Entropy optimized MHD fluid flow over a vertical stretching sheet in presence of radiation

The present article describes the influence of radiation on two-dimensional laminar magnetohydrodynamic fluid flow passing over a convective surface. The behavior of the thermal equation is explored through Joule heating, heat generation/absorption, and viscous dissipation. The aim of this study is to examine the physical behavior of the entropy optimization rate. The Cartesian coordinates system is used to model the flow equations. Using similarity variables, a system of partial differential equations is converted into a system of ordinary differential equations. The problem is solved using HAM. The influence of various pertinent parameters on fluid characteristics is graphically explored. Velocity decreases for an increased amount of magnetic parameter, suction parameter, and velocity slip parameter, while behaves the opposite for Grashof number. Temperature increases for a large amount for Brinkman number, magnetic parameter, and radiation parameter, while decreases for Prandtl number. Entropy generation rate increases for Brinkman number, magnetic parameter, and temperature difference parameter. Bejan number decreases for Brinkman number while behaves the opposite for magnetic parameter and temperature difference parameter. Skin friction decreases for large values of magnetic parameters while behaving the opposite for a large amount of velocity slip parameter. Nusselt number decreases for a large amount of Brinkman number. For a better understanding of the study, comparison between numerical outcomes of entropy generation rate and Bejan number for different values of Prandtl number has been done through tables. Also, numerical outcomes of skin friction and Nusselt number are discussed using pertinent parameters through tables.     

Unsteady magnetohydrodynamic couple stress fluid flow from a shrinking porous sheet: Variational iteration method study

Motivated by magnetic polymer manufacturing applications, the present research article examines theoretically the hydromagnetic boundary layer flow of an electrically conducting non-Newtonian couple stress fluid due to a transient shrinking (contracting) porous sheet. The conservation partial differential equations for mass and momentum are rendered into a fifth-order nonlinear ordinary differential equation via similarity transformations with associated boundary conditions. A semi-analytical/numerical scheme employing Lagrangian multipliers and known as the variational iteration method (VIM) is implemented to solve the ordinary differential boundary value problem. Validation of the solutions is conducted by benchmarking against earlier Newtonian studies and very good agreement is achieved. A detailed assessment of the impact of couple stress (rheological), unsteadiness, magnetic body force parameter, and wall transpiration (suction/injection) parameter on flow characteristics is conducted with the aid of graphs. A significant deceleration in the flow is computed with increasing injection (acceleration is caused with greater suction) and acceleration is induced with higher unsteadiness parameter values. Increasing magnetic field (higher magnetic number) generates flow acceleration, rather than the customary deceleration, due to the shrinking sheet dynamics. A stronger couple stress effect manifests in strong retardation in the boundary layer flow and an increase in momentum (hydrodynamic|) boundary layer thickness. VIM demonstrates excellent convergence and accuracy and shows significant promise in studying further magnetic polymer fabrication flow problems.     

Velocity slip,chemical reaction,and suction/injection effects on two-dimensional unsteady MHD mass transfer flow over a stretching surface in the presence of thermal radiation and viscous dissipation

The purpose of this study is to analyze the impact of velocity slip, chemical reaction, and suction/injection on two-dimensional mass transfer effects on unsteady MHD flow over a stretching surface in the presence of thermal radiation and viscous dissipation. The governing time-dependent nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformations. The converted equations are solved using the numerical technique with the help of Keller-Box method. The effect of nondimensional variables is studied and graphically illustrated on velocity, temperature, concentration, friction factor, Nusselt number, and Sherwood number. Concentration and temperature profiles are enhanced and the contrasting pattern for velocity profiles as increasing the velocity slip and magnetic parameter. The concentration profile is diminished as the Schmidt number (Sc) and chemical reaction (C_r) increase. The concentration, velocity, and temperature profiles display a reversal pattern, as the suction and unsteady parameter (A) increase. The findings of this study are very well-acknowledged with current research.     

MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation,slip condition,and viscous dissipation

This study presents the problem of MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation, slip condition, and viscous dissipation. The partial differential equations with the corresponding boundary conditions that govern the fluid flow are reduced to a system of highly nonlinear ordinary differential equations using scaling group transformations. The fourth-order method along shooting technique is applied to solve this system of boundary value problems numerically. The effects of flow parameters on the velocity, temperature, and concentration profiles are presented via graphs. The impact of the physical parameters on the skin friction coefficient reduced Nusselt numbers and reduced Sherwood numbers are investigated through tables. Comparison of the present findings with the previously published results in the literature shows an excellent agreement. It is also noted that a rise in the Eckert number results in a drop in the temperature of the fluid in the thermal boundary layer region of the fluid flow.     

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.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

This paper analyzed the steady two‐dimensional magnetohydrodynamic mixed convective viscous nanofluid and heat transfer toward an inclined stretching cylinder with chemical reaction and uniform magnetic field. The governing partial differential equation in a cylindrical form is reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformation and solved numerically by spectral quasilinearization methods (SQLMs). A new approach of this method is employed to derive numerical expressions for velocity, temperature, and concentration profile. The convergence and accuracy of our numerical scheme are observed. The SQLM is employed to find out the convergent series solution. There is an increase in the temperature profiles due to the increase in the thermophoresis parameter. The increase in effective Eckert number results in the increase of the temperature profile.     

Effect of coriolis force on vorticity covariance in MHD turbulent flow of dusty fluid

In this paper vorticity covariance in MHD turbulent flow of dusty fluid in the presence of coriolis force have been obtained. The obtained result shows that the defining scalars α(s, t), β(s, t) and γ(s, t) of the vorticity covariance depend on the defining scalars of the tensors W_ij, P_ik,j, F_kj,i, D_ik,j, H_kj,i, T_ij and R_ij already defined in the text. © 1997 by John Wiley & Sons, Ltd.     

Comprehensive analysis of radiation impact on the transfer of heat and mass micropolar MHD free convective fluid flow across a stretching permeability sheet with suction/injection

As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built-in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.     

MHD slip flow and heat transfer of UCM fluid with the effect of suction/injection due to stretching sheet: OHAM solution

In this study, the optimal homotopy analysis (OHAM) technique has been examined to solve the laminar magnetohydrodynamic flow (MHD flow) on the upper-convected Maxwell fluid on an isothermal porous stretch surface. A study on the effects of parameters like the relaxation time, suction/injection velocity, as well as the magnetic number on velocity over a sheet was conducted and these results are compared to the corresponding previously available results. It was observed that the thickness of the boundary layer is lowered by enhancing $s$, $\beta$, and $M$ values. Opposing this, it was observed that large $\beta$ values increase the $f″\left(0\right)$ magnituIIde. It is found that OHAM is an efficient method capable of giving a greater degree of accuracy in numerical values of flow parameters even after fewer approximations.     

MHD heat transfer flow over a moving wedge with convective boundary conditions with the influence of viscous dissipation and internal heat generation/absorption

In this investigation, the problem of the study is the effect of the magnetic field and viscous dissipation on heat transfer flow through a moving wedge in the existence of the internal heat generation/absorption and also suction/injection. The governing equations are changed to some coupled nonlinear differential equations with aid of similarity variables. The numerical calculations of the equations are solved by the MATLAB package solver bvp5c. The changes of the pertinent constraints on the momentum and temperature have been discussed through graphs and numerical values of skin friction and heat transfer factor are listed in the tabular pattern. Although maintaining a constant value for the convection parameter, the Nusselt number is increased for $Q>0$ and decreased for $Q<0$. The temperature rises in conjunction with an increase in $\mathit{Ec}$ and $\mathit{Nc}$ variables.     

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple‐stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040 PACS: 44.15.+a, 44.30.+f, 44.27.nd, 47.50.Cd     

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

A steady two‐dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters.     

Analytical solutions of triple-diffusive magnetohydrodynamic fluid flowing through a stretching/shrinking sheet

The aim of this article is to investigate the dual nature solutions of the triple diffusive magnetohydrodynamic flow due to stretching/shrinking surfaces. The system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations with the help of compatible transforms. Analytical dual solutions are obtained for every unknown velocity, temperature, and concentration profile in terms of known physical parameters. Heat and mass transfer analyses have been carried out in the presence of convective boundary conditions. The graphic interpretation of the possible dual solutions of dimensionless velocity, temperature, concentration, skin-friction coefficient, and Nusselt and Sherwood numbers is analyzed under the influence of different known physical parameters. The obtained results are validated against previously published results for a special case of the problem.     

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.     

Cu‐Al2O3/H2O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation

The resent development of research in the field of nano technology introduced hybrid nanofluids which are advanced classes of fluids with augmented thermal properties and it gives better results comparing to regular nanofluid. The aim of the present work is to study the significant effects of variable viscosity and viscous dissipation on a porous stretching sheet in the presence of hybrid nanofluid and radiative heating. In this model, two types of nanoparticles, namely copper (Cu) and alumina oxide (Al₂O₃), are suspended in the base fluid H₂O to form a hybrid nanoliquid. The novelty of this study is to introduce variable viscosity along with natural convection in the momentum equation and viscous dissipation in the energy equation. Mathematical modeling is employed in this study, whereby partial differential equations for the fluid flow are constructed and transformed to a set of ordinary differential equations, and hence resolved computationally by Runge‐Kutta‐Fehlberg method along with shooting scheme. The most important results for relevant parameters concerning the flow heat measure, surface drag, and heat transfer coefficients are thoroughly examined and presented graphically for both Cu‐Al₂O₃/water hybrid nanofluids. There is an increase in hybrid nanofluid velocity profile with mounting values of $\lambda$, and the Cu‐water nanofluid converges to the boundary more quickly than the hybrid nanofluid due to the occurrence of variable viscosity. The results concluded that the Nusselt number of the viscous fluid is lower than that of the nanofluid and hence the hybrid nanofluid (ie, heat transfer rate: normal fluid < nanofluid < hybrid nanofluid). The outcomes of present investigations are in close agreement with the viscous fluid as a particular case.     

Heat and mass transfer of water-based copper and alumina hybrid nanofluid over a stretching sheet

Hybrid nanofluids (HNFs) are vital in engineering and industrial applications due to significant effective thermal conductivity as compared with regular fluid and nanofluid (NF). The HNF is a process of the conglomeration of two or more nanoparticles of different thermophysical properties to affect the thermal transport characteristics of base fluid, particularly in gearing up heat switch charge. Further, the impact of HNF combined with stretching and squeezing of bounding surface has direct application in thinning/thickening of polymeric sheets in the chemical industry. The current study analyzes the flow of HNF over a stretching sheet under the influence of chemical reaction as well as suction/injection. We have considered water $\left({\mathrm{H}}_2\mathrm{O}\right)$ as the base fluid and copper $\left(\mathrm{Cu}\right)$, and aluminum oxide $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$ as nanoparticles. The consequences of the magnetic field, viscous dissipation, and Joule heating are also to be investigated. The resulting partial differential equations are transformed into nonlinear ordinary differential equations using suitable similarity transformations. The numerical solutions to governing equations are obtained with the help of MATLAB software using the bvp4c solver. The important finding is: the rate of heat transfer of HNF is higher than that of NF as well as base fluid. Moreover, contributions of higher Eckert number and radiation parameter are to increase the temperature in the flow domain, whereas the Prandtl number reduces it. It is further noticed that heavier species as well as viscous dissipation decline the level of concentration across the flow field.     

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non‐Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non‐Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The nondimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter (), unsteadiness parameter (), Prandtl number (Pr), buoyancy parameter . The semi‐analytical differential transform method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built‐in solver “bvp4c” to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter, whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter, whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid), whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness, and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.     

Mass transfer of viscous gas flow over porous stretching/shrinking sheet in the presence of slip and mass transpiration

The effect of the mass transpiration parameter on the viscous gas flow past a porous stretching/shrinking sheet in the presence of Navier's slip is investigated, and also, the mass transfer characteristics are examined. The physical flow problem executes the Navier–Stokes and the mass equation, which forms the system of nonlinear partial differential equations. These are transformed via similarity variables into a system of ordinary differential equations. The slip flow model of the total mass transfer on the moving sheet is modeled by introducing gas slip velocity. The total mass transfer on the moving sheet is modeled by inducing slip models of first and second order. Further, the suction which induces the slip velocity as opposed to the surface movement is examined. The mass suction-induced slip forces the adjacent gases to flow in the reverse direction to sheet movement. Thus, the solution space expands with the slip-induced suction and sheet movement. In the mass injection case, the induced slip increases the effect of the fluid flow for sheet movement. Upon all previous flow models, the present investigation is significant due as it investigates the mass transfer of viscous gasses flow past a porous medium in the presence of slip and mass transpiration.