Abstract
The aim of this article is to investigate MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The constitutive equations of Carreau fluid are modeled in the form of partial differential equations (PDEs). Concerning boundary conditions available, the PDEs are converted to ordinary differential equations (ODEs) by means of similarity transformation. The homotopy analysis method (HAM) is used for solution of the system of nonlinear problems. The effects of various parameters such as Weissenberg number mathit{We}^{2}, magnetic parameter M^{2}, power law index n, porosity parameter D, wall thickness parameter α, power index parameter m, slip parameter λ, thermal conductivity parameter ε, radiation parameter R and Prandtl number on velocity and temperature profiles are analyzed and studied graphically.
Highlights
The study of heat transfer and boundary layer flow over a stretching sheet has received a great deal of attention from many researchers due to its importance in many engineering and industrial applications, such as paper production, glass-fiber production, solidification of liquid crystals, petroleum production, exotic lubricants, suspension solutions, wire drawing, continuous cooling and fibers spinning, manufacturing plastic films and extraction of polymer sheet
The aim of the present work is to model and analyze the steady boundary layer flow of MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effects of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity
3 Solution by the homotopy analysis method we apply the HAM to obtain approximate analytical solutions of the MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity
Summary
The study of heat transfer and boundary layer flow over a stretching sheet has received a great deal of attention from many researchers due to its importance in many engineering and industrial applications, such as paper production, glass-fiber production, solidification of liquid crystals, petroleum production, exotic lubricants, suspension solutions, wire drawing, continuous cooling and fibers spinning, manufacturing plastic films and extraction of polymer sheet. Crane [ ] was the first person who studied the boundary layer flow past a stretching sheet. He concluded that velocity is proportional to the distance from the slit. Gupta and Gupta [ ] discussed the problem of the continuous moving surface with constant temperature. The constant surface velocity case with a power law temperature variation was studied by Soundalgekar et al [ ]. Grubka et al [ ] studied the stretching flow problem with a variable surface temperature. Hayat et al [ ] obtained the series solutions for stretching sheet problem with mixed convection by using the homotopy analysis method (HAM). In the presence of a transverse magnetic field, Chaim [ ] studied boundary layer flow due to a plate stretching with a power law
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