# Computational study of combined effects of conduction-radiation and hydromagnetics on natural convection flow past magnetized permeable plate

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## Abstract

The computational study of the combined effects of radiation and hydromagnetics on the natural convection flow of a viscous, incompressible, and electrically conducting fluid past a magnetized permeable vertical plate is presented. The governing non-similar equations are numerically solved by using a finite difference method for all values of the suction parameter *ξ* and the asymptotic solution for small and large values of *ξ*. The effects of varying the Prandtl number *Pr*, the magnetic Prandtl number *Pr* _{m}, the magnetic force parameter *S*, the radiation parameter *R* _{d}, and the surface temperature *θ* _{w} on the coefficients of the skin friction, the rate of heat transfer, and the current density are shown graphically and in tables. An attempt is made to examine the effects of the above mentioned physical parameters on the velocity profile, the temperature distribution, and the transverse component of the magnetic field.

## Key words

hydromagnetic fluctuating natural convection magnetized plate current density heat transfer## Nomenclature

*H*_{0}reference magnetic field velocity

*H*_{∞}free stream magnetic field

*S*magnetic field parameter

*f*transformed stream function

*Pr*_{m}magnetic Prandtl number

*Re*_{x}local Reynolds number

*Gr*_{x}local Grashof number

*C*_{fx}skinfriction

*H*_{x}magnetic field along the surface

*H*_{y}magnetic field normal to the surface

*Nu*_{x}local Nusselt number

*ū*dimensional axial velocity, m·s

^{−1}- \(\bar v\)
dimensional normal velocity, m·s

^{−1}- \(\bar T_w\)
wall temperature, K

- \(\bar T_\infty\)
ambient fluid temperature, K

*V*_{0}surface mass flux

*R*_{d}Plank number (conduction-radiation parameter)

- \(\bar x\)
axial distance, m

- \(\bar y\)
normal distance, m

*g*acceleration due to gravity, m·s−2

## Greek symbols

*ψ*fluid stream function, m

^{2}·s^{−1}*ϕ*transformed stream function for the magnetic field

*ξ*transpiration parameter

*α*thermal diffusivity, m

^{2}·s^{−1}*μ*dynamical viscosity, kg·m

^{−1}·s^{−1}*η*similarity transformation

*ν*kinematic viscosity, m

^{2}·s^{−1}*θ*dimensionless temperature function

*θ*_{w}surface temperature ratio to the ambient fluid

*ρ*density of the fluid, kg·m

^{−3}*σ*electrical conductivity

*σ*_{s}Stefan-Boltzman constant

*γ*magnetic diffusion

*β*coefficient of cubical expansion

- \(\bar \mu\)
magnetic permibility

## Subscripts

- w
wall condition

- ∞
ambient condition

## Chinese Library Classification

O351## 2010 Mathematics Subject Classification

76D05## Preview

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