A Simplified Model for Flow Boiling in Expanding Circular Micro-Channels
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A computational model to study flow boiling in a diverging micro-channel of circular cross section is advanced. The applicable conservation of mass and linear momentum equations, coupled with Young-Laplace relation are derived analytically under the assumptions of steady, incompressible, uniaxial annular flow. Numerical solutions of the governing nonlinear system of differential equations, subject to appropriate initial conditions, yield predictions of vapor core radius and liquid and vapor velocities and pressures. Validation of the model by comparison with a previous model for flow boiling in a constant cross-section micro-channel reveals excellent agreement. Results for an expanding micro-channel indicate that dry-out conditions may be delayed or avoided in contrast with straight micro-channel, depending on expansion ratio. Both liquid and vapor velocity decrease while the pressures increase as a consequence of channel expansion, in accordance with mass conservation in steady flows. The model may be easily implemented to stabilize two-phase flow boiling and avert burn-out conditions in micro-channels used for electronic cooling applications
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