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.

The most important plastic resins used for wire coating are polyvinyl chloride (PVC), nylon, polysulfone, and low-/high-density polyethylene (LDPE/HDPE). In this article, the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adomian decomposition method (ADM). The convergence of the series solution is established. The results are also verified by Optimal Homotopy Asymptotic Method (OHAM). The effect of different emerging parameters such as non-Newtonian parameters α and β, magnetic parameter Mand the Brinkman number Br on solutions (velocity and temperature profiles) are discussed through several graphs. Additionally, the current results are compared with published work already available.

The aim of this article is to provide an analytical and numerical investigation to the viscous fluid flow, heat and mass transfer under the influence of a variable magnetic field. The governing system of partial differential equations are transformed by means of similarity transformations to a system of ordinary differential equations which are solved by Homotopy Analysis Method (HAM) and BVP4c. The effects of involved physical parameters are illustrated for the velocity components, magnetic field components, heat and mass transfers. Authentification of HAM results for various involved physical parameters are supported by comparison with numerical results obtained by BVP4c. It is observed that increasing distance between discs increase pressure on lower disc and torque on upper disc. It is also observed that increase in axial component of magnetic field increase fluid's axial velocity and increase in magnetic Reynold's number decrease magnetic flux it lower disc. Heat flux from lower to upper disc is increased by increase in Dufour number.

A similarity solution is obtained for the modeled system of differential equations that accounts for the squeezing and rotation effects. The governing equations are coupled with advection diffusion and energy equation which defines heat/mass flux going from the lower to the upper disc. The similarity solution of modeled equations is obtained by the Homotopy Analysis Method (HAM) via mathematica package BVPh 2.0 and is compared with the numerical results obtained by BVP4c to assure the accuracy of HAM. The combined effects of the rotational motion of two discs, upward/downward motion of the upper disc, thermal radiation effect, as well as the Soret and Dufour effects are studied both graphically and numerically.