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Analytical and chpdm analysis of MHD mixed convection over a vertical flat plate embedded in a porous medium filled with water at 4${}^{\circ }$C. (English) Zbl 1228.76190
Summary: A two-dimensional mixed convection boundary-layer flow over a vertical flat plate embedded in a porous medium saturated with a water at ${4}^{\circ }C$ (maximum density) and an applied magnetic field are investigated theoretically and numerically using the new Chebyshev pseudospectral differentiation matrix (ChPDM) approach. Both cases of the assisting and opposing flows are considered. Multiple similarity solutions are obtained under the power law variable wall temperature (VWT), or variable heat flux (VHF), or variable heat transfer coefficient (VHTC). The boundary-layer equations, which are partial differential equations are reduced, via the similarity transformations, to a pair of coupled of nonlinear ordinary differential equations. The resulting problem, which depends on two parameters, namely $m$, VWT (or VHF, or VHTC) parameter and $\xi$, the magnetohydrodynamic (MHD) mixed convection parameter, is analyzed analytically. Comparing with the other researcher’s results, it is found, under VWT condition, that the problem has multiple similarity solutions for $-1\frac{1}{4} and $\xi >0$ (assisting flows). Solutions for $\xi \gg 1$ (free convection), $\xi =0$ (forced convection) and $-1<\xi <0$ (opposing flows) are also deduced. ChPDM approach is applied to validate and evidence the current analytical analysis.
##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics