J. of Thermal Science Vol.5, No.2 Local Non-Similarity Solution of Coupled Heat-Mass Transfer of a Flat Plate with Uniform Heat Flux in a Laminar Parallel Flow Yuwen Zhang Zhongqi Chen Mingyong Chen Department of Power Machinery Engineering, Xi'an Jiaotong University, Xi'an 710049, China The coupled heat and mass transfer problem of gas flow over a UHF flat plate with its wall coated with sublimable substance has been solved by local non-similarity method. Considerations have been given also to the effect of non-saturation of the sublimable substance in the oncoming flow and the normal injection velocity at the surface. Analytical results are given for local Nusselt and Sherwood numbers at the various locations. Keywords: heat-mass transfer, uniform heat flux, laminar flow. INTRODUCTION Heat transfer surface coated with a layer of sub- limable substance is a practical problem of interest such as in ablation cooling system, evaporative film cooling, experimental techinque using heat and mass analogy. This kind of problems is very complicated owing to the very strong coupling between heat and mass transfer. Kurosaki [11 has investigated analyti- cally one of the problems by similarity method, but he did not take the normal injection velocity into ac- count, which is not negligible in many practical cases (e.g. ablation cooling, transpiration coohng). He also assumed that the sublimable substance in the oncom- ing flow is saturated at the gas temperature. However, it is conflicted with most practical situations. The similarity solution will not be able to obtain when the normal velocity and the non-saturation of the sub- limable substance in the oncoming flow are being con- sidered. Therefore, local non-similarity method [2] was employed to solve the above-mentioned problem in this paper. As a fundamental research work, the present pa- per has no intention of directly solving practical prob- lems, yet the solution obtained here does relax some assumptions made by Kurosaki [11. FORMULATION OF THE PROBLEM As schematic view of the problem studied and its coordinate system are shown in Fig.1. The flat wall is coated with a layer of sublimable substance and is heated with external uniform heat flux. The on- coming gas has velocity Uoo and temperature Too. In addition, the oncoming gas flow may contain vapor of sublimable substance in the amount of Coo which is equal to or less than the saturation value C~ cor- responding to the oncoming flow temperature. The flow over the plate is considered to be two dimen- sional, steady and laminar flow, with incompressible fluid. The normal injection velocity at the wall and the non-saturation of the oncoming flow were taken into account in this study. Then the mathematical for- mulation of the just-described problem is as follows: Ou Ov + w- = 0 (1) O---x oy Du Ou 02u ,~ + ~,~ = roy- ~ Y OT OT 02T u~ + ~,~ = a~ Y OC + V~y 02C u ~ = D -b-~y ~ (~) (3) Received, 1996. (4)