Turbulent heat transfer in the developing and fully developed regions of a vertical channel

Turbulent heat transfer in a vertical parallel-plate channel heated both symmetrically and asymetrically is studied using an implicit finite-difference method. The problem is formulated by applying the conservation laws with the turbulent motion being described by a low-Reynolds-number k-D model. A variable-grid pattern is employed in the numerical computation along with the use of a combined inner and outer iteration procedure. The inner iteration treats the problem of velocity-pressure coupling utilizing a predictor-corrector approach weighted by an under-relaxation factor, whereas the outer iteration minimizes the error associated with the lagging technique. Numerical calculations have been performed over wide ranges of Grashof and Graetz numbers covering both the developing and fully developed flow regions. Based upon the numerical solutions, correlations are developed for the induced flow rate and the local Nusselt numbers in different flow regions. The correlations obtained in this study can be conveniently used to predict the maximum wall temperature and the induced flow rate in both performance and design calculations of a reactor-vessel air cooling system.