Forced convection on isothermal plates and channels using diffusion velocity

Abstract

In many industrial applications, such as electronic systems, performance failure and breakdown usually occur due to poor thermal management, which could be adequately controlled through a proper understanding and management of the forced convection system and use of the vortex element method. The main contribution of this paper is that it shows how the vortex element method is capable of producing results similar to those reported in literature. The paper utilised vortex element method to model familiar problems in heat transfer, which is laminar flow over isothermal flat plate and isothermal two parallel-plate channels. Numerical models were developed using diffusion velocity method, a version of vortex element method, from vorticity transport equation and the energy equation for each of the cases. The velocity and temperature distributions, obtained for both plates and channels, were utilised to calculate Nusselt numbers with Reynolds numbers in the range of 20 to 120. The logarithmic plot of Nusselt number versus Reynolds number for forced convection on single horizontal plates yielded a slope of 0.46 and an intercept of -0.29 while that for forced convection in horizontal channels had a slope of 0.87 and an intercept of -0.88. The results obtained in this work show the diffusion velocity method to be a viable numerical tool for modelling fluid flow problems and also heat transfer problems.