Aurang Zaib

Thermal diffusion and diffusion thermo effects on unsteady MHD free convection flow over a stretching surface considering Joule heating and viscous dissipation with thermal stratification, chemical reaction and Hall current

The present investigation is concerned with the effects of thermal-diffusion and diffusion-thermo on an unsteady MHD free convection boundary layer flow with heat and mass transfer of an electrically conducting fluid over a stretching sheet in the presence of strong magnetic field with Hall current, thermal stratification, chemical reaction, heat generation, thermal radiation, Joule heating and viscous dissipation. The transformed nonlinear boundary layer equations are numerically solved by applying Keller-box method. The influence of various embedded flow parameters on the local skin friction, the local Nusselt number and the local Sherwood number has been carefully analyzed through graphs. It is found that the shear stress and the rate of mass transfer increase with an increasing of current density Jh while the reverse trend is observed on the rate of heat transfer. It is also found that the shear stress and the rate of heat transfer increase with an increasing of Sr, whereas the reverse trend is observed on the rate of mass transfer. Further, the shear stress and the rate of mass transfer increase with an increasing of Du while the reverse trend is seen on the rate of heat transfer. The numerical results are compared and found to be in good agreement with previously published results under special cases.

Impact of nonlinear thermal radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy:

This research peruses the characteristics of nanoparticles on stagnation point flow of a generalized Newtonian Carreau fluid past a nonlinear stretching sheet with nonlinear thermal radiation. The process of mass transfer is modeled using activation energy and binary chemical reaction along with the Brownian motion and thermophoresis. For energy activation a modified Arrhenius function is invoked. With regard to the solution of the governing differential equations, suitable transformation variables are used to obtain the system of nonlinear ordinary differential equations before being numerically solved using the shooting method. Graphical results are shown in order to scrutinize the behavior of pertinent parameters on velocity, temperature profiles, and concentration of nanoparticle. Also, the behavior of fluid flow is investigated through the coefficient of the skin friction, Nusselt number, Sherwood number, and streamlines. Results showed that the velocity ratio parameter serves to increase the velocity of fluid and reduces the temperature distribution and nanoparticle concentration. The results were compared with the available studies and were found to be in excellent agreement.

Thermal radiation effect on a mixed convection flow and heat transfer of the Williamson fluid past an exponentially shrinking permeable sheet with a convective boundary condition

The thermal radiation effect on a steady mixed convective flow with heat transfer of a nonlinear (non-Newtonian) Williamson fluid past an exponentially shrinking porous sheet with a convective boundary condition is investigated numerically. In this study, both an assisting flow and an opposing flow are considered. The governing equations are converted into nonlinear ordinary differential equations by using a suitable transformation. A numerical solution of the problem is obtained by using the Matlab software package for different values of the governing parameters. The results show that dual nonsimilar solutions exist for the opposing flow, whereas the solution for the assisting flow is unique. It is also observed that the dual nonsimilar solutions exist only if a certain amount of mass suction is applied through the porous sheet, which depends on the Williamson parameter, convective parameter, and radiation parameter.

Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation

The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number viscous dissipation it is enhanced.

Dual solutions of an unsteady magnetohydrodynamic stagnation-point flow of a nanofluid with heat and mass transfer in the presence of thermophoresis

The unsteady two-dimensional magnetohydrodynamic stagnation point flow of a nanofluid with thermophoresis effect is investigated numerically. The technique of similarity transformation is implemented to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This analysis explores the conditions of the existence, non-existence, uniqueness, and duality of the solutions of self-similar equations numerically. Dual solutions of velocity, temperature and concentration profiles are reported for different values of the each parameter involved for two types of nanoparticles, namely copper (Cu) and gold (Au) in the water-based fluid. It is found that the dual solutions exist for negative values of unsteady parameter A, whereas for positive values of unsteady parameter, the solution is unique. The results also indicate that the nanoparticle volume fraction reduces the skin friction coefficient, the heat transfer rate as well as mass transfer rate. Further, due to increase of thermophoresis parameter, the concentration inside the boundary layer reduces and the mass transfer rate enhances. In addition, to validate the present numerical results, comparison with published results is made and found to be in excellent agreement.

Slip Effect on an Unsteady MHD Stagnation-Point Flow of a Micropolar Fluid towards a Shrinking Sheet with Thermophoresis Effect

The effect of slip and thermophoresis on an unsteady magnetohydrodynamic stagnation-point-flow micropolar fluid with heat and mass transfer towards a shrinking sheet has been investigated. The governing equations are reduced to a system of non-dimensional partial differential equations by using similarity transformation, before being solved numerically using the Keller-box method. The effects of various physical parameters on the velocity, microrotation, temperature, and concentration profiles as well as the reduced skin friction, the reduced Nusselt number, and the reduced Sherwood number are analyzed and discussed graphically. It is found that the concentration boundary layer thickness decreases with increasing values of the thermophoresis. Comparison with previously published results under the limiting cases is made and found to be in excellent agreement.

Impact of homogeneous–heterogeneous reactions on mixed convection flow of a copper–water nanofluid past a permeable shrinking cylinder with thermal radiation:

The effect of thermal radiation on mixed convective flow of a copper–water nanofluid past a porous shrinking cylinder with homogeneous–heterogeneous reactions is studied. Using suitable transformations, the partial differential equations are converted into ordinary differential equations. The resulting self-similar equations are numerically solved using shooting method for several values of the pertinent parameters. Both assisting flow and opposing flow are considered in this study. The numerical results signify that the multiple solutions exist for the opposing flow, while for the assisting flow the solution is unique. The results also indicate that dual solutions only exist when a certain value of suction is implemented through the permeable cylinder. Further, the nanoparticle fraction and mixed convective parameter delay the boundary layer separation. A comparison is made with the available published data and is found to be in good agreement.

Impact of nanoparticles on flow of a special non-Newtonian third-grade fluid over a porous heated shrinking sheet with nonlinear radiation

Abstract This research peruses the characteristics of heat and mass transfern of a special non-Newtonian third-grade fluid over a porous convectively-heated shrinking sheet filled with nanoparticles. The Buongiorno model is used for the special non-Newtonian third-grade fluid that includes both the Brownian motion and the thermophoresis effects with non-linear radiation. The nonlinear system of ordinary differential equations are obtained using a suitable transformation. The converted system of equations are then numerically solved using shooting method. The numerically-obtained results for the skin friction, local Nusselt number and the local Sherwood number as well as velocity profile, temperature distribution and concentration of nanoparticle are illustrated for different physical parameters through graphs and tables. On the behalf of the whole studies, final conclusions are made and it is observed that multiple solutions are achieved for certain values of the suction parameter. Further, the non-Newtonian parameter reduces the velocity of the fluid and increases the temperature and the concentration profiles for the first solution while the reverse trend is seen for the second solution. Finally, a comparative analysis is made through previous studies in limiting cases and shown good correlation.

Effect of thermal radiation on heat transfer in an unsteady copper–water nanofluid flow over an exponentially shrinking porous sheet

The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a copper–water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.

Numerical solution of second law analysis for MHD Casson nanofluid past a wedge with activation energy and binary chemical reaction

Purpose This paper aims to peruse the influence of second law analysis for electrically conducting fluid of a Casson nanofluid over a wedge. For activation energy, a modified Arrhenius function is used. Design/methodology/approach The highly non-linear governing equations are developed using similarity transformations and then computed numerically via Keller–Box method. Findings The influences of emerging parameters on velocity, temperature distribution and concentration of nanoparticle are explained and presented via graphs and tables. Also, the behavior of fluid flow is investigated through the coefficient of skin friction, Nusselt and Sherwood numbers. Results reveal that the velocity profile enhances due to increasing Casson parameter and magnetic parameter, whereas the temperature distribution and concentration of nanoparticle decrease with larger vales of Casson parameter. It is inspected that the concentration boundary layer increases due to activation energy and decreases due to reaction rate and temperature differences. Originality/value The authors believe that all the numerical results are original and significant which are used in biomedicine, industrial, electronics and transportation. The results have not been considered elsewhere.