Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

Abstract

Purpose

This paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated.

Design/methodology/approach

The governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB.

Findings

If the temperature of the obstacle T_w coincides with the environment temperature T₀, then the motion reduces to the usual orthogonal stagnation-point flow; if T_w = T₀, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies.

Originality/value

The present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

Citation

Borrelli, A., Giantesio, G. and Patria, M.C. (2018), "Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 6, pp. 1315-1334. https://doi.org/10.1108/HFF-05-2017-0186