Heat transfer characterization of rhombic microchannel for H1 and H2 boundary conditions

In this paper, the characterization of laminar convective heat transfer in rhombic shaped microchannel with H1 (axially constant heat flux and circumferentially constant temperature) and H2 (constant axial and circumferential wall heat flux) boundary conditions is presented. A three-dimensional numerical model is developed for hydrodynamically and thermally developing flow in different rhombic geometries with side-angles varying from 10° to 90°. The numerical model is first validated with the other model developed in the literature for rectangular geometry and subsequently the results are compared with rhombic channel with different side-angles. This model is then extended to determine the temperature and heat flux distributions in rhombic microchannel, which is used to find the local and hydrodynamically and thermally fully developed Nusselt numbers. It is found that the fully developed Nusselt number varies only with the side-angles of rhombic channel and generalized correlations are developed as a function of side-angles for H1 and H2 boundary conditions. Correlations for developing length, local and fully-developed Nusselt numbers for rhombic channels are currently not available. These results will be useful in design and optimization of rhombic microchannel for electronic cooling applications.