The solution of the heat conduction equation in the liquid layer beneath a moving bubble’s base and the resulting local heat transfer coefficient are presented. An analytical model was constructed using separation of variables to solve the heat conduction equation for the thermal profile in the liquid film beneath the base of a bubble moving through a microchannel at a given velocity. Differentiating the resulting liquid thermal profile and applying the standard definition for the local heat transfer coefficient resulted in a solution for local heat transfer coefficient as a function of bubble length. Analysis included varying pertinent parameters such as film thickness beneath the bubble base, wall heat flux, and superheated temperature in the microchannel. Water and FC-72 were analyzed as prospective coolant fluids. Analytical data revealed that as the superheated temperature in the microchannel increases, local heat transfer coefficients increase and arrive at a higher steady-state value. Increasing wall heat flux achieved the same result, while increasing film thickness resulted in lower heat transfer coefficients. The model indicated that water had superior performance as a coolant, provided the dielectric fluid (FC-72) is not mandated.

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