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Steady state mathematical modelling for thermal performance of T-shaped multi-branched micro heat pipe

A mathematical model for predicting a thermal performance of T-shaped multi-branched micro heat pipe (T-MBMHP) is developed. T-MBMHP, an efficient passive thermal management device with branched condenser section, uses two-phase evaporation and condensation processes in transporting the heat from the source. A square cross-sectional micro groove aids the working fluid to flow between the condenser section and evaporator section. On addition of thermal energy to the evaporator section of T-MBMHP, the working fluid evaporates and generates vapor. Due to the prevailing conditions in condenser section, the vapor condenses back to the liquid by releasing the latent heat of vaporization. The condensate wets the evaporator by the capillary action which is responsible for functional stability of T-MBMHP. The movement of the condensate mainly depends on the pressure difference and its surface tension. The one-dimensional steady-state governing equations are formulated based on the conservation laws of mass, momentum and energy, along with this pressure difference is characterized by the Young-Laplace equation. The non-linear governing equations are coupled and solved numerically with respective boundary conditions using explicit schemes of 4th order Runge-Kutta method. A damping term is used to stabilize the solution. Thermal performance of T-MBMHP, at two different heat inputs, is analyzed by the developed model to predict its performance.