Exact Solution for Slug Flow Laminar Heat Transfer Development in a Rectangular Duct With Isothermal Walls

Abstract

The transfer of heat to or from a fluid in the entrance region of a straight duct is almost independent of the momentum transfer that is taking place simultaneously if the Prandtl number of the fluid is very low, as is the case with liquid metals. The thermal boundary layer develops much faster than the corresponding hydrodynamic boundary layer; it is therefore a good approximation to assume that a uniform velocity profile (slug flow) exists. The differential equation describing the conservation of energy is written in terms of constant fluid density, heat capacity, and thermal conductivity. The solution of the equation can be written in a simple closed form for the case of a rectangular duct with isothermal walls. This solution (for the rectangular duct) cannot be found in the literature. The exact solution is developed here.