# Unsteady mixed convection on the stagnation-point flow adjacent to a vertical plate with a magnetic field

- First Online:

- Received:

DOI: 10.1007/s00231-004-0537-1

- Cite this article as:
- Takhar, H.S., Chamkha, A.J. & Nath, G. Heat Mass Transfer (2005) 41: 387. doi:10.1007/s00231-004-0537-1

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## Abstract

An analysis is performed to study the unsteady combined forced and free convection flow (mixed convection flow) of a viscous incompressible electrically conducting fluid in the vicinity of an axisymmetric stagnation point adjacent to a heated vertical surface. The unsteadiness in the flow and temperature fields is due to the free stream velocity, which varies arbitrarily with time. Both constant wall temperature and constant heat flux conditions are considered in this analysis. By using suitable transformations, the Navier–Stokes and energy equations with four independent variables (*x*,* y*,* z*,* t*) are reduced to a system of partial differential equations with two independent variables (η, τ). These transformations also uncouple the momentum and energy equations resulting in a primary axisymmetric flow, in an energy equation dependent on the primary flow and in a buoyancy-induced secondary flow dependent on both primary flow and energy. The resulting system of partial differential equations has been solved numerically by using both implicit finite-difference scheme and differential-difference method. An interesting result is that for a decelerating free stream velocity, flow reversal occurs in the primary flow after certain instant of time and the magnetic field delays or prevents the flow reversal. The surface heat transfer and the surface shear stress in the primary flow increase with the magnetic field, but the surface shear stress in the buoyancy-induced secondary flow decreases. Further the heat transfer increases with the Prandtl number, but the surface shear stress in the secondary flow decreases.

### List of symbols

*C*_{f}specific heat of the fluid

*C*_{fx}local skin friction coefficient

*f*dimensionless stream function

*g*acceleration due to gravity

- Gr
Grashof number

- Gr
_{x} local Grashof number

*M*magnetic parameter

- Nu
_{x} local Nusselt number

- Pr
Prandtl number

- Re
_{m} magnetic Reynolds number

*x*,*y*,*z*Cartesian co-ordinates

*T*temperature

*u*,*v*,*w*velocity components along radial and axial directions

- β
volumetric coefficient of thermal expansion

- η, ξ
ransformed co-ordinates

- θ
dimensionless temperature

- μ
coefficient of viscosity

- ν
kinematic viscosity

- ρ
_{f} density of the fluid

- Ψ
dimensional stream function

### Subscripts

- w, ∞
conditions at the wall and in the ambient fluid

### Superscript

- ′
derivative with respect to η