Numerical Study of Heat Transfer from an Isothermal Vertical Plate in an Air Enclosure

Abstract

The numerical study of the heat transfer from a vertical isothermal plate in an air enclosure is undertaken in this work to simulate heat transfer from electronic elements and similar devices as functions of plate locations and Grashof number. The walls of the enclosure are assumed to be adiabatic and the full two-dimensional time-dependent partial differential forms of the conservation equations of continuity, momentum, and energy governing the flow field are cast and solved by a numerical method employing the finite difference scheme. During the initial short period, heat flow is found to be by conduction irrespective of plate location and Grashof number. Shortly after conduction, sets in convection indicated by increase in the heat transfer coefficient following a temporal minimum in the coefficient at the end of the conduction regime. Heat transfer by convection is found to be maximum when the plate is symmetrically located within the enclosure, the rate decreasing as the plate is moved away from this location along a horizontal direction. It is also found that there is very little change in the heat transfer rate when the plate is moved downwards from the centre of the enclosure along the vertical direction, indicated by the collinearity of the curves along the direction, but a sharp decrease occurs when the plate is moved upwards along the axis. During convection, the rate of heat transfer is found to increase with Grashof number. For low Grashof numbers, e.g. for H/L=1/4 and GR = 4650, and for H/L=1/4 and Gr = 46500. The regime of heat transfer is found to be entirely the one-dimensional conduction regime. At large times, the temperature field stratifies and heat transfer from the heated surface into the fluid medium approaches zero, the velocity field decaying gradually and the flow approaching its eventual quiescence.