This paper looks at the influence of melting heat transfer in stagnation point flow of Powell–Eyring fluid toward a linear stretching sheet. The mathematical modeling is characterized by conservation laws of mass, linear momentum, and energy. Appropriate similarity transformations are employed for the reduction of partial differential systems into the ordinary differential systems. Series solutions to the resulting problems are presented. Variations of embedded parameters into the derived problems are graphically illustrated. The skin-friction coefficient and the Nusselt number are computed and examined.

Melting Heat Transfer in the Stagnation Point Flow of Powell–Eyring Fluid

A two-dimensional magnetohydrodynamic boundary layer flow of the Eyring–Powell fluid on a stretching surface in the presence of thermal radiation and Joule heating is analyzed. The Soret and Dufour effects are taken into account. Partial differential equations are reduced to a system of ordinary differential equations, and series solutions of the resulting system are derived. Velocity, temperature, and concentration profiles are obtained. The skin friction coefficient and the local Nusselt and Sherwood numbers are computed and analyzed.

Influence of thermal radiation and Joule heating in the Eyring–Powell fluid flow with the Soret and Dufour effects

This letter describes the characteristics of homogeneous-heterogeneous reaction in the boundary layer flow of a Jeffrey fluid due to an impermeable horizontal stretching sheet. An analysis is carried out through the similar values of reactant and auto catalyst diffusion coefficients. Heat released by the reaction is not accounted. The exact solution for the flow of the Jeffrey fluid is constructed. The series solution for the concentration equation is derived. The velocity and concentration fields reflecting the impact of interesting parameters are plotted and examined.

Note on characteristics of homogeneous-heterogeneous reaction in flow of Jeffrey fluid

This article analytically studies the combined laminar free convection flow with thermal radiation and mass transfer of non-Newtonian power-law fluids along a vertical plate within a porous medium. The mathematical model takes the diffusion-thermo (Dufour), thermaldiffusion (Soret), thermal radiation and power-law fluid index effects into consideration. The governing boundary-layer equations along with the boundary conditions are rendered into a dimensionless form by a similarity transformation. The powerful homotopy analysis method (HAM) is applied to obtain approximate analytical solutions for the resulting nonlinear differential equations. The effects of the radiation parameter (R), the power-law index (n), the Dufour number (Df), and the Soret number (Sr) on the velocity, temperature and species concentration fields are discussed in detail. The results indicate that when the buoyancy ratio of concentration to temperature is positive, 0 N  , the local Nusselt number increases with an increase in the power-law index and the Soret number or a decrease in the radiation parameter and the Dufour number. In addition, the local Sherwood number for different values of the controlling parameters is also obtained. The obtained solution, in comparison with the numerical solutions (fourth- order Runge–Kutta scheme) admit excellent accuracy.

Homotopy analysis of soret and dufour effects on free convection non-newtonian flow in a porous medium with thermal radiation flux

In this paper, the couette flow of fluid with variable viscosity is studied analytically by using Homotopy Pertubation Method (HPM). At first the basic idea of Homotopy Pertubation Method (HPM) is presented. The mathematical formulation and application of HPM to nonlinear problem are presented in section three. In order to check the validity of solution the analytical results are compared with exact ones for various numerical cases. The good agreement between exact method and Homotopy Pertubation Method has been assures us about the solution accuracy.

/pdf/application-of-hpm-to-find-analytical-solution-of-coette-4tg4bhdvhc.pdf

Application of HPM to Find Analytical Solution of Coette Flow with Variable Viscosity

In this study, the steady buoyancy-induced thermal convection boundary layer flow of a nonNewtonian fluid over a non-isothermal horizontal flat plate immersed in a porous medium is examined by employing the general similarity transformation procedure and the power law model to characterize the non-Newtonian fluid behaviour. Temperature profiles and the heat transfer rate at the wall are presented for different values of the non-Newtonian power law index (n) and the exponent associated with the wall temperature distribution (A). The similarity transformation is applied to reduce the governing nonlinear coupled partial differential equations to nonlinear ordinary differential equations in dimensionless form. The robust Homotopy Analysis Method (HAM), is applied to obtain approximate analytical solutions of the dimensionless nonlinear equations. The obtained solutions demonstrate very high accuracy and excellent agreement with numerical solutions (fourth-order Runge–Kutta scheme).

M. M. Rashidi

Papers

Homotopy study of buoyancy-induced flow of non-newtonian fluids over a non-isothermal surface in a porous medium