Effect of channel shape on axial back conduction in the solid substrate of microchannels

Abstract

Microchannels machined on flat solid substrates (metallic/non-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 has been carried out. 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 varies from 1.0 to 4.0 to find the effect of microchannel aspect ratio on axial back conduction. Considering the fact that axial conduction dominates at low flow rates, the flow Reynolds number of the working fluid considered is 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. Detailed parametric study reveals that depending on channel aspect ratio and thermo-physical properties of fluid-solid combination, conjugate heat transfer effects must be accounted for, to correctly estimate the local Nusselt number along the channel. The average Nusselt number is found to be minimum corresponding to channel aspect ratio of 2.0, irrespective of the conductivity ratio of the solid substrate and the working fluid.