In this paper, we present a transient mathematical model for a V-shaped microgrooved heat pipe considering the temporal variations in the fluid flow, and heat and mass transfer, and utilizing a macroscopic approach. Unlike other heat pipe models, the shear stress at the liquid-vapor interface and the disjoining pressure have been used in the momentum balance equation of the model. The sensible heat used by the substrate is also taken into account using a pseudo-lump capacity model. The coupled nonlinear partial differential equations governing the transient fluid flow, heat and mass transfer have been solved numerically. The transient and steady-state profiles for the radius of curvature, liquid and vapor velocity, liquid pressure, and substrate temperature have been obtained. The mathematical model is capable of predicting the time required for the onset of dry out at the hot end, and for a micro heat pipe to reach steady state. The time required to reach steady state is independent of heat input, heat pipe inclination, groove angle, and $Qss$ profile. However, the time required for the onset of dry out at the hot end decreases with increasing heat input, inclination, and groove angle. The model predicted results have been successfully compared to the results from the literature. The general nature of this model and the associated study can be useful for many practical applications in the microscale heat exchange.

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