Unsteady MHD flow and heat transfer with viscous dissipation past a stretching sheet

In this paper a study is carried out to analyze the unsteady heat transfer effects of viscous dissipation on the steady boundary layer flow past a stretching sheet with prescribed constant surface temperature in the presence of a transverse magnetic field. The sheet is assumed to stretch linearly along the direction of the fluid flow. The assumed initial steady flow and temperature field neglecting dissipation effects becomes transient by accounting dissipation effects when time t′ > 0. The temperature and the Nusselt number are computed numerically using an implicit finite difference method. The obtained steady temperature field with dissipation is of practical importance.     

MHD dissipative fluid past a stretching sheet in the presence of Soret effect with Newtonian convective heat and mass conditions

This article deliberates a theoretical study on a two‐dimensional magnetohydrodynamic free convection flow of an electrically conducting, heat generation/absorption fluid flowing past a linearly stretching sheet, placed vertical in a non‐Darcian porous medium with Soret effect. As the magnetic Reynolds number of the flow field considered very small (due to noncomparability of the induced and applied magnetic fields), the influence of the induced magnetic field is thus neglected. Again due to weak applied voltage differences at the lateral ends, the influence of the electric current is also ignored. A homotopy analysis method is developed to solve the similarity transformed equations subject to a set of convective heat and mass boundary conditions. Numerical data simulations are made on various fluid variables by using some practical/selected values of the governed parameters and illustrated through graphs and tables. It is found that the Newtonian heating parameter enhanced the velocity, temperature, and concentrations, while the solutal Newtonian heating parameter accelerates the rate of flow of heat and masses but minimizes the temperature gradient. The local Forchheimer and dissipation parameters are found to raise the temperature and concentrations, while the flow rate accelerates due to dissipation parameter but decelerates in presence of Forchheimer parameter.     

Analytical study of heat and mass transfer in unsteady MHD radiant flow of Williamson nanofluid over stretching sheet with heat generation and chemical reaction

This paper presents the analytical study of heat and mass transfer in a two-dimensional time-dependent flow of Williamson nanofluid near a permeable stretching sheet by considering the effects of external magnetic field, viscous dissipation, Joule heating, thermal radiation, heat source, and chemical reaction. Suitable transformations are introduced to reformulate the governing equations and the boundary conditions convenient for computation. The resulting sets of nonlinear differential equations are then solved by the homotopy analysis method. The study on the effects of relevant parameters on fluid velocity, temperature, and concentration profiles is analyzed and presented in graphical and tabular forms. Upon comparison of the present study with respect to some other previous studies, a very good agreement is obtained. The study points out that the transfer of heat can substantially be enhanced by decreasing viscoelasticity of the fluid and the transfer of mass can be facilitated by increasing permeability of the stretching sheet.     

Mixed convection flow over a stretching sheet of variable thickness: Analytical and numerical solutions of self‐similar equations

In this study, a mixed convection flow over a nonlinearly stretching sheet of variable thickness is examined. Governing equations are modeled and transformed into dimensionless forms by utilizing dimensionless variables. For further investigation, dimensionless, coupled nonlinear differential equations with suitable boundary conditions are numerically solved using the Matlab built‐in function bvp5c tool, and analytical solutions are also computed using the homotopy analysis method. A comparative study is carried out to check the efficiency and accurateness of the proposed solution methodologies. Convergence of the derived series solutions is carefully checked. The impact of wall thickness parameter, velocity index parameter, Prandtl number, and mixed convection parameter on nondimensional velocity, temperature, skin friction coefficient, and local Nusselt number is examined. The novelty of this examination is that the dimensionless equations are self‐similar in the presence of mixed convection. These self‐similar equations are acquired by establishing a relationship between velocity and temperature power index parameters, and similarity solutions exist only for a particular form of variable surface temperature.     

Impacts of variable viscosity and chemical reaction on Ohmic dissipative fluid flow in a porous medium over a stretching sheet with thermal radiation

This study investigates the chemical reaction influence on heat transfer flow of viscous Newtonian fluid over a moving surface under the intensity of nonuniform heat source/sink. Variable fluid viscosity and ohmic heating effects are considered in the model equation. The uniqueness of the present investigation is to scrutinize the significance of nonuniform heat source/sink and ohmic heating on the heat transfer flow of optically thin radiative fluid in a permeable medium. The flow equations of continuity, momentum, thermal and solutal fields are converted by invoking relevant dimensionless variables. Also, the converted nonlinear equations are analyzed numerically by using the fourth order Runge–Kutta Fehlberg approach. The significance of model parameters are scrutinized and discussed in detail via graphs and tables. The important findings of this study are the effects of Joule heating $J$, viscous dissipation parameter $B_r$, variable fluid property parameter $ϵ$ and radiation parameter $R_a$ on fluid flow, energy profile and solutal field. The results show that the thermal field depreciates as the Prandtl number increases but escalates against higher values of Joule heating parameter and Brinkman number. Also, the outcome of this study reveals that an enhancement in the values of variable viscosity parameter declines velocity distribution. Concentration distributions behave as a growing function of the Soret number and diminishing function of the Schmidt number. Furthermore, contrasting this study with existing results reveals excellent agreement.     

Thermally radiative slip flow of viscous fluid through a microfluidic vessel having sinusoidal walls with variable viscosity

This article explores the influence of variable viscosity on the peristaltic movement of viscous fluid through a tapered microfluidic vessel having sinusoidal walls. The aspect of slip velocity has been considered on the channel walls. Furthermore, the heat transfer phenomenon is explored under the effectiveness of thermal radiation and viscous dissipation. The nonlinearity of the problem is scrutinized by the lubrication approximation hypothesis. Analytic outcomes have been acquired for liquid velocity, temperature, pressure rise, and streamlines. The impact of dissimilar physical parameters influencing the liquid flow features is revealed and deliberated through graphs. The study revealed that the velocity at the central region diminishes with increasing values of the velocity slip parameter. The number of boluses in the streamlines pattern is enhanced by enhancing the viscosity parameter. The current model has been used in bio-engineering processes, industrial fluid mechanics, thermal processing, and cooling systems.     

Symmetry analysis of MHD Casson fluid flow for heat and mass transfer near a stagnation point over a linearly stretching sheet with variable viscosity and thermal conductivity

In this article, the impacts of variable viscosity and thermal conductivity on magnetohydrodynamic, heat transfer, and mass transfer flow of a Casson fluid are analyzed on a linearly stretching sheet inserted in a permeable medium along with heat source/sink and viscous dissipation. To reduce the ascendant partial differential equations into ordinary differential equations, Lie group transformation is utilized. Further, the fourth-order Runge–Kutta strategy is utilized to solve the ordinary differential equations numerically. The numerical results obtained for various parameters by employing coding in MATLAB programming are investigated and considered through graphical representation and tables. We anatomize the impacts of distinctive parameters on velocity, temperature, and concentration distributions.     

Thermochemistry and viscous heat dissipative effects on unsteady upper-convected Maxwell fluid flow past a stretching vertical plate with thermophysical variables

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.     

Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids

The purpose of this paper is to investigate a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet utilizing nanofluid. The governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are considered in our problem. Furthermore, four different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. The variations of dimensionless surface temperature, dimensionless surface temperature gradient as well as the flow and heat transfer characteristics with the governing parameters are graphed and tabulated. Comparison with published results for pure fluid flow is presented and it is found to be in excellent agreement.     

MHD mixed convective radiative flow of Eyring‐Powell fluid over an oscillatory stretching sheet using bivariate spectral method on overlapping grids

The bivariate spectral quasilinearization method (BSQLM) on overlapping grids is presented and applied in the analysis of unsteady magnetohydrodynamic mixed convection flow of Eyring‐Powell fluid over an oscillatory stretching sheet embedded in a non‐Darcy porous medium with nonlinear radiative heat flux and variable thermophysical properties. The fluid properties, namely the fluid viscosity, thermal conductivity, and mass diffusivity, are assumed to vary with temperature. It is assumed that the first‐order chemical reaction with heat generation/absorption takes place in the flow. The flow domain is subject to uniform transverse magnetic field perpendicular to the stretching surface. The transformed flow equations are solved numerically using BSQLM on overlapping grids. The convergence properties and accuracy of the method are assessed. The proposed method is computationally efficient, and it gives stable and highly accurate results after few iterations and using few grid points in each subinterval. The improved accuracy rests upon the use of the overlapping grid, which produces sparse coefficient matrices that are easy to invert and have small condition numbers. The effects of physical parameters on the flow fields, local skin friction, the Nusselt number, and the Sherwood number are exhibited through graphs and tables. Amongst other findings, we found that the amplitude of the fluid flow along with flow characteristics may efficiently improve through the utilization of variable fluid viscosity. Heat and mass transportation processes enhance with the inclusion of nonlinear radiative heat flux, temperature‐dependent thermal conductivity, and mass diffusion coefficient, whereas they diminish with the increase in the local inertia coefficient. The current flow analysis can be useful in various engineering applications including paper production, polymer solution, glass blowing, extrusion of thermal system manufacturing process, and heat transportation enhancement.     

Entropy and radiation on a pipe MHD flow with variable viscosity

The present work, the entropy generation due to radiation and variable viscosity magnetohydrodynamic effects with a porous medium in a circular pipe, has been obtained and studied numerically. The governing continuity, momentum, and energy equations in cylindrical coordination are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically by a Runge-Kutta method and shooting technique. Numerical results are presented for velocity, temperature profiles, pressure profile, entropy generation rates, and Bejan number for different physical parameters of the problem. Also, the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.     

Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

Variable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time-dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.     

Impact of viscous dissipation and Dufour on MHD natural convective flow past an accelerated vertical plate with Hall current

The present research work concentrates on viscous dissipation, Dufour, and heat source on an unsteady magnetohydrodynamics natural convective flow of a viscous, incompressible, and electrically conducting fluid past an exponentially accelerated infinite vertical plate in the existence of a strong magnetic field. The presence of the Hall current induces a secondary flow in the problem. The distinguishing features of viscous dissipation and heat flux produced due to gradient of concentration included in the model along with heat source as they are known to arise in thermal-magnetic polymeric processing. The flow equations are discretized implicitly using the finite difference method and solved using MATLAB fsolve routine. Numerical values of the primary and secondary velocities, temperature, concentration, skin friction, Nusselt number, and Sherwood number are illustrated and presented via graphs and tables for various pertinent parametric values. The Dufour effect was observed to strengthen the velocity and temperature profile in the flow domain. In contrast, due to the impact of viscous dissipation, the local Nusselt number reduces. The study also reveals that the inclusion of the chemical reaction term augments the mass transfer rate and diminishes the heat transfer rate at the plate.     

Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity

The aim of this paper is to present the unsteady boundary layer flow and heat transfer of a fluid towards a porous stretching sheet. Fluid viscosity and thermal diffusivity are assumed to vary as linear functions of temperature. Using similarity solutions partial differential equations corresponding to the momentum and energy equations are converted into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the help of shooting method. It is noted that due to increase in unsteadiness parameter, fluid velocity decreases up to the crossing over point and after this point opposite behaviour is noted. The temperature decreases significantly in this case. Fluid velocity decreases with increasing temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity) up to the crossing over point but increases after that point and the temperature decreases in this case. Due to increase in thermal diffusivity parameter, temperature is found to increase.     

Exploration of radiative heat energy on the peristaltic blood flow of a nanofluid in conjunction with a heat source

The peristaltic flow of a conducting nanofluid associated with the Buongiorno model observed within a wavy channel is proposed in this article. In a peristaltic flow, the process of pumping takes place from a lower pressure to a high-pressure region. It is treated as a vehicle through which the liquid passes in a channel due to its dynamic rush and expands in its length. Therefore, an analysis is carried out for the interaction of thermal radiation and heat source on the peristaltic flow of nanofluid past a tapered channel. The crux of this investigation is the interaction of Hall current due to the conjunction of conducting medium. An analytical technique is used to get the solution of the transformed governing equations, and furthermore, the pressure gradient is also evaluated. The flow phenomena characterized by certain parameters are obtained and presented via graphs. An important observation is seen in that the contribution of magnetic field and Hall current may favor the pumping process and the pressure gradient lowering in the conducting medium is one of the important characteristics.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Influence of thermophoretic deposition and viscous dissipation on magnetohydrodynamic flow with variable viscosity and thermal conductivity

In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow-regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth.     

Free surface dynamics of MHD third-grade fluid model over a heated stretching sheet with variable fluid properties

A thorough investigation of MHD third-grade differential-type fluid flow over a heated stretching sheet is performed in this work. In particular, we analyze the film thinning process, when the thermal sensitive fluid parameters vary due to the effect of heat supplied to the stretching sheet. Starting with a two-dimensional (2D) free surface boundary value problem of non-Newtonian third-grade fluid, we present a systematic derivation of a 1D transient thin-film height equation using longwave analysis with respect to the small aspect ratio of the fluid domain. The derived model is used to study the impact of Newtonian and non-Newtonian parameters with variable fluid properties on the thin film height. The model is discretized using an upwind discretization in space and implicit time integration to guarantee first-order convergence. The model is analyzed thoroughly with the help of numeric computing software MATLAB. The existing findings for a Newtonian fluid are in excellent agreement with derived evidence. In comparison to Newtonian fluid, the study finds that the third-grade parameter causes thinning under different parametric restrictions. Simulations on the coupling effect explain that, the film thickness can be reduced with a high Marangoni number for highly viscous fluids. Also, since the effect of the conductivity parameter can be reduced at a low Prandtl number, the fluid shows a thinning effect. The film thinning rate, on the other hand, is reduced by the magnetic field.     

Influence of heat transfer on the nonorthogonal stagnation point flow of a third‐order fluid towards a stretching surface

The present article looks at the theoretical analysis of a steady stagnation‐point flow with heat transfer of a third‐order fluid towards a stretching surface. The formulation of the problem has been carried out for a third order fluid and constructed partial differential equations are rehabilitated into ordinary differential equations. The consequential ordinary differential equations are solved analytically using the homotopy analysis method (HAM). Graphical illustrations are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients and heat flux are computed and presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21042