electrically conducting stretching surface is explored. • A stretching surface subjected to prescribed surface temperature and constant wall surface temperature is analyzed. • Through similarity transformations, the governing equations are solved using MATLAB's bvp4c function. • Employing a numerical and perturbative approach, the study examines critical parameters' effects. • The study's findings hold promise for optimizing processes in environmental remediation, bioengineering, and nanotechnology. [ABSTRACT FROM AUTHOR]

The literature showed that an empirical experiment creates another part of exploration that has been made in the field of thermal science, such that today, modern researchers are more directed to utilize hybrid types of nanoparticles due to their efficient thermal conductivity compared to single nanoparticles. The study of the hybrid flow of nanofluid is essential in many scientific and industrial arguments, such as power generation, medical equipment, oil refineries, and so forth. Furthermore, it has distinctive features to advance the expertise of their energy sources and cooling methodologies. Incentives by this research postulation: The significant objective of this investigation is to design a mathematical model of Prandtl hybrid nano liquid flow over a Riga plate when nanoparticles of aluminum alloys (AA7072 and AA7075) are suspended in engine oil. Mixed convection, activation energy, and heat radiation are also considered. The nanomaterial is modeled using a modified Buongiorno model that considers the functional qualities of hybrid nanofluids. The simulated PDEs are converted into a collection of nonlinear ODEs with appropriate and relevant similarity transformations, which are numerically addressed using finite‐difference‐oriented bvp4c procedure in MATLAB. Graphs and tables are used to evaluate and show the impacts of different factors on velocity, temperature, concentration fields, skin friction number, and Nusselt number. The velocity profile develops with the enhancement of Prandtl fluid parameters. With the increment in the magnetic parameter, both temperature and concentration profiles improve, but in the case of the Brownian motion parameter, the concentration profile declines. In terms of heat transfer, hybrid nanofluids outperform ordinary nanofluids. The current results provide an equitable contrast against the results that already exist. [ABSTRACT FROM AUTHOR]

The authors have investigated the axisymmetric and three-dimensional, steady, incompressible, and bioconvective flow of Ag-TiO2/water hybrid nanofluid between two infinite and parallel rotating disks. Practical uses of flows between two rotating disks include brake systems in vehicles, engines, disks in computers, atomizers, rotating air cleaners, gas turbines, and evaporators. This study was conducted within a Darcy-Forchheimer porous medium and considered the impact of a magnetic field, heat source, and thermal radiation. The governing mathematical equations are transformed into coupled and nonlinear ordinary differential equations through similarity transformations. Subsequently, these equations are numerically solved using MATLAB's built-in function "bvp4c". A multilayer perceptron based artificial neural network (ANN) model has been formulated to predict the Nusselt number (heat transfer rate) on both the lower and upper surfaces of the disk. The model utilizes the Levenberg-Marquardt training algorithm, renowned for its exceptional learning capability, as the training method for the ANN. Moreover, the authors generated a dataset consisting of 84 data points for each case using numerical methods to construct the proposed Multilayer Perceptron Artificial Neural Network. The computed mean squared error values for the developed ANN model, targeting Nusselt number predictions, were found to be 2x10-6, 5x10-6, 9x10-6, and 3x10-6. Additionally, the regression (R²) values, serving as an additional performance parameter, were determined as 0.999317, 0.997672, 0.999963, and 0.999840, respectively. A comprehensive assessment of these outcomes, strongly affirms that the ANN model has been crafted with a high degree of accuracy for predicting Nusselt numbers. [ABSTRACT FROM AUTHOR]

AbstractIncorporating slip conditions into computational fluid dynamics (CFD) simulations and experiments helps engineers predict and improve the effectiveness of superhydrophobic surfaces in reducing drag. This optimization approach leads to significant enhancements in fuel efficiency and performance across a range of fluid-flow systems, including marine vessels and aircraft. This study models the phenomena of velocity and temperature slip, coupled with MHD, within the context of nanofluid flow undergoing bioconvection over a stretching sheet. Subsequently, the study seeks to analyze the resulting effects on heat and mass kinematics. The bvp4c solver effectively calculates analytical solutions for the reduced problem obtained through similarity transformation from the underlying partial differential equations. Velocity and temperature slip both impact temperature, with velocity slip increasing heat transfer rates and temperature slip decreasing them. The thermal radiation parameter enhances nanoparticle concentration, although it’s offset by an increased Lewis number. Brownian motion amplifies mass transfer, but the thermal radiation parameter hampers it. The escalation in the microorganism density profile correlates with the increase in both the Bioconvection Lewis number and the Peclet number. Likewise, as thermophoresis parameters and the bioconvection constant increase, the microorganism density along the profile also rises. [ABSTRACT FROM AUTHOR]

The research of heat and mass transfer enhancement is influenced by several physical effects such as thermal conductivity, heterogeneous catalytic reaction, heat source/sink, thermal radiation and suction/injection, and is a significant area of study, particularly in the field of applied materials science, nanotechnology and mechanical engineering. The main objective of this research is to analyze and explore the heat and mass transfer of a novel ternary hybrid nanofluids binary nanofluid flow while considering the influences of the control parameters mentioned earlier. The model is developed for Hamilton and Crosser to analyze the radiation mechanism in a fluid system subjected to a Riga wedge. Due to the upgraded thermal transportation, the novel ternary hybrid nanofluids (THNs) show great potential in addressing these difficulties because of their significant properties, which include enhanced thermal conductivity, convective thermal transport and the ability to improve autocatalysis reactions. The governing model equations and boundary conditions are nondimensionalized by introducing suitable similarity transformations. Thereafter, the computational Chebyshev collocation spectral technique implemented in the MATHEMATICA 11.3 environment is used to calculate the numerical solution. The THNs demonstrate an efficiency rate of about 2.79%, with a minimum efficiency rate of 3.27%. It has been revealed that heat generation and solar radiation parameters are significant physical features for enhancing heat transfer processes. [ABSTRACT FROM AUTHOR]

AbstractIn this article, an effort is made to analyze the 3−D flow of hybrid nanofluid over a rotating stretching sheet. The hybrid nanofluid contains engine oil as a base fluid amalgamated with nano-particles MoS2 and ZnO. The flow is assumed to pass through a Darcy–Forchheimer medium subjected to the influence of an inclined magnetic field. In addition, heat radiation, Joule heating, viscous dissipation, nonlinear heat source, and quartic autocatalytic chemical reaction are applied to discourse heat and mass transfer features. The PDEs representing the physical problem are converted to ODEs with the introduction of similarity transformations. The solution of the problem is determined numerically by using MATLAB built-in bvp4c method. The proposed mathematical model’s validation is ascertained by comparing it with an earlier study in limiting case. In this regard, an excellent consensus is accomplished. The current investigation reveals that the flow along axial direction gets retarded by enhancing the values of rotational parameter, inertial parameter, and magnetic parameter, whereas the flow along radial direction gets accelerated. The increasing value of angle of inclination admirably resists the motion of nanofluid and hybrid nanofluid. The concentration profile gets decreased under the increasing influence of inclination angle and Schmidt number while it enhances for homogeneous reaction parameter. The enhancing values of rotational parameter, solid volume fraction and temperature, and exponential dependent heat generation parameters enhance the value of Nusselt number. [ABSTRACT FROM AUTHOR]

This work examines the numerical representation of boundary layer flow across a horizontal plate using the non-Darcian Maxwell model. The inspiration of mass transfer, heat generation, the Soret effect, the non-Darcy effect, Arrhenius activation energy and thermal radiation are all covered in this study. The relevant similarity transformations are applied in primary equations and a built-in bvp4c program is employed for solutions. The effectiveness of the numerical approach is demonstrated by a thorough agreement with results that have been published in the past. The results are shown in tables and graphical representations that highlight multiple parameters including the non-Darcy parameter, Deborah number, magnetic parameter, Soret parameter, chemical reactions, activation energy, etc. Figures show that fluid velocity is enhanced by Deborah number whereas it slips due to non-Darcy parameter and magnetic parameter. Eckert number, Radiation enhances the temperature profile and slips due to the Prandtl number. Activation energy enhances the Concentration field but it declines due to chemical reaction. [ABSTRACT FROM AUTHOR]

AbstractThis research is carried out to observe the fluid flow across a stratified sheet in the presence of non-linear thermal radiation. Through the process of similarity transformations, the partial differential equations (PDEs) governing the flow model are transformed into ordinary differential equations (ODEs), which are then numerically solved using the shooting method. This study comprehensively examines the influence of various flow parameters, including the inertial coefficient, magnetic parameter, Brownian motion parameter, radiation parameter, Prandtl number, thermophoresis parameter, and Brinkman number, on key thermophysical characteristics, such as the skin friction coefficient, and the rates of heat, mass, and entropy generation. Notably, the relative difference in the skin-friction coefficient increases with the Weissenberg number, ranging from approximately 1.8 to 2.5. The results indicate that reducing the Cattaneo–Christov temperature parameter decreases the temperature profile while increasing the concentration profile, whereas entropy generation initially rises with increasing Weissenberg number, but decreases near the surface. [ABSTRACT FROM AUTHOR]

The behavior of a Maxwell nanofluid in mixed convection Darcy–Forchheimer inclined MHD flow across a stretched sheet is investigated in this research study. In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. These ODEs are then solved using the shooting method and a fourth‐order Runge‐Kutta methodology. The study explores how fluid flow velocity is affected by magnetic field inclination and suction/injection effects. This is attributed to the strengthening of the magnetic field with an increase in the inclination angle α. Additionally, the imposed magnetic field generates an opposing force, known as the Lorentz force, which contributes to a reduction in the velocity curve. Furthermore, various parameters affect the profiles of concentration, temperature, velocity, and Nusselt number. A number of parameters are looked at, such as the response rate constant, mixed convection, buoyancy ratio, suction/injection, Brownian motion, Lewis number, and thermophoresis. Interestingly, the results show that activation energy and mixed convection parameters, respectively, have an increasing effect on concentration and velocity curves. [ABSTRACT FROM AUTHOR]

In this study, the Darcy–Forchheimer model is examined in relation to magnetohydrodynamic (MHD) Casson fluid flow over a stretchable exponential surface. The investigation incorporates several factors not previously considered, including Arrhenius activation/instigation energy, second-order slip, Joule heating, thermal radiation, viscous dissipation, and chemical reactions. The Darcy–Forchheimer model is employed to characterize flows within permeable materials under the influence of instigation energy. Additionally, we analyze the electrically conducting flows induced by an exponentially stretched and dissipated sheet. To transform the partial differential equations (PDEs) into ordinary differential equations (ODEs), appropriate similarity transformations are applied. Numerical and graphical results are presented using the Lobatto IIIA technique across various system scenarios, demonstrating the effectiveness of this approach as a reliable, accurate, and viable solver. Through the utilization of the BVP4C technique in MATLAB, a numerical representation of the formulation is achieved. Graphs are generated, illustrating the variations in ongoing parameters such as concentration velocity. This velocity increases with higher values of E and Γ , but decreases with σ. The fluid temperature rises with larger values of R , and it responds positively to first-order slip while decreasing with second-order slip. [ABSTRACT FROM AUTHOR]

This paper describes the fundamental characteristics of cavitation in non-Newtonian liquids and bubble dynamics and then applies them to the domains of bioengineering and biomedicine. The goal of this paper is to examine how Newtonian nanomaterial flows hydromagnetically when subjected to a spinning disc considering such biomedical and bioengineering applications. The vertical axis of the disc rotates with a uniform angular frequency. The fundamental mathematical expressions are governed by the Navier–Stokes equations with the Maxwell equations of magnetism, we obtained ordinary differential equations utilizing Von Kármán's similarity transformations. Additionally, the effects of the magnetic field and radiation restrictions are considered. The RK-4 technique is used to solve the transmuted nonlinear ODEs. The analysis of MATLAB generated flow profiles has looked for changes in the values of key parameters. It is discovered that an increase in the thermal radiation parameter causes a decrease in the nanofluid temperature while an increase in the volume fraction of magnetite nanoparticles causes an increase. The skin-friction and heat-transfer rate at the disc are highly influenced by its rotational, the porosity of the porous media, thermal radiation and nanoparticle size. The rotational parameter, which regulates the disk's rotation, is a result of the rotating phenomenon. The research demonstrates that when the disk's rotation increases, the fluid motion accelerates in both the radial and cross-radial directions. Additionally, increasing the Prandtl number significantly improves heat transport, and a higher value for the rotation parameter shows a lesser concentration phenomenon. Additionally, the Nusselt number shows a decrease curve for a changeable thermal conductivity parameter. Finally, the current research can effectively close a gap in the physique of knowledge. [ABSTRACT FROM AUTHOR]

In the present analysis, tangent hyperbolic fluid is assumed to be flowing over a stretching cylinder. The thermophysical characteristics of fluids are assumed to be variable. The thermal and solutal rates are investigated by using viscous dissipation, activation energy, and thermal radiation. The governing equations occur in the form of partial differential equations, and then these equations are transformed into ordinary differential equations by using similarity transformations. Then, by using the BVP4C method, we obtain the numerical solution to the equations. The impacts of the involved parameters, such as Prandtl, Weissenberg, Schmidt, Eckert number, viscosity coefficient, and thermal radiation parameters, are presented through the graphs. The velocity profile decreases due to the power law index, Weissenberg number, and temperature-dependent viscosity. However, it increases due to the Darcy-Forchheimer number and curvature parameter. The temperature distribution rises with the Eckert number, curvature parameter, and radiation parameter. On the other hand, it declined for the Prandtl number and power law index. Similarly, the concentration profile increases for the activation energy, reaction rate, and temperature difference parameter, but it decreases for the curvature parameter and Schmidt number. • Darcy-Forchheimer and temperature dependent viscosity of tangent hyperbolic fluid. • Viscous dissipation, activation enrgy and thermal radiation is assumed. • The MATLAB programme is used to graphically analyze the behavior. • Stretching cylinder is considered. [ABSTRACT FROM AUTHOR]

Industry and space technology have significant issues managing heat energy and controlling mass dispersion. The purpose of this study is to develop motion caused by boundary layer thickness sheets that are increasingly being used in various engineering fields (civil engineering, mechanical, aeronautical, maritime processes and constructions). The activation energy is a critical factor in chemical reactions due to the existence of many applications in gas-cooled reactors, nuclear thermal rockets and liquid-fluoride reactors. This study presents the numerical analysis of activation energy on three dimensional (3D) nanofluid (NFs) motion via Stretching Surface (SS) with nonlinear thermal radiation effect. This is in contrast to the conventional slip condition, convective condition applied at surface. The governing basic equations are translated into nonlinear ODEs by suitable similarity transformations. The relevant boundary value problem was explored for a numerical solution for applying the MATLAB based on Runge–Kutta–Fehlberg (RKF) scheme via shooting technique. The major outcomes of current work have more concentration (ϕ (η 1)) and Mass Transfer Rate ( Sh x Re x − 1 ∕ 2 ) for various numerical values of Activation Energy ( E A ). The present solutions determine very good correlation with the previously studied ones in a special case as predicted in the tables. [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 addresses the intricate interplay of magnetohydrodynamics (MHD), thermal radiation, and porous media effects, which are crucial in numerous engineering applications, including aerospace, energy systems, and environmental processes. The development of a mass-based hybrid nanofluid model signifies a novel approach, potentially yielding more accurate predictions and insights into the thermal behavior of fluids in diverse scenarios. Thus, the current research explores the heat transfer characteristics of a unique nanofluid known as TiO2 (titania)-CuO (copper oxide)/H2O (water) hybrid nanofluid. This nanofluid flows past a static or moving wedge considering the impact of thermal radiation and magnetic field in the appearance of porous medium. To calculate the effective thermophysical attributions of the hybrid (TiO2-CuO) nanofluid, a mass-based strategy is employed. This approach involves analyzing the masses of both the first and second nanoparticles, along with the mass of the base fluid, as essential input parameters. The proposed mathematical model is modified to a dimensionless form by applying similarity transformations. The numerical solution is obtained by utilizing the bvp4c built-in function within the MATLAB environment. Graphs illustrate the influence of various parameters on temperature and velocity trends, including the magnetic field parameter and heat absorption/generation parameter as well as the thermal radiation parameter. It is noted that along with the enhancement in the values of parameters related to porous medium or magnetic field, the velocity of the hybrid nanofluid improves. This occurs when the moving wedge parameter's value is below 1. Conversely, when the moving wedge parameter's value exceeds 1, the velocity of the hybrid nanofluid decreases. The shape factor is more effective in the temperature profile for developed inputs of heat absorption/generation parameter. A juxtaposition of enhancement in heat transfer rate due to nanofluid (TiO2/H2O) and hybrid nanofluid (TiO2-CuO/H2O) is likewise presented. The main outcome indicates that the hybrid nanofluid exhibits superior thermal conductivity relative to the conventional nanofluid. [ABSTRACT FROM AUTHOR]

In this paper, the importance of mass and heat transfer characteristics of mixed convective conditions on nonlinear free convection flow embedded with non-Fourier flux and thermal radiation is numerically investigated. A partial Casson slip and mixed impact of thermophoresis and Brownian motion is considered at the elastic surface. To change the highly nonlinear partial differential equations into ordinary differential system, we used the similarity transformations and then the shooting method is employed to solve resulting equations. The significance of various physical parameters on the velocity, concentration and temperature profiles are investigated for both negative value of ferromagnetic interaction ( β 1 = − 0. 2) and positive value of ferromagnetic interaction ( β 1 = 0. 2). The governing physical aspects of coefficient of skin friction, the Sherwood and Nusselt numbers are obtained for various embedded parameters. Our findings concluded that the ferromagnetic interaction is positive and then more mass transfer rate is identified compared to the negative value of ferromagnetic interaction, but whereas in friction and heat transfer rate, it was completely mixed sense (i.e., different effects have different results). Brownian motion has less Nusselt number values in positive ferromagnetism compared to negative ferromagnetism and quite opposite behavior is observed in the presence of thermophoresis, this happened due to nonlinear flux and buoyancy. [ABSTRACT FROM AUTHOR]

In this analysis, the MHD ow and nth-order dispersion of chemically reactive species over a slendering stretching sheet are studied numerically. The partial slip boundary condition and non-linear form of thermal radiation are also considered in this research. To get non-linear ordinary differential equations from the system of partial differential equations governing the ow, energy, and concentration, similarity transformations are applied. Using the shooting technique and the Runge-Kutta scheme, the resultant equations are integrated numerically. The numerical results in terms of temperature, velocity, and concentration are represented graphically. Results from this research indicate that an increase in the wall thickness parameter reduces momentum and heat transfer effects when a magnetic field is present. [ABSTRACT FROM AUTHOR]

Many real‐world devices, such as heat exchangers, geothermal reservoirs, and cooling systems, utilize the concept of boundary layer flow across a cone geometry. The current study presents and analyses the mathematical formulation for the mixed convection flow of a hybrid nanofluid over a permeable stationary cone. The heat transfer analysis considers the effects of thermal radiation and convective boundary condition. Numerical and statistical analyses of this flow problem yield new, physically significant results. The numerical analysis is carried out using the bvp4c solver in Matlab. Similarity transformations are performed to obtain a system of nonlinear ordinary differential equations from the governing partial differential equations and boundary conditions. In both assisting and opposing flows, spherical‐ and platelet‐shaped nanoparticles are observed to produce the lowest and highest local skin friction coefficient, respectively. The spherical‐ and blade‐shaped nanoparticles also offer the highest and lowest local Nusselt number, respectively, with a difference of 6.4% (assisting) and 6.03% (opposing). Meanwhile, the increase in the mixed convection parameter raised the velocity profile but diminished the temperature profile of the hybrid nanofluid. Then, the relationship of the Biot number (Bi)$({Bi})$, suction (S)$(S)$, and thermal radiation (R$(R$) parameters with the local Nusselt number is investigated through the response surface methodology (RSM). The local Nusselt number for the current flow problem is estimated to be maximized at 0.814323 (assisting) and 0.814629 (opposing) when these parameters are at the highest range of S=2.0$S\ = \ 2.0$, R=1.0$R\ = \ 1.0$, and Bi=0.5$Bi\ = \ 0.5$. Several researchers had presented experimental studies conducted at different temperatures (15, 25, 35°C), mass flow rates (ranging from 0.00076 to 0.041 kg/s), and nanoparticle concentrations (0.387, 0.992, 3.12, 4.71 mass%). [ABSTRACT FROM AUTHOR]

The main objective of this work is to investigate viscous dissipation with thermal radiation impact on hybrid nanofluid flow past an exponentially stretching/shrinking surface along with magnetic field, and heat source/sink, slip boundary conditions. Water ( H 2 O ) is taken into account as a host fluid with copper (Cu) and alumina ( Al 2 O 3 ) as nanoparticles to form a hybrid nano liquid (Cu- H 2 O - Al 2 O 3 ). The coupled nonlinear partial differential equations are transmuted into ordinary differential equations using similarity transformations with boundary conditions and these ODEs are simplified using numerical solver, bvp4c in MATLAB. The behavior of momentum profiles, thermal profiles, coefficient of heat transfer ( Nux 1 ) and skin friction ( C f ) are explored using the pertinent parameters such as Eckert Number ( Ec 1 ), Suction Parameter ( S 1 ), Magnetic Parameter ( M 1 ), Radiation Parameter ( Nr 1 ), Stretching/Shrinking Parameter (λ ), Velocity and thermal slip Parameters ( A 1 and B 1 ), Heat source/sink Parameter ( β 1 ), variable thermal Parameter (ϵ ), thermal conductivity (K) are depicted through tables and graphs. The present simulation is more stable and convergence when compared with the existing literature, which is portrayed in the tables. The presence of dual solution is noticed for Ec 1 = 0.1, 0.11,0.12 when the critical value of λ (= λ c ) are λ c 1 = - 1.60355799, λ c 2 = - 1.60322884 and λ c 3 = - 1.6031348, respectively. The existence of the dual solution is reported due to the presence of shrinking surface and suction, further, the first solution is found to be more stable. The novelty of the current simulation includes MHD hybrid nano liquid flow stability with the impact of viscous dissipation and thermal radiation past stretching/shrinking permeable plane to fill the research gap in the existing literature. The applications of transmission of heat by stretching/shrinking surface in boundary layers is used in various fields such as polymer and material processing, biomedical engineering, heat exchangers, etc. [ABSTRACT FROM AUTHOR]

The non-Newtonian characteristic of the fluid flow phenomena has several applications in industries and the production of engineering gadgets. Based upon the role, the present work deals with the flow of Williamson nanofluid past two inclined parallel sheets. Further, the influence of radiating heat due to thermal radiation, Ohmic heating because of the magnetization, and inclined angle on Williamson fluid are presented, which are vital for the heat transfer enhancement. The proposed study became novel due to the scrutiny of entropy for the irreversibility processes within the system that is obtained due to heat transfer. The designed model with dimensional form is developed by converting to dimensionless forms with the help of similarity transformations. The finalized transformed equations are handled analytically using the Homotopy perturbation method (HPM). Heat irreversibility is calculated by inserting the observed values into entropy generation and Bejan number. The suggested method of solution for the momentum profile is verified by comparing it to a previously published numerical result in some limited circumstances, and great agreement is found. The result reveals that the entropy generation is enhanced near the upper wall of the channel for the magnetized particle but thermal radiation attenuates it, however, the fluid temperature boosts up for the enhanced coupling constraint i.e. for the existence of Eckert number. [ABSTRACT FROM AUTHOR]

This paper discusses the impact of unstable bioconvection microbial nanofluid drift with a revolving vertical funnel / cone in the spinning microbial nanofluid with a time-critical angular speed and chemical reaction, thermal radiation with the thermal, solute and microbial Biot numbers as the boundary conditions. The governing unsteady and the coupled partial differential equations equipped with non-linear terms are resolved mathematically using suitable similarity transformations. Further, these equations are analytically solved by the spectral quasilinearisation method (SQLM). The consequences of different physical constraints and other parameters are explained and analysed with the help of graphs. The surge of solute and microbial profiles was reflected in the rise of solutal Biot number and microbial Biot numbers, respectively, while the temperature profile of the fluid was enhanced for the increasing values of thermal, solutal and microbial Biot number parameters. The higher values of bioconvection Brownian motion increases the velocity and decreases the microbial profiles. The bioconvection Schmidt number and Peclet numbers enhance and discriminate the microbial profile correspondingly. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) influenced nanofluid is gaining popularity in the industry for solar energy and scratch heat exchanger applications. Consequently, this research focuses on evaluating the impact of nonlinear thermal radiation from a CNT-based nanofluid on an unsteady three-dimensional nonasymmetric Homann stagnant flux as a function of length and radius. CNTs have remarkable thermal physical properties that appear to be critical for nonlinear thermal transport. As a result, the nonlinear heat transfer properties of H2O composed of single or multiple wall CNTs are studied. The nanomaterial has a length and radius of approximately 3 nm ≤ L ≤ 7 0 nm and 1 0 nm ≤ R ≤ 4 0 nm. Partially differential equations with appropriate similarity transformations serve as a mathematical model for the process. The numerical solution of the simplified system of equations is achieved via the use of the well-known Runge–Kutta (RK) method in conjunction with the shooting approach. An effective way to show how a component affects velocity and temperature, skin frictions in both direction and Nusselt number are utilized in graphical representations. Increasing the unsteadiness parameter causes a reduction in the temperature profile and the velocity profile in both directions. As ε grows larger with ϕ , the skin friction in both directions decreases, while the Nusselt number profile grows larger. In addition, the variation in the Nusselt number is included in the tables, along with a comparison of the model without radiation to the model with radiation. [ABSTRACT FROM AUTHOR]

In this paper, the impact of thermal slip and slip velocity on ZrO2 (Zirconia)–water nanofluid flow through a vertically heated permeable stretching sheet surrounded by a porous medium has been deliberated. The concept of thermal radiation is assimilated into the study. Using similarity transformations, the concerned governing flow model is changed into nonlinear ODEs and gets a solution by the R-K method. The consequence of numerous pertinent parameters in the fluid flow arena is deliberated by employing graphical and tabular approaches. The current investigation will be supportive of understanding the thermal features of heat transfer nanofluids. Outcomes of the present effort are compared with that of previously published works and found a commendable level of settlement. Our analysis sightsees that Zirconia–water achieves high temperatures due to thermal radiation. Also, it is found that Zirconia–water nanofluid lessens the heat transfer rate related to their base fluid. [ABSTRACT FROM AUTHOR]

This study investigates the effects of an unsteady mixed convection nanofluid flow in a rotating vertical cone submerged in spinning nanofluid. Our analysis considered the impacts of heat flux, chemical reactions, and thermal radiation, with the thermal and concentration Biot numbers serving as constraints at the boundary. The governing unsteady and coupled partial differential equations were solved through appropriate similarity transformations, addressing the nonlinear terms inherent in these equations. The spectral quasi-linearisation method (SQLM) was employed to solve the higher-order nonlinear differential equations. This study elucidates and assesses the impact of diverse physical constraints and parameters through the use of graphical representations. Notably, the temperature distribution of the liquefied substance was intensified as the thermal and solutal Biot numbers increased. [ABSTRACT FROM AUTHOR]

The present study numerically explores an unsteady flow due to a rotating and vertically moving disk with the inclusion of an applied magnetic field and thermal radiation effects. Self-similar equations are obtained by utilizing the appropriate similarity transformations, and then the similarity solutions are evaluated in Matlab software using the "BVP4c" solver. First time in the literature, triple solutions are reported for this flow geometry. Although these solutions are mathematically valid, the first solution branch is physically more reliable and describes the main flow dynamics. The calculated results of several flow fields like shear stresses, heat transfer rate, fluid velocity and temperature for the triple solution branches are apparently discussed through graphs and tabular forms. The results indicated that the shear stresses and heat transfer rate decreased in all three solution branches with an increase in magnetic parameter. As reported in the study, the influence of magnetic parameter leads to a decrease in radial and tangential fluid velocities near the disk surface in all three branches, whereas axial and temperature profiles depict opposite trends. It is observed that the intensity of temperature ratio and thermal radiation parameters enhance the fluid temperature in the first solution branch. The common feature is that both the momentum and thermal boundary layer thicknesses in the third solution branch are higher than the remaining two solution branches. In fact, they are found in ascending order. [ABSTRACT FROM AUTHOR]

The primary objective of this article is on examining the impacts of mixed convection flow of Carreau fluid past a permeable stretched surface with Soret and Dufour effects occurring. For the flow analysis, the Darcy–Forchheimer porosity medium is taken into account. In order to explore the transference analysis of heat and mass rate, the impressions of thermal radiation, viscous dissipation, heat generation, Arrhenius activation energy, convective heat, and mass conditions impacts are taken into consideration. The flow equations initially exist as PDEs, and we then employ appropriate similarity transformations to change them into ODEs. The R–K 4th order strategy based on the shooting approach is used to numerically solve these ODEs. Through various emergent variables, the numerical results for the velocity, temperature, and concentration fields are shown. For a variety of distinct variables, the physical quantities such as friction factor, local Nusselt number, and local Sherwood numbers are shown. It is noted that the velocity field is reduced by the magnetic field, but the Weissenberg number buoyancy ratio parameter exhibits the opposite tendency. Further, it is noticed that temperature and concentration distributions have an improving tendency for the Soret and Dufour parameter. [ABSTRACT FROM AUTHOR]

This present study involves examining the nature of 3D rotational MHD nanofluid flow through a stretching sheet. Alumina Al 2 O 3 –ethylene glycol C 2 H 6 O 2 -based nanofluid is considered in this investigation. A normal magnetic field acts on the sheet. Radiative thermal boundary condition with slip velocity has been considered. Suitable similarity transformation is used to derive a system of ordinary differential equations. The spectral quasilinearisation method (SQLM) is applied to solve this system. For curiosity, the skin friction coefficient and Nusselt number have been calculated. Due to effective heat generation and heat radiation, a significant temperature difference is produced. Besides, the impact of the variation in the volume fraction of nanoparticles is remarkable. The influence of key parameters has also been shown graphically. The graphical representation shows that the magnetic parameter declines in the radial velocity component, while the layout of the tangential component of velocity enhances in the form of a parabola with an enhancement of the magnetic parameter. Temperature layout is enhanced with the increasing values of the magnetic parameter, nanoparticle volume fraction, temperature ratio parameter, radiation parameter and Biot number. The generation of entropy enhances with the increase in the magnetic parameter, Brinkman number and Reynolds number, while nanoparticle volume fraction and temperature difference parameters decrease the entropy generation. For the engineering interest, the skin friction coefficient along the x-axis, y-axis and the local Nusselt number have also been calculated. The impacts of pertinent parameters on the skin friction coefficient along the x-axis, y-axis and the local Nusselt number are scrutinised numerically. We have compared our current result with the available studies for special cases ϕ = 0 , M = 0 and found that the results are in good agreement. [ABSTRACT FROM AUTHOR]

This research focuses on energy convention and mass transpiration in magnetohydrodynamic hybrid nanofluid (Al2O3–Cu) flows driven by a moving surface, which build numerous applications such as inducing hypothermia in cancer tumors, reducing bleeding in severe injuries, and performing magnetic resonance imaging are only a few medical applications applying magnetohydrodynamics A similarity transformation describes the representational construction of the steady two‐dimensional nonlinear partial differential equations (PDEs) to a set of nonlinear ordinary differential equations (ODEs). Above equations subject to corresponding boundary conditions are analytically solved. Specifically, the energy equation with radiation effect is solved analytically using incomplete Gamma function. Moreover, the graphs included physical representations of the measurement can be found in this paper. In summary, our findings demonstrate that mass‐transfer induced slip has a non‐negligible impact on flows driven by a moving sheet. Mass transfer induced slip may even be able to dominate the flow driven effect of the moving sheet by changing the flow directions to flow against the sheet motion and also thermal radiation parameter increases as thermal boundary layer increases. [ABSTRACT FROM AUTHOR]

An extended Jaffrey–Hamel problem with heat and mass transfer attributes of viscoelastic fluid over an isothermal porous conduit, where the flow is produced by injecting the fluid at the inlet of the convergent section, has been described. The homogeneous processes dictated by first-order kinetics take place in the adjacent fluid, whereas the heterogeneous reactions supplied by cubic autocatalytic dynamics are believed to take place on the channel wall. To simulate both inertial drag and bulk permeable drag of the porosity medium, a non-Darcy-drag force concept is used. Slow velocity leads to the disregarding of viscous dissipation. Thermal radiation and a heat source or sink work together to keep the temperature in equilibrium in the flow domain. The simulation-based numerical solutions for dimensionless temperature, velocity, and concentration have been derived by applying appropriate similarity transformations to the highly nonlinear momentum equation, thermal, and species concentration equations. A more secure velocity profile results from a longer strain retardation time and a shorter stress relaxation time, whereas both viscoelastic times have reverse consequences. The thermal distribution is quantitatively improved with an increase in the radiation parameter, suggesting a higher rate of heat transmission. Concentration drops as heterogeneous reaction parameters are amplified. With an increase in the porosity number, surface viscous drag becomes more intense. Divergent cross section shows a greater tendency for heat and mass transfer. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids play a crucial role in applications involving heat transfer and mass transfer. The inclusion of nanoparticles in these fluids improves the efficiency of heat and mass transfer processes. This study employs a numerical solution approach to examine the flow of non-Newtonian hybrid nanofluids over a plumb cone/plate surface, considering the effects of magnetohydrodynamics (MHD) and thermal radiation. Additionally, we investigate how heat and mass transfer are affected by a fluid containing microorganisms. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a similarity transformation to simplify this complex system. We then use the Keller-box finite-difference method to solve these equations. Along with a table presenting the results for skin friction, Nusselt number, Sherwood number, and microbe density number, we present graphical representations of velocity, temperature, concentration, and microorganism diffusion behavior. Our results indicate that the addition of MHD and thermal radiation improves the diffusion of microorganisms, thereby enhancing the rates of heat and mass transfer. Through a comparative analysis with prior research, we demonstrate the reliability of our conclusions. [ABSTRACT FROM AUTHOR]

Bioconvection research is essential due to its widespread use in the domains of biofuels and bioengineering. This study investigates the numerical behavior of megnetohydrodynamic bioconvection boundary layer flow of motile microorganisms in upper convected Maxwell fluid via a renewed bvp4c-based Lobatto IIIA solver. To stabilize the nanoparticles in suspension, microorganisms are used that cause bioconvection. The flow past stretchable sheets is under the influence of heat and mass transfer, nonlinear thermal radiation, and viscous dissipation. Suitable similarity transformations are adopted to amend PDEs' system of governing equations into ODEs' system. Visualize graphical and numerical presentations that show the influence of physical parameters, such as flow rate, temperature gradient, nanofluid concentration, and gyrotactic motile microorganism concentration. Physical quantities such as skin friction, Nusselt number, Sherwood number, and local density of microorganisms are also taken into consideration. [ABSTRACT FROM AUTHOR]

The primary aspect of this study is a theoretical analysis of heat transport enhancement in the time-independent three-dimensional ternary hybrid nanofluid flow with base fluid water and engine oil under the effects of thermal radiation over a linear as well as a nonlinearly stretching sheet. Three different shaped nanoparticles, namely SiO2in blade form, MoS2in cylindrical form, and Cu in platelet form, are considered in this research. Utilizing similarity transformations, the resultant flow equations are reduced into non-linear ordinary differential equations (ODE's). These nonlinear differential equations are solved numerically by employing the shooting method in conjunction with Runge–Kutta (RK) method. The physical significance of various fluid parameters such as radiation parameter, stretching parameter, the volume fraction of particles dispersed in the base liquid is discussed in the flow velocity and temperature distribution. It is concluded that temperature increases in the case of MoS2-SiO2-Cu-water over a linearly stretching sheet as well as a nonlinearly stretching sheet when the volume fraction of nanoparticles is increased as compared to MoS2-SiO2-Cu-engine oil. It should be notable that this study is helpful for the advancement of a cooling system in voltaic devices, hybrid-powered engines and solar energy applications. [ABSTRACT FROM AUTHOR]

A mathematical model is proposed to analyze the impacts of an inclined magnetic field and velocity slip on a hybrid nanoliquid over an exponentially elongated sheet in the presence of thermal heat flux. In this study, single wall and multiwall carbon nanotubes (SWCNT and MWCNT's) are considered as nanoparticles with water as a base fluid due to their distinctive nanostructures and excellent thermal conductivity in many industrial and engineering applications. The governing equations are converted into ordinary differential equations by employing appropriate similarity transformations and are then solved by utilizing the bvp4c technique with the help of MATLAB software. The influence of various parameters such as magnetic field ( 0 ≤ M ≤ 2), velocity slip parameter ( 0 ≤ λ ≤ 1.5), angle of inclination ( 30 o ≤ γ ≤ 90 0 ), thermal radiation ( 0 ≤ R ≤ 1.5), Prandtl number ( 0.71 ≤ Pr ≤ 10), the volume fraction of the nanoparticles ( 0.05 ≤ ϕ 1 , ϕ 2 ≤ 0.25) on fluid velocity and dimensionless temperature are discussed graphically. The fluid momentum and dimensionless temperature are dominant for hybrid nanoliquid against a single wall or multi-wall carbon tubes/water. Also, the heat transfer rate decelerates by increasing the slip parameter and the magnetic parameter. [ABSTRACT FROM AUTHOR]

This research analyzes the three-dimensional magneto hydrodynamic nanofluid flow through chemical reaction and thermal radiation above the dual stretching surface in the presence of an inclined magnetic field. Different rotational nanofluid and hybrid nanofluids with constant angular velocity ω ∗ for this comparative study are considered. The constitutive relations are used to gain the equations of motion, energy, and concentration. This flow governing extremely non-linear equations cannot be handled by an analytical solution. So, these equations are transformed into ordinary differential equalities by using the similarity transformation and then handled in MATLAB by applying the boundary values problem practice. The outcomes for the considered problem are accessed through tables and graphs for different parameters. A maximum heat transfer amount is observed in the absence of thermal radiation and when the inclined magnetic field and axis of rotation are parallel. [ABSTRACT FROM AUTHOR]

The aim of this article is to explore the characteristics of fluid flow using the process of melting and entropy generation past on the Riga plate. Cross fluid is competent to explore the characteristics of fluid with high and low deformations under the influenced force. Transport of heat mechanism is inspected with key facts about melting conditions, viscous dissipation and thermal radiation. For the inspection of electromagnetic hydrodynamic aspects of fluid, Riga geometry due to this Lorentz force is produced. The partial differential form of the equations has been converted into an ordinary differential system with the use of similarity transformations. The reliable numerical Keller Box scheme is being applied to solve the obtained system of ordinary equations and comparison of the results have been performed through the built-in Matlab solver bvp4c. The obtained solutions have also been compared with the literature results. The physical quantities and their numerical attitude are provided in the form of statistical graphs. The Lorentz forces produce to slow down the fluid's velocity, while the Hartman number accelerated the velocity. [ABSTRACT FROM AUTHOR]

The present paper investigates analytically a continuous stream of viscoelastic fluid and magnetohydrodynamic flow of second‐grade fluids owing to protracted sheets in a permeable medium with the help of the Cattaneo–Christov pattern. This idea is a new generalization of the classical Fourier law. Also, in this analysis, heat as well as mass transfer in second‐grade fluid past wall suction/injection is assumed. A few similarity transformations are used to simplify the addressing of boundary layer expressions. An analytical solution is obtained by applying the Appell hypergeometric properties. Furthermore, our work also describes an effect of the relaxation time variable, elasticity number, and Prandtl number together with temperature fields. Also, we studied the newly introduced parameter, that is, the thermal radiation parameter by Cattaneo, over a Fourier heat flux pattern. In addition, some physical presentation of the measurements is illustrated in the graphs. [ABSTRACT FROM AUTHOR]

In the context of advancements in both heat and mass transfer, the current study intends to analyze the impacts of thermal radiation, Soret, and Dufour on the magnetohydrodynamic boundary layer flow through a vertical spinning cone in porous media. The Dufour effect is the energy flux due to the mass concentration gradient with a reciprocal phenomenon, the Soret effect. Energy expression considers the physical aspects of heat generation and absorption. It is expected that the tangential, circumferential, and normal directions will all have velocity components in flow through a porous media. The governing equations are nonlinear partial differential equations that are rearranged into ordinary differential equations via similarity transformation, and then they are numerically solved using the Runge–Kutta method along with a proper shooting strategy. Graphs are used to examine the impacts of many parameters on flow characteristic velocity, temperature, and concentration, including magnetic parameters, porous parameters, Dufour and Soret parameters, chemical reaction parameters, and more. The numerical findings of the gradient of velocity, the Nusselt and Sherwood numbers, and the surface drag force are tabulated and compared with the current result and the one from the literature. The findings are found to be in good agreement. Circumferential and normal velocities are improved visually for greater values of the porosity parameter, but the tangential velocity behavior of the magnetic parameter exhibits the reverse behavior. In addition, the Dufour parameter and chemical reaction both exhibit diminishing behavior when the Soret parameter increases. [ABSTRACT FROM AUTHOR]