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This study investigates the various uses of density of motile microorganisms in the context of the flow of a binary base fluid with double diffusion past a vertical surface. The research aims to comprehend the interactions between motile microorganisms and the fluid dynamics, as well as the heat and mass transport mechanisms in this system. The analysis involves mathematically constructing the governing equations, transforming them into dimensionless nonlinear ordinary differential equations using similarity transformations, and numerically solving them using the MATLAB bvp4c solver. An analysis of the influence of several parameters on the profiles of velocity, temperature, concentration, nanoparticle concentration, and density of motile microorganisms is conducted using graphical representation. The findings demonstrate that boosting the thermophoresis parameter intensifies the temperature profile. In addition, an increase in the nanofluid Schmidt number results in a larger concentration of nanoparticles, whereas a higher bioconvection Lewis number reduces the density of the motile microorganism profile. These findings may find use in biomedical engineering as well as industrial processes that include enhancing the efficiency of mass transfer and bioconvection. Numeric simulation prophesies 99.9% for both shear stress and heat transfer rate intensification for Prandtl values are noticed. [ABSTRACT FROM AUTHOR]

This study conducts a computational analysis to explore how magnetic fields, radiation, heat, and mass transfer collectively influence a horizontal stretching sheet within a porous medium. The research focuses on elucidating the dynamics of thin film flow through the formulation of time‐dependent equations and subsequent transformation of fluid flow equations into ordinary differential equations via similarity transformation. The numerical solution is attained employing the Runge–Kutta fourth‐order method coupled with a shooting technique. MATLAB software is utilized to generate graphs and numerical values, offering a detailed representation of engineering‐relevant physical quantities in tabular form. The investigation revealed notable trends associated with varying parameters. Increasing unsteadiness parameters lead to a reduction in velocity, temperature, and concentration fields, while the temperature distribution demonstrates a positive correlation with radiation parameters. Moreover, elevated Prandtl numbers and unsteadiness parameters correspond to augmented heat and mass flux, respectively. Of particular significance is the observed heightened heat transfer rate during the transition from a Prandtl number of 1 (representing air) to 2 (representing oil), alongside an increased mass transfer rate with the escalation in Schmidt number from 0.62 (representing hydrogen) to 0.78 (representing ammonia). A comparative analysis of the numerical findings with existing literature demonstrates excellent agreement, affirming the validity and relevance of the present study. These insights offer valuable implications for understanding and optimizing heat and mass transfer processes in porous media, with potential applications in various engineering and scientific domains. [ABSTRACT FROM AUTHOR]

In recent times, bioconvection has numerous uses, like, biological and biotechnological problems. The present study describes the magnetic bioconvective Buongiorno's flow model with microorganisms in a stretchable area with convective heat transfer and second‐order velocity slip in a non‐Darcian porous regime. Here, the influence of variable viscosity, viscous dissipation, Joule heating, and heat source/sink are considered in the occurrence of higher‐order chemical reactions. Employing proper similarity transformations leading equations are transformed to dimension‐free form. The transformed equations are solved via MATLAB bvp4c problem solver. This study's main objective is to graphically analyze the effects of different pertinent factors on the density of motile microorganisms, velocity, concentration, temperature, number of motile microorganisms' density, skin friction, mass transport rate, and heat transport rate. The main findings drawn from this study are viscosity (−5≤θr≤−1) $(-5\le {\theta }_{r}\le -1)$ and magnetic parameter (0.5≤M≤3) $(0.5\le M\le 3)$ lowers the fluid velocity. Biot number (0.4≤Bi≤0.6) $(0.4\le {B}_{i}\le 0.6)$ increases fluid temperature, but reduces heat transport rates and skin friction. Schmidt (0.5≤Sc≤1) $(0.5\le Sc\le 1)$ and Eckert numbers (0.1≤Ec≤3) $(0.1\le {E}_{c}\le 3)$ reduce the fluid concentration. A rise of 0.3 in bioconvective Rayleigh number (0.3≤Rab≤0.9) $(0.3\le R{a}_{b}\le 0.9)$ and 0.2 in buoyancy ratio number (0.1≤Nr≤0.5) $(0.1\le {N}_{r}\le 0.5)$ causes a percentage drop in velocities of 8.79% and 3.91% (approximately), respectively, in the neighborhood of the sheet. Furthermore, the increase in Peclet number (0.8≤Pe≤1.5) $(0.8\le {P}_{e}\le 1.5)$ by 0.2 lowers the density number of microorganisms by 28%. Additionally, the profile of motile microorganisms is improved by thermophoresis impact, while it is diminished by chemical reaction. [ABSTRACT FROM AUTHOR]

This paper presents a technique to find the closed‐form solution of the boundary‐value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed‐form solution is obtained. The accuracy of the closed‐form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed‐form solution closely matches the exact solution. [ABSTRACT FROM AUTHOR]

The two‐dimensional mixed convective MHD flow with heat and mass transfer is investigated for its behavior with Dufour and Soret mechanisms over the porous sheet. The copper–alumina (Cu–Al2O3) hybrid nanoparticles are used in the base fluid water. The governing system of partial differential equations is converted into a system of ordinary differential equations via similarity transformations, obtaining the solution for velocity, temperature, and concentration fields in exponential form. The problem is demonstrated in the Darcy–Brinkman model, the impact of included parameters such as Richardson number, magnetic field, and Dufour numbers are studied for the obtained solution with the help of graphs. Increasing the magnetic field decreases both transverse and axial velocity profiles. Increasing the magnetic field and Richardson's number decreases the solution (Al2O3–H2O). Increasing the values magnetic field and Richardson's number decreases both transverse and axial velocity profiles. Increasing the values of the Dufour effect increases the axial and transverse velocity boundary layer. The magnetohydrodynamic hybrid nanofluid flow over porous media works efficiently in liquid cooling and, therefore, has significant applications in industrial heating and cooling systems, solar energy, magnetohydrodynamic flow meters and pumps, manufacturing, regenerative heat exchange, thermal energy storage, solar power collectors, geothermal recovery, and chemical catalytic reactors. [ABSTRACT FROM AUTHOR]

The Jeffery–Hamel flow phenomenon appears in a variety of real‐world applications involving the flow of two nonparallel plates. BY using a similarity transformation derived from the equation of continuity, partial differential equations determining flow characteristics are translated into nonlinear ordinary differential equations. The problem involves the flow of a specific type of fluid, namely, an incompressible and electrically conducting fluid, between two nonparallel plates. The flow is assumed to be steady, two‐dimensional, and subject to certain boundary conditions. Specifically, the plates are impermeable, and the fluid adheres to a no‐slip condition, resulting in zero fluid velocity at the plates' surfaces. Moreover, the problem incorporates the effects of magnetic fields and pressure fluctuations, making it highly applicable to scenarios, such as blood flow through arteries in the human body, which can be modeled as a special case of the magnetohydrodynamic (MHD) Jeffery–Hamel problem referred to as the (MHD) blood pressure equation. This work compares two numerical approaches for solving the MHDs Jeffery–Hamel problem: B‐spline and Bernstein polynomial collocation. The given approaches are used to discretize and transform the equation into a system of algebraic equations. Matrix algebra techniques are then used to solve the resultant system. A complete error analysis and convergence rates for different grid sizes are derived for both methods and are used to compare the accuracy and efficiency of the two approaches. Both approaches produce correct solutions, according to the numerical findings, although the Bernstein polynomial collocation method is more efficient and accurate than the B‐spline collocation. [ABSTRACT FROM AUTHOR]

The squeezing flow bears a major importance in everyday phenomena and has vast industrial and biomedical applications. The current study looks at the nanofluid flow among two infinite "parallel plates" that are squeezed. The velocity slip and first‐order compound response have been considered in this problem for a clear understanding of their consequences in the flow of nanofluid and heat transport mechanism. This fluid replica thinks about "Brownian motion" and the influences of "thermophoresis" of nanofluid. The novelty of this work lies in exploring the combined effects of first‐order chemical reaction and the velocity slip on unsteady squeezing flow of nanofluid between two parallel plates as one has not yet reported such effects. The prevailing equations are altered into simplified forms by deploying suitable similarity transformations. Then "numerical solutions" of these equations are obtained by applying the fourth‐order "Runge–Kutta method" with the help of the shooting technique. The accuracy is verified by using two different methods and also comparing our data with the available existing literature. The main goal is to study heat and mass transfer through unsteady squeezing plates by the influence of velocity slip and chemical reaction. The consequences of diverse pertinent parameters on fluid flow, thermal, and concentration fields have been explored in this study. With the rise in "velocity slip parameter" from 0 to 1, 81.37% decrease in skin friction coefficient, 15.81% increase in Nusselt number, and 29.13% increase in Sherwood number are observed. Rising values of the chemical reaction parameter from 0.3 to 0.5, the mass transfer coefficient increases by 66.94%. [ABSTRACT FROM AUTHOR]

The dispersion of solid particles in a viscous fluid leads to a two‐phase flow nature. The present study incorporates the time‐dependent three‐dimensional dusty fluid flow generated by a periodically oscillatory rotating disk. The disk is stretchable along the radial axis with time‐based sinusoidal fluctuations. The governing incompressible flow equations for two‐phase equilibrium are normalized in the form of similarity systems consisting of the fluid stage and dust phase. The whole normalized system reduces to the familiar Von Kármán similarity system for the flow configuration of rotating disk by removing the dust phase and periodic oscillations of the disk. The two‐phase flow model is then numerically solved by a built‐in method namely "pdsolve" in Maple built program. The graphical aspects of the obtained physical parameters on velocity and thermal fields of the dust particle stage are investigated to show how the oscillatory disk contributes to the dusty flow features. The wall shears and thermal rates of the fluid and dust particles are also calculated in limiting case of disk rotation. It is observed that in time‐based flow, the oscillatory profiles preserve a phase shifting phenomenon. For centrifugal forces, the particle cloud moves away from the surface along a tangential direction. The thermal field is reduced by the dust particle stages. [ABSTRACT FROM AUTHOR]

In this study, a numerical solution of the velocity and heat transfer on the magnetohydrodynamic suction–injection model of viscous fluid flow has been studied. We use the differential transformation method and Bernoulli wavelet method to solve the highly nonlinear governing equations; applying appropriate similarity transformations and reducing governing equations to highly nonlinear coupled ordinary differential equations. The objective of this analysis is to determine how the suction parameter, Hartmann number, squeeze number, thermophoresis parameter, and Prandtl number affect the velocity and temperature profiles. When the current findings are compared with those that have already been published in the literature, confident suppositions are made, and it is discovered that there is considerable agreement. Graphs have been used to discuss the influence of nondimensional characteristics on velocity and temperature. [ABSTRACT FROM AUTHOR]

The analysis of magnetized micro–nanoliquid flows generated by the movable disk is executed in this study. The disk is contained under the porous zone influence. The heat generation, heat sink, and temperature‐dependent conductance analysis are reported through the energy equation. The activation energy in terms of a chemical reaction is incorporated through the mass equation. The flow model is normalized through the implementation of similarity transformations. The numerical algorithm Runge–Kutta–Fehlberg is used to solve the reduced system. Results are plotted graphically and in tabular format to investigate the velocity, thermal, and concentration fields. Numeric benchmarks of couple and shear stresses, thermal and concentration rates are also computed. The temperature is augmented against the incremented thermophoretic, variable conductivity, and Brownian movement parameters. The presence of variable conductivity parameter resulted in a weaker rate of heat transportation. The heat transportation rate is boosted with an incremented Prandtl number. [ABSTRACT FROM AUTHOR]

The present study aims to discuss the Williamson fluid flow and heat transfer across a permeable stretching cylinder with heat generation/absorption effects. The effects of viscous dissipation, Joule heating, and magnetic field are also taken into account. The BVP‐4C numerical solver in MATLAB is adopted for all the numerical simulations in the present study. For this, the modeled partial differential equations are translated into dimensionless ordinary differential equations using some well‐developed similarity transformations. A good agreement between the numerical results of the present study and existing literature is exhibited. The dimensionless physical parameters being investigated are Reynolds number, magnetic field parameter, suction parameter, heat source/sink parameter, Williamson fluid parameter, and mixed convection parameter. The numerical calculations are also performed for the skin friction coefficient and local Nusselt number to get an understanding of the shear stress rate and heat transfer rate, respectively. Furthermore, the impact of all these physical parameters on the velocity and temperature profiles is investigated and represented throughout the literature. [ABSTRACT FROM AUTHOR]

In this study, micropolar fluid flow in a porous channel is investigated using the differential transform method (DTM) and the Hermite wavelet method (HWM). By exploiting Berman's similarity transformation, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations (ODEs). The concepts of DTM and HWM are briefly introduced and employed to derive solutions of nonlinear coupled ODEs. Our results compared with solutions already existing in the literature. When we compare DTM and HWM, HWM is more efficient and also requires less time to maintain a higher level of accuracy. The results are presented to study the velocity and microrotation profiles for various physical parameters such as Reynolds number, coupling parameter, spin‐gradient viscosity parameter, and micropolar fluid constant. As an important result, increases in the values of the coupling parameter and micropolar fluid constant have different results in comparison with the spin‐gradient viscosity parameter increasing. [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]

In this study, the aim is to find the numerical solutions of steady, two‐dimensional, incompressible, viscous, electrically conducting magnetohydrodynamic (MHD) boundary‐layer nanofluid flow towards a vertical cone in the presence of thermal diffusion, diffusion thermo, thermophoresis, and Brownian motion effects subject to porous medium and convective boundary condition. For this investigation, the method of similarity transformations is used for the objective of converting nonlinear partial differential equations into the system of ordinary differential equations. Approximate solutions are obtained using a numerical method of the Runge–Kutta method with the shooting technique for the flow, heat, and mass transfer equations together with boundary conditions. For this flow, the impact of various engineering parameters on MHD, thermal, and solutal boundary layers is investigated and the results are displayed graphically. In addition, the numerical values of the local skin‐friction coefficient, rate of heat transfer, and rate of mass transfer coefficients are calculated, and the results are presented numerically. Finally, the comparison with previously published work is made and found in good agreement. [ABSTRACT FROM AUTHOR]

In this article, we have inspected multiple slippery consequences along a stretching cylinder. Brownian migration along with thermophoresis is clutched together with an external heat source. Magnetic influence is considered perpendicular to the cylinder. Standard flow systems are transfigured to ordinary differential equations by well‐qualified similarity transformations. They are solved by the Runge–Kutta scheme of the fourth‐order (shooting technique) method with the assistance of MAPLE software. The entire simulation is done with a proper accuracy rate and the upshots are portrayed by graphs and tables. All results are compared under no slip and with slip provisions. Augmentation in Reynolds number and magnetic parameter uprise the velocity lines and the slip effect reduces the magnitude decently. The thermal jump effect reduces the magnitude of the heat transfer rate. The solutal slip effect decreases the concentration boundary layer for magnetic and Brownian migration specifications. Approximately 6.69% and 6.79% drop in Nusselt number is spotted for Brownian migration and thermophoresis parameters. The external heat source parameter brings out 14.98% inflation in the Nusselt number significantly. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate the flow and heat transfer of thermal radiation on the Jeffery fluid flow within a microchannel for the effects of the superhydrophobic surface (SHS) within suction/injection. The governing differential equations of motion and heat transfer are transformed into nonlinear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. The ODEs are solved along with boundary conditions by adopting Runge–Kutta with shooting technique. Symbolic computational software such as MATLAB, the solver bvp4c syntax examines the behavior of the relevant physical parameters. However, some effective emerging parameters on the flow problem reveal that the microchannel walls within the suction/injection parameter increase the temperature, and the SHS is heated. In contrast, without slip, the opposite behavior is rendered. It is clearly shown that the velocity profile diminishes with increasing the Prandtl number. Furthermore, it is noticed that velocity decreases for increasing values of Hartmann number. Comparison with available results for particular cases is an excellent agreement. [ABSTRACT FROM AUTHOR]

In this paper, unsteady magnetohydrodynamics nanofluid flow with thermo‐diffusion and heat generation effects is studied. The fluid flow at the plate is considered exponentially accelerated through a porous medium. The governing system of equations is made dimensionless with the help of similarity transformation. A Caputo–Fabrizio fractional‐order derivative is employed to generalize the momentum, energy, and concentration equations, and the exact expression is obtained using Laplace transformation techniques. To realize the physics of the problem, numerical results of velocity, temperature, and concentration profiles are obtained and presented through graphs. Also, the numerical values of the Nusselt number and Sherwood number are obtained and compared which strongly agree with the previous studies. From the results, it is concluded that velocity distribution decline by improving the value of the chemical reaction and magnetic field while the reverse trend is observed for volume fraction and micropolar parameter. It is also seen that the heat transfer process improves with heat generation and thermal radiation whereas, mass transfer declines with the chemical reaction parameter. [ABSTRACT FROM AUTHOR]

We examine the heat and mass transfer on magnetohydrodynamic Casson fluid motion via a curved sheet. The fluid flow is assumed to be along a stretched curved sheet. The effects of Soret ("viscous dissipation") and Dufour ("cross dispersion") are taken into account. The governing partial differential equations have been transformed into ordinary differential equations by using relevant similarity transformations. These converted equations are solved using a combination of Runge–Kutta–Fehlberg along with the shooting technique algorithm. We find out the various physical parameter behavior of F′(η) $F^{\prime} (\eta)$, Θ(η) $\Theta (\eta)$, and Φ(η) $\Phi (\eta)$. We found that the Θ(η) $\Theta (\eta)$ ("temperature profile") enhances while opposite behavior of Φ(η) $\Phi (\eta)$ ("concentration profile") with enlarge values of Sr $Sr$ and Df $Df$. Also, we get a good agreement with the present results when compared with the previous study. [ABSTRACT FROM AUTHOR]

In the present work, the mathematical model for the solar thermal collectors is considered in the form of a nonlinearly stretching sheet. The radiative heat transfer due to solar radiation in magnetohydrodynamic Sisko nanofluid flow over a stretching sheet in the presence of variable thermal conductivity and a heat source is analyzed effectively. The Sisko fluid has been used as a working fluid in the solar collector. The governing boundary value problem is transformed into a system of nonlinear ordinary differential equations using the similarity transformation technique, which is then solved numerically using the finite difference method combined with the quasilinearization technique. The results shown graphically are discussed for the effects of the thermal conductivity parameter, radiation parameter, and heat source parameter on the flow regime. It is observed that increasing values of radiation parameters imply greater thermal conduction and less thermal radiation, as a result of which the nanofluid temperature in the fluid regime will decrease. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of three‐dimensional magnetohydrodynamic flow for a couple of stress fluids on an exponentially stretching sheet. The magnetic field is implemented normally to the surface. To observe the transfer of heat phenomenon, the Cattaneo–Christov flux model of heat is employed. Using similarity transformation, the substantial differential equations are reformed into ordinary differential equations. Eventually, the effects of different physical parameters are studied graphically. The drawback in Fourier heat flux model is removed by adding a new paramter known as thermal relaxation time by Cattaneo. This perimeter allows heat transportation by way of propagation of waves thermally at a defined speed. After this, the Cattaneo law is further modified by Christov–Christov to replace the ordinary derivative along Oldroyd's upper‐convective derivative. [ABSTRACT FROM AUTHOR]

In this communication, thermodynamic irreversibility arising in dissipative Casson fluid flow inside a cone is investigated. The boundary–layer flow is considered wherein the motion is caused due to a point sink at the cone's vertex and the movement of the wall of the cone. The wall of the cone is subjected to mass transpiration that alters the flow and thermal regime. The cone having fluid‐saturated porous medium experiences Cattaneo–Christov heat flux. The configuration admits a similarity transformation that yields a boundary value problem (BVP) comprising an ordinary differential equation. The BVP is treated by the fourth‐order R‐K method along with the shooting algorithm. The system yields a dual solution for momentum and energy, which gives rise to a dual regime for entropy distribution. Numerical computations provide quantities of interest viz. velocity and temperature distributions, skin friction coefficient, Nusselt number, and entropy distribution. Phenomena exhibited through profiles/tables for velocity, temperature, entropy, streamlines, and other quantities of interest reveal interesting results. [ABSTRACT FROM AUTHOR]

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number. [ABSTRACT FROM AUTHOR]

Herein, the off‐centered stagnation flow and heat transfer of zinc oxide–silver/water hybrid nanofluid over a rotating disk according to the mass‐based algorithm is studied. It is assumed that the nanoparticles have a spherical shape. Also, the velocity slip between the base fluid and nanoparticles is negligible. The Prandtl number is kept constant at 6.2. In addition, it has been used an experimental relation for effective thermal conductivity which is a function of volume fraction and temperature. The governing partial differential equations are converted to dimensionless ordinary differential equation (ODE)s by the similarity transformation method. The simplified ODEs are solved numerically by the bvp4c function from MATLAB which is an efficient and reliable code according to the three‐stage Lobatto IIIa formula. The influence of rotational parameters and both nanoparticles masses on the profiles and quantities of engineering interest are presented and discussed in detail. It is shown that the flow becomes complicated when there is a distance between the flow axis and the disk axis. Under determined conditions for a hybrid nanofluid with 30‐g mass for both nanoparticles and 100‐g mass for pure water, adding 30 g of the second nanoparticle's mass into the base fluid leads to enhance all hydrodynamic quantities of engineering interest by about 4.3%, while dispersing 30 g of the first nanoparticle's mass inside water results in decreasing the similarity temperature gradient at the surface about 3.6%. Also, when the disk rotates faster, the maximum radial velocity near the disk, s′(0) and f″(0) increases. [ABSTRACT FROM AUTHOR]

The aim of the present work is to focus on heat and mass transfer characteristics of the magnetohydrodynamic three‐dimensional flow of nanofluid over a permeable stretching porous sheet. The significance of this study is the consideration of copper‐based and aluminum oxide‐based nanofluids. The physical parameters like a chemical reaction, Soret effect, radiation, and heat generation, and radiation absorption being involved in this examination are novel. The nonlinear partial differential equations are transformed into ordinary differential equations by adopting suitable similarity transformations. The numerical solutions are obtained by applying the Runge–Kutta method of fourth‐order with the Shooting technique using MATLAB. The results obtained are presented through graphs and tables for various parameters. A comparison with published results has been done to validate the methodology and found good coincidence. It is claimed that the increase in heat generation parameters results in increasing the temperature. With an increase in the Soret effect, the skin friction coefficient along x‐axis increases and skin friction coefficient along the y‐axis, Nusselt number and Sherwood number decrease. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids are formulated with various kinds of base fluids. They are designed to provide good heat transfer performance. They can achieve this by dispersing various kinds of nanoparticles in the base materials. This new technology of formulating hybrid nanofluids has a wide range of applications in various industries such as solar energy, medical equipment, and aerospace. Keeping these applications in view, this study provides an insight into the effects of convective heat transport on a Hybrid nanofluid, across a rotating sheet with a variable heat source. In this investigation, the governing boundary layer partial differential equations were modified into the ordinary differential equations, by using the proper similarity transformations. Later, they were solved numerically, with the support of the Lobatto IIIA technique in MATLAB. The influence of the Richardson number on flow parameters was studied, and it was discovered that increasing Ri increases the velocity while decreasing temperature and concentration profiles. The impact of various other flow parameters on the flow fields and also on the behavior of Nusselt number, coefficient skin friction, and Sherwood number were studied and represented graphically. The outcomes were found to be in excellent accord when compared with quoted studies. [ABSTRACT FROM AUTHOR]

The Buongiorno model Maxwell nanofluid flow, heat and mass transfer characteristics over a stretching sheet with a magnetic field, thermal radiation, and chemical reaction is numerically investigated in this analysis. This model incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a coupled nonlinear ordinary differential equation by using the similarity transformation technique. The resultant nonlinear differential equations are solved by using the Finite element method. The sketches of velocity, temperature and concentration with diverse values of magnetic field parameter (0.1 ≤ M ≤ 1.5), Deborah number (0.0 ≤ β ≤ 0.19), radiation parameter (0.1 ≤ R ≤ 0.7), Prandtl number (0.5 ≤ Pr ≤ 0.8), Brownian motion parameter (0.1 ≤ Nb ≤ 0.7), thermophoretic parameter (0.2 ≤ Nt ≤ 0.8), Chemical reaction parameter (1.0 ≤ Cr ≤ 2.5) and Lewis number (1.5 ≤ Le ≤ 3.0) have investigated and are depicted through plots. Moreover, the values of the Skin‐friction coefficient, Nusselt number, and Sherwood numbers are also computed and are shown in tables. The sequels of this analysis reviewed that the values of Skin‐friction coefficient and Sherwood number intensified with hiked values of Deborah number (β), whereas, the values of Nusselt number decelerate as values of (β) improves. [ABSTRACT FROM AUTHOR]

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well‐known scheme, namely the shooting method along with the Runge‐Kutta‐Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non‐Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters. [ABSTRACT FROM AUTHOR]

In this paper, we have attempted to study the steady two‐dimensional hydromagnetic convective flow through porous medium and heat transfer effects. Fluid is containing dust particles and is moving under the influence of Lorentz, buoyancy, Darcy, and viscous forces. Motion is considered to be governed by the volume fraction of the dust grains and the increment of shear stress and rate of heat transfer at the surface has been analyzed. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The converted differential equations are figured numerically using the MATLAB built‐in technique bvp4c. The results are depicted in graphical forms for different values of the flow parameters. The findings are obtained considering the volume fraction and compared with the results of the previous paper. It is observed that the shear stress enhances with diminishing resistance and decreases for the higher values of the Hartmann number, permeability parameter, and volume fraction of the dust phase. Also, improving the Nusselt number gives a boost to thermal diffusivity. [ABSTRACT FROM AUTHOR]

The rheology of non‐Newtonian liquids has fascinated several researchers due to their wide‐ranging applications in manufacturing and engineering sectors like plastic processing, the mining industry, and lubrication. Also, the features of ferromagnetic non‐Newtonian fluids make it supportive for extensive usage in loudspeakers, magnetic resonance imaging, computer hard drives, directing of magnetic drugs, and magnetic hyperthermia. Owing to such potential applications, the current study is concerned with the heat and mass transfer analysis in a ferromagnetic Jeffrey liquid flow over a stretching sheet. In the flow problem, Brownian moment, magnetic dipole, and thermophoresis features are used. The active and passive control of nanomaterials is also considered in the modeling. Using appropriate similarity transformations, the modeling equations are converted to ordinary differential equations, then these equations are solved using the Runge–Kutta process and the shooting approach. The numerical and graphical solutions for the thermal profile, concentration profile, skin friction, rate of heat, and mass transfer characteristics are obtained. The significant results of the current study are that the thermal profile is strongly stimulated and increases faster for active control case than passive control case for augmented values of thermophoresis parameter. The heat transfer is strongly stimulated and decreases faster for passive control case than active control case for growing values of Deborah number. The mass transfer rate decreases faster for the active control case for increasing values of Schmidt number. [ABSTRACT FROM AUTHOR]

A mathematical model is developed for viscous slip flow and heat transfer in water/Ethylene glycol‐based nanofluids containing metallic oxide nanoparticles, through a converging/diverging channel. We adopt the single‐phase Tiwari–Das model. The governing equations are transformed to a set of similarity differential equations with the help of similarity transformation, before being solved numerically using Maple 20. Validation of the velocity gradient and temperature solutions is achieved with the second‐order implicit finite difference Keller Box method. Further validation is included for the special case of no‐slip nanofluid flow in the absence of viscous heating. The effects of the parameters, namely velocity slip, thermal jump, channel apex angle, Eckert number, Prandtl number, Reynolds number, and nano‐particle volume fraction on velocity, temperature, skin friction, and heat transfer rate are investigated in detail. It is found that with increasing velocity slip, for water‐TiO2 and ethylene glycol‐TiO2 nanofluids, the channel bulk flow is decelerated whilst with greater solid (nanoparticle) volume and in the presence of momentum slip, the flow is also retarded. With the increasing semivertex angle, the channel flow is generally accelerated. An increase in divergent semiangle leads to decelerate the flow from the centerline for the core flow region, whereas near and at the channel wall, it results in a weak acceleration. Higher temperatures are achieved with greater thermal slip values, for both water‐TiO2 and ethylene glycol‐TiO2 nanofluids, whereas for greater nanoparticle volume fraction, temperatures are weakly decreased for water‐TiO2 whereas a more significant decrease is observed for ethylene glycol‐TiO2 nanofluid. With a greater diverging channel angle, a substantial decrease in temperatures is caused by greater Reynolds numbers, and the reverse effect is computed for the converging channel. The novelty of the current work is that it extends previous studies to include multiple slip effects and viscous heating (Eckert number effects), which are shown to exert a significant influence on heat and momentum transfer characteristics. The study is relevant to certain pharmaco‐dynamics devices (drug delivery), next‐generation 3D nanotechnological printers, and also nano‐cooling systems in energy engineering where laminar flows in diverging/converging channels arise [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the heat transfer effect of γ–Al2O3 nanofluid flow with Marangoni convection over a porous stretching surface. Here, the aligned magnetic field is also considered. Ethylene glycol (C2H6O2) and water (H2O) are taken as base fluids. Thermal radiation is incorporated nonlinearly for the temperature field. Comparisons between two Ethylene glycol and water‐based γ–Al2O3 nanofluids have been discussed graphically. The governing model of the flow is solved by the Runge–Kutta fourth‐order method using the appropriate similarity transformations. Temperature and velocity field are presented for various flow pertinent parameters. It is observed that the Ethylene glycol‐based γ–Al2O3 nanofluid is more significant in the cooling process than the water‐based. nanofluid. An increment in the temperature field has been noticed for increased values of ψ with θw, and Rd for both the γ–Al2O3–H2O nanofluid and γ–Al2O3–C2H6O2 nanofluid. [ABSTRACT FROM AUTHOR]

In the present study, we investigated the steady, twodimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge-Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter. [ABSTRACT FROM AUTHOR]

This study investigates the heat and mass transfer in an unsteady squeezing flow between parallel plates under the influence of novel variable diffusivity. In most of the literature, it is believed that the thermophysical properties of the fluid are unchanged. However, this present study bridges this gap by assuming that viscosity, conductivity, and diffusivity are all temperature-dependent. Physically, an appropriate analysis of thermophysical variables in such a system is required to achieve the best performance for effective heat and mass transfer processes. The equations controlled were first nondimensional and then simplified by a similarity transformation to ordinary nonlinear differential equations. The present study provides a fast convergent method on finite parallel plates, namely, the optimal homotopy analysis method (OHAM) and spectral collocation method (SCM) are used to analyze the fluid flow, heat, and mass transport. The graphical and table understanding is given via an error table and flow behavior of physical parameters. The result reveals that the SCM is more accurate than OHAM. However, the method employed in this paper offers excellent convergence solutions with good accuracy. The solution convergence is also discussed. In this type of problem, squeeze numbers play an important role and the rise in the squeezing parameter increases the fluid temperature. [ABSTRACT FROM AUTHOR]

The aim of the current study is to develop a mathematical model for unsteady mixed convective radiative chemically reactive fluid flow with Hall current, cross‐diffusion, Newtonian cooling impacts and boundary conditions are influenced by second‐order slip velocity. Effectively a viscous formulation combining different novel effects model is deployed. The basic Navier–Stokes derived flow equations are transformed into dimensionless form via particular similarity transformations for which numerical simulations utilize the finite element method. The numerical results for velocity components, temperature, and concentration on various flow parameters are sketched. For validation of the present results a comparison with previously published studies are conducted for some limiting conditions and reveals an excellent accuracy. Engineering items of interest like shear stresses, Nusselt number, and Sherwood number are computed and dis- cussed extensively with the foremost parameters. Our analysis explores the fact that the physical parameters have a substantial influence upon boundary layer profiles. [ABSTRACT FROM AUTHOR]

A report is prepared for the free convection of micropolar nanofluid past a continuously moving plate. Free convection of polar fluid is obtained due to the interaction of thermal buoyancy acted against the gravitational force. In addition to that, the novelty of the current investigation is to carry over the coupling impact of the governing equations arises because of the inclusion of dissipative heat energy, and the variation of heat source/sink in the presence of suction/blowing. The governing equations are distorted into their ordinary form by the suitable choice of similarity transformation. Furthermore, the homotopy perturbation method (HPM) is employed for the solution of the set of transformed equations. The behavior of the contributing parameters is presented via graphs and the comparison between the analytical HPM and the conventional numerical technique using the in‐built code bvp5c is presented in tabular form. The numerical simulation shows its good concurrency between the methodologies employed. In few major outcomes, it is seen that the shear rate enriches with an increase in nanoparticle volume fraction. Furthermore, the rate of heat transfer decelerates significantly for the enhanced value of thermal radiation whereas the coupling parameter is favorable for the enhancement. [ABSTRACT FROM AUTHOR]

This article explores the impacts of the solid–liquid interfacial layer and nanoparticle diameter on the unsteady ferrous‐water nanoliquid flow over a spinning disk. The existence of velocity slip is presumed on the disk. Additionally, the low oscillating magnetic field effect is included to extract the hydrothermal consequences of the problem. Shliomis theory has been presented to verbalize the foremost equations of the mentioned flow problem. The similarity transformation renders the dimensionless equations. Spectral quasilinearization technique along with the residual error profile is presented to resolve the converted equations. An adequate number of pictures and tables are portrayed to improve the parametric study of the problem. Several streamlines, isotherms, contour plots, and three‐dimensional figures are presented to disclose the hydrothermal integrity of the nanofluidic transport. Effective magnetization parameter produces 4.67% skin frictional increment. Heat transport declines for nanoparticle diameter but is enhanced for nanolayer conductivity ratio. The presence of an oscillating magnetic field always promotes heat transference as compared with the absence of the oscillating field. The nanolayer conductivity ratio conveys the highest 8.69% heat transport rate, whereas the magnetization factor provides the lowest, 1.79%. It has novel applications in magnetic drug targeting, hard disk scaling, magnetic resonance imaging, spin coating, lubrication, and so forth. [ABSTRACT FROM AUTHOR]

In this investigation, the foremost aim is to study the impact of a higher‐order chemical reaction and second‐order slip on the bioconvective nanoliquid flow comprising gyrotactic microorganisms between two squeezed parallel plates. The existence of magnetic strength, thermophoretic, and Brownian migration is considered to model the flow. Similarity transformations are implemented to reduce our mathematical model into a set of nonlinear ordinary differential equations along with the requisite boundary conditions. The classical Runge‐ Kutta‐Fehlberg method technique is employed to avail the numerical outcomes of the aforementioned nonlinear foremost equations correlated with the relevant boundary conditions. Parametric flow discussions, like, velocity profile, thermal profile, and heat and mass transport, have been portrayed through indispensable charts and graphs. Physical quantities, like, skin friction, Nusselt number, Sherwood number, and microorganism density number, have been estimated to analyze their numerous applications. The results communicate that temperature diminishes for squeezing factor and first‐order velocity slip parameter, but augments for second‐order slip parameter. Mass transport accelerates for chemical reaction but reduces for the order of reaction. Microorganism density number amplifies owing to chemical reaction and Peclet number while it decays for chemical reaction. This has advantageous applications in bio‐microsystems, bioreactors, biosensors, biochromatography, magnetic bioseparation devices, biocoating, and ecological fuels. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics flow of a nanofluid over an exponentially curved stretching surface is deeply focused in the current study. By using the assumption on the curved stretching surface, the governing equations are established. We obtain nonlinear partial differential equations by utilizing the boundary layer estimation on the Navier–Stokes condition. These equations are converted into nondimensional system ordinary differential equations, using a suitable similarity transformation. The governing system of equations is tackled through an analytical method. The impacts of different pertinent parameters involved in the governing equations are illustrated graphically, whereas the numerical values of Res1/2Cf, Res1/2Shs, and Res1/2Nu are also tabulated. The velocity profile declines with an increase in values of magnetic parameter and porosity parameter. The temperature profile is increasing, when the value of a thermophoretic parameter and Brownian motion parameter increases. A higher activation energy displays a stronger concentration profile. The concentration profile decreases for increasing values of the Schmidt number. The concentration profile shows the inverse impact for increasing values of the thermophoretic parameter and Brownian motion parameter. The focus of this study was to examine the heat transfer rate of nanoparticles. [ABSTRACT FROM AUTHOR]

Variable properties play a prominent role in analyzing the blood flow in narrow arteries. Specifically, considering the variation of thermal conductivity and viscosity helps in the understanding of the rheological behavior of blood and other biological fluids, such as urine, spermatozoa, and eye drops. Inspired by these applications, the current study incorporates the impact of variable thermal conductivity and viscosity for modeling the peristaltic flow of a Ree–Eyring liquid through a uniform compliant channel. The governing equations are nondimensionalized with the assistance of similarity transformations. The long‐wavelength and small Reynolds wide variety approximation are utilized for solving the governing differential equations. Furthermore, the series solution method (perturbation technique) is utilized for solving the nonlinear temperature equation. The obtained results show that the velocity is greater in the case of the Newtonian liquid than that of the non‐ Newtonian liquid. [ABSTRACT FROM AUTHOR]

An unsteady stagnation point flow of a Maxwell fluid over a unidirectional linearly stretching sheet is studied under the influence of a magnetic field. The parabolic energy equation, which is based on parabolic Fourier law is replaced with a hyperbolic energy equation incorporating the heat flux model of Cattaneo–Christov. The Buongiorno model is used to characterize the properties of nanofluids using thermophoresis and Brownian diffusion coefficients. The phenomenon of melting heat transfer and slip mechanism is also embodied in the present study. Coupled nonlinear differential equations have appeared when the specified similarity transformations are applied. The mathematical problem is tackled via the homotopy analysis method. The impact of important physical parameters on the velocity, concentration, and temperature are highlighted via graphs. To verify our present results, a comparison is given with a limiting case with an already published article. It is witnessed through the graphs that the higher unsteadiness parameter and melting heat coefficient both are responsible for the reduction in the velocity and temperature of the nanofluid. Also, the velocity slip parameter detracts the velocity profile and affiliated boundary layer thickness of theMaxwell nanofluid. [ABSTRACT FROM AUTHOR]

To solve the problem of braking torque decline or even brake failure of vehicle retarders caused by high temperature due to long‐time or high‐power braking, the nanofluid with high thermal conductivity is introduced into the previously proposed novel retarder. To evaluate the nanofluid cooling capabilities, a model depicting the vertical fluid flow in the retarder is formulated. Adopting similarity transformations and a shooting method coupled with Runge–Kutta iterative technology, the model boundary value problem is tackled numerically. The cooling capabilities of three typical ethylene glycol (EG)‐based nanofluids: Cu–EG, Al2O3–EG, and TiO2–EG are investigated and compared. Finally, an experimental test is carried out to examine the temperature rise and the variation of braking torque for the retarder. It is demonstrated that Al2O3–EG nanofluid has the highest Nusselt number (rate of heat transfer), and more importantly, the braking torque of the proposed retarder decreases by only 8.2% under high‐power braking condition. [ABSTRACT FROM AUTHOR]

This work analyzed the effects of variable viscosity and thermal conductivity, with mixed convection, thermal radiation and viscous dissipation effects, on multiwalled carbon nanotubes (MWCNTs)–aluminum oxide (Al2O3)/engine oil hybrid nanofluid flow due to a vertically inverted spinning cone embedded in a porous medium. Using suitable similarity transformation, the boundary layer fluid flow governing equations are transformed into dimensionless systems of coupled nonlinear ordinary differential equations. Then, the solutions are obtained numerically employing the spectral relaxation method. The influences of involved parameters are examined, and the results are presented with graphs and tables. The obtained results disclose that both the tangential and azimuthal skin friction coefficients increase with increasing values of temperature‐dependent viscosity and mixed convection parameters. The local heat transfer rate reduces with increasing values of the Eckert number and variable thermal conductivity parameter, whereas it enhances with greater values of the thermal radiation parameter. Generally, hybrid nanofluids of (MWCNTs–Al2O3)/ engine oil show better flow distributions with good stability of thermal properties than MWCNTs/engine oil and Al2O3/engine oil mono‐nanofluids. [ABSTRACT FROM AUTHOR]

In this analysis, the effect of Catteneo–Christov model on heat alongside mass transport magnetohydrodynamics of a Casson nanoliquid with thermal radiation and Soret–Dufour mechanism is considered. The fluid flow is considered through porous media as the thermophysical attributes such as viscosity along with thermal conductivity are considered to be constant. Suitable similarity transformations were employed on the governing coupled flow equation to yield total differential equations (ODE). An accurate and newly developed spectral method called spectral homotopy analysis method (SHAM) was employed to provide solution to the simplified equations. The numerical method of homotopy analysis method (HAM) is SHAM. SHAM portrays the division of nonlinear equations into linear as well as nonlinear parts. The findings in this study show that an increment in the Casson parameter is seen to elevate the velocity plot at the wall and lessen the velocity far away from the plate. An increase in the Brownian motion and thermophoresis term is observed to speed up the local skin friction coefficient. [ABSTRACT FROM AUTHOR]

In this paper, unsteady upper‐convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature‐dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature‐dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence. [ABSTRACT FROM AUTHOR]

Unsteady magnetohydrodynamic heat and mass transfer analysis of hybrid nanoliquid flow over a stretching surface with chemical reaction, suction, slip effects, and thermal radiation is analyzed in this study. A combination of alumina (Al2O3) and titanium oxide (TiO2) nanoparticles are taken as hybrid nanoparticles and water is considered as the basefluid. Using the similarity transformation method, the governing equations are changed into a system of ordinary differential equations. These equations together with boundary conditions are numerically evaluated by using the Finite element method. The influence of various pertinent parameters on the profiles of fluids concentration, temperature, and velocity is calculated and the outcomes are plotted through graphs. The values of nondimensional rates of heat transfer, mass transfer, and velocity are also analyzed and the results are depicted in tables. Temperature sketches of hybrid nanoliquid intensified in both the steady and unsteady cases as the volume fraction of both nanoparticles rises. [ABSTRACT FROM AUTHOR]

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge‐Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes. [ABSTRACT FROM AUTHOR]

This study investigates the Williamson nanofluid flow through a nonlinear stretching plate. It aims to analze the global influence of Williamson parameter (λ) rather than local, which is researched for a linear stretching case in the literature. In addition, the features of activation energy are also taken into account in the current review. The developed model with the consequent similarity transformation has still not been perceived. The transformed partial differential equations are solved analytically. The consequences of embedded parameters on the velocity, temperature, and concentration profiles are displayed through figures. Also, the consequences of embedded parameters on skin friction, heat transfer, and mass transfer are demonstrated through tables. [ABSTRACT FROM AUTHOR]

The study of squeezing flow has attracted considerable interest in recent years for its important applications in industrial, biomedical and engineering domains such as fibre‐reinforced, cell squeeze technology. The aim of this study is to analyze the flow and heat transfer of a squeezed particle fluid with thermal radiation effects between parallel plates. The governing partial differentials are reduced to ordinary differential equations by a similarity transformation and solved numerically using the finite difference method. The effects of different physical parameters on the velocity and temperature profiles are discussed with the help of graphs coupled with comprehensive discussions. The results indicate that the thermal radiation parameter enhanced the fluid and particle temperature distribution and for the plate oscillation case, reverse flow is observed. To show the biological relevance of the analysis, the results obtained analyzed the influence of the squeezed artery wall on the suspension blood flow for normal and diseased blood using the experimental data from the published literature. Finally, a comparison between the present similarity solutions and previously published results shows the accuracy of the current results. [ABSTRACT FROM AUTHOR]

This paper investigates the Sakiadis flow of a Al2O3-H2O nanoliquid with consistently scattered dust particles over a vertical plate. To account for the effect of the Brownian movement, the Koo-Kleinstreuer-Li model is considered. In some thermal systems such as reactor safety areas, and solar collectors, combustion works from moderate to high temperature, making the relationship between the temperature and density nonlinear. To consider this temperature-dependent density, the nonlinear Boussinesq estimation is utilized. The present physical structure, which includes energy and momentum equations, is converted into a system of ordinary, coupled, and nonlinear differential conditions through the help of similarity transformations. By using the finite difference code, the subsequent equations have been numerically solved. The impact on the velocity and the thermal profiles of the non-dimensional parameters is visualized through graphs. Both the Nusselt number and friction factor strengthen with a higher nonlinear thermal parameter in the case of nonlinear Boussinesq approximation compared to the linear Boussinesq case. Growing estimations of nonlinear thermal parameter deteriorate the thermal profile but it boosts the velocity profile of both liquid and dust phases. [ABSTRACT FROM AUTHOR]