Heat and Mass Transfer in a Cylindrical Heat Pipe with Idealized Porous Lining

Abstract

Many devices use heat pipes for cooling. They can be of different cross-sectional shapes and can range from 15 m long to 10 mm. In this work, the heat and mass transfer in a cylindrical heat pipe is modelled. The heat pipe is lined with a wick next to the wall. The wick consists of straight capillaries that run the whole length of the pipe and radially aligned capillaries that span the width of the wick. The capillaries are filled with a partially wetting liquid, and the center of the pipe is filled with its vapor. The radial capillaries are connected to the axial capillaries and are opened to the vapor region at the wick surface. The pipe is initially charged with an amount of liquid such that the liquid-vapor interface at the radial capillary openings is flat. When one end of the pipe is heated, the liquid evaporates and increases the vapor pressure. Hence, the vapor is driven to the cold end where it condenses and releases latent heat. The condensate moves back to the hot end through the capillaries in the wick. Steady-flow problem is solved in this work assuming a small imposed temperature difference between the two ends making the temperature profile skew-symmetric. So, we only need to focus on the heated half. Also, since the pipe is slender, the axial flow gradients are much smaller than the cross-stream gradients. Therefore, evaporative flow in a cross-sectional plane can be treated as two-dimensional. Evaporation rate in each pore is solved in the limit the evaporation number to find that the liquid evaporates mainly in a boundary layer at the contact line. An analytical solution is obtained for the leading order evaporation rate. Therefore, we find the analytic solutions for the temperature profile and pressure distributions along the pipe. Two dimensionless numbers emerge from the momentum and energy equations: the heat pipe number, H, which is the ratio of heat transfer by vapor flow to conductive heat transfer in the liquid and wall, and the evaporation exponent, S, which controls the evaporation gradient along the pipe. Conduction in the liquid and wall dominates in the limit and . When and , vapor-flow heat transfer dominates and a thermal boundary layer appears at the hot end whose thickness scales as S-1L, where L is the half length of the pipe. A similar boundary layer exists at the cold end. The