EFFECT OF ASPECT RATIO OF RECTANGULAR MICROCHANNELS ON THE AXIAL BACK CONDUCTION IN ITS SOLID SUBSTRATE

摘要

Microchannels machined on flat solid substrates (metallicon-metallic) are widely used in many engineering heat transfer applications. Such applications, on most occasions, involve conjugate effects, overlooking of which often leads to misinterpretation of transfer coefficients. In this background, a conjugate three-dimensional numerical simulation of simultaneously developing laminar flow in rectangular microchannels is reported to quantify the effect of channel aspect ratio on axial back conduction in the substrate, which eventually affects the heat transfer coefficient. A substrate of fixed size (0.6 mm × 0.4 mm × 60 mm) is considered while the channel width and height are independently varied such that the channel aspect ratio (width/height) varies from 0.45 to 4.0. Considering the fact that axial conduction dominates at low flow rates, the flow Reynolds number is kept constant at 100. The thermal conductivity of the solid substrate as well as the working fluid are considered in the conjugate formulation. Constant heat flux is applied at the bottom of the substrate while all its other surfaces are kept insulated. To understand the effect of channel aspect ratio on axial back conduction, this ratio is varied in four different ways so as to maintain a constant (i) area of channel cross-section, (ii) heating perimeter, (iii) channel width, and (iv) channel height. It is found that there exists an optimum value of conductivity ratio of solid to fluid, at which the average Nusselt number over the channel length is maximum. For a given flow configuration, the local and the average Nusselt number over the total channel length is found to be function of channel aspect ratio, with a minimum in the Nusselt number always observable. This minimum value corresponds to an aspect ratio of approximately two or slightly less than two, depending on the way channel aspect ratio is varied. As a result of this conjugate heat transfer behaviour, two channels having different channel aspect ratios can have same thermal performance in terms of average Nusselt number.