# NUMERICAL RESOLUTION OF CONJUGATE HEAT TRANSFER PROBLEM IN PARALLELPLATE MICRO-CHANNEL

DOI: 10.1615/ICHMT.2009.CONV.280
13 pages

Yassine Kabar
Université de Jijel, Laboratoire d'Energétique Appliquée et des Matériaux, Faculté des Sciences et de la Technologie, BP. 96, 18000 Jijel, Algeria

University of Reims Champagne-Ardenne GRESPI / Faculte des Sciences PB 1039, 51687 Reims, France

Constantinel University, Laboratory of Applied Energetics and Pollution, Faculty of Technology Sciences, Department of Mechanical Engineering, Constantine 25000, Algeria

University of Reims Champagne-Ardenne, GRESPI/Laboratoire de Thermomécanique, Faculté des Sciences PB1039, 51687 Reims, France

## Abstract

The present paper deals with the characterization of the conjugated two-dimensional steady state heat transfer problem in two parallel-plate micro-channel heat sink. The fluid is assumed to be incompressible and with constant properties. Hydrodynamic and thermal developing region is taken into consideration here. The Axial conduction is also taken into account. Analysis is performed for constant wall temperature at the outer surfaces of the plates. The heat wave generated at these surfaces is crossing through the plates to reach the interface with the fluid in the micro-channel. Due to the fact that channel height (H) is in the same order of dimension of the plate thickness (E) in micro-channel heat problem, the conduction in the plate cannot be assumed as negligible. Therefore, the convective heat transfer in micro-channel is conjugated with the conduction in the solid plates. The two-dimensional Naviers-Stockes equations and the energy equation are solved by finite-control-volume method. Detailed temperature profiles in the fluid and solid, the fluid bulk temperature and the heat flux distributions on the fluid-solid interface are provided. The influences of the plate thickness and the solid to fluid thermal conductivities ratio (K = ks/kf) are studied for a water flow with a Reynolds number Re = 100. The results of the different simulations are analysed, and the axial distributions of the Nusselt number are deduced for each case. The results show that viscous heating of the fluid can significantly influence the heat transfer in the micro-channel heat sink. The thickness plate (E) may have an influence on both thermal developing length and the asymptotic Nusselt number value which corresponds to the fully developed flow. The bulk fluid temperature is shown to vary in a non-linear form along the flow direction.

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