Analytical Analysis of Thermal Conductivity by Laminar Flow Under the Influence of MHD Using Vogel’s Model

Abstract

Abstract The main aim of this work is to study the influence of thermal conductivity of uniform couple stress fluid of inclined Poiseuille flow in the presence of magneto hydrodynamic (MHD) between two parallel plates. A well-known Vogel’s viscosity model is used. The momentum and energy equations are solved analytically by utilizing Homotopy Perturbation method (HPM) and Optimal Homotopy Asymptotic Method (OHAM). The results include the velocity profile, average velocity, volume flux, Shear Stress, Skin friction and the temperature distribution between the plates. Particular attention is given to the effect of MHD Γ on the velocity field and temperature distribution. As can be seen, that there exists direct relation between MHD parameter Γ and velocity profile and bears inverse relation with temperature distribution. In addition to that, influence of non-dimensional parameters like G, A, a, B and γ on the velocity field and temperature distribution are also discussed graphically. The physical characteristics of the problem have been well discussed in graphs for several parameters of interest. The results reveal that both techniques are reliable and are in great agreement with each other.