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Direct numerical simulation of liquid flow in a horizontal microchannel

Kükrer, Cenk Evren
Numerical simulations of liquid flow in a micro-channel between two horizontal plates are performed. The channel is infinite in streamwise and spanwise directions and its height is taken as m, which falls within the dimension ranges of microchannels. The Navier-Stokes equations with the addition of Brinkman number (Br) to the energy equation are used as the governing equations and spectral methods based approach is applied to obtain the required accuracy to handle liquid flow in the microchannel. It is known for microchannels that Br combines the effects of conduction and viscous dissipation in liquids and is also a way of comparing the importance of latter relative to former. The present study aims to simulate the unusual behavior of decreasing of Nu with increasing Re in the laminar regime of microchannels and to show that Br can be introduced to explain this unexpected behavior. Consequently, it is seen at the end of the results that secondary effect of the Br is observed for the single-phase convective heat transfer. Therefore, a laminar flow of a liquid in a microchannel shows different characteristics compared to a similar flow in a macrochannel. To observe the differences, three different cases are run over each of a range of Reynolds numbers: one with no axial conduction assumption that corresponds to a case similar to macrochannel flow, another case with axial conduction included in the energy equation to simulate one of the main differences and lastly a case with the inclusion of Br number in the governing equations. A similar study is made for natural convection with the same numerical set-up for the same three cases. Formation of Rayleigh-Benard cells are observed for the critical numbers widely accepted in the literature. The results are compared with each other to see the effects of axial conduction and Br inclusion, in addition to Ra for natural