Network Electro-thermal Simulation of Non-isothermal Magnetohydrodynamic Heat Transfer from a Transpiring Cone with Buoyancy and Pressure Work

Abstract

The steady, axisymmetric laminar natural convection boundary layer flow from a non-isothermal vertical circular porous cone under a transverse magnetic field, with the cone vertex located at the base, is considered. The pressure work effect is included in the analysis. The governing boundary layer equations are formulated in an (x, y) coordinate system (parallel and normal to the cone slant surface), and the magnetic field effects are simulated with a hydromagnetic body force term in the momentum equation. A dimensionless transformation is performed rendering the momentum and also heat conservation equations. The thermal convection flow is shown to be controlled by six thermophysical parameters—local Hartmann number, local Grashof number, pressure work parameter, temperature power law exponent, Prandtl number and the transpiration parameter. The transformed parabolic partial differential equations are solved numerically using the network simulation method based on the electrical-thermodynamic analogy. Excellent correlation of the zero Hartmann number case is achieved with earlier electrically non-conducting solutions. Local shear stress function (skin friction) is found to be strongly decreased with an increase in Prandtl number (Pr), with negative values (corresponding to flow reversal) identified for highest Pr with further distance along the streamwise direction. A rise in local Hartmann number, is observed to depress skin friction. Increasing temperature power law index, corresponding to steeper temperature gradient at the wall, strongly reduces skin friction at the cone surface. A positive rise in pressure work parameter decreases skin friction whereas a negative increase elevates the skin friction for some distance along the cone surface from the apex. Local heat transfer gradient is markedly boosted with a rise in Prandtl number but decreased principally at the cone surface with increasing local Hartmann number. Increasing temperature power law index conversely increases the local heat transfer gradient, at the cone surface. A positive rise in pressure work parameter increases local heat transfer gradient while negative causes it to decrease. A rise in local Grashof number boosts local skin friction and velocity into the boundary layer; local heat transfer gradient is also increased with a rise in local Grashof number whereas the temperature in the boundary layer is noticeably reduced. Applications of the work arise in spacecraft magnetogas dynamics, chemical cooling systems and industrial magnetic materials processing.