Liquid solidification in a convectively‐cooled parallel‐plate channel

A theoretical analysis of liquid solidification in the thermal entrance region of a parallel‐plate channel with a uniform external convection is carried out by using the confluent hypergeometric function in the solution for laminar flow and steady‐state conditions. Theoretical results are obtained for liquid solidification‐free length, liquid‐solid interface profile, pressure drop, bulk temperature, heat transfer rate and local Nusselt number for the cases of Biot numbers Bi = 0.25, 0.5, 1, 2, 10, ∞, superheat ratios ∈ = 1, 2, 4, 8, Pr = 13.2 and k 1 /k 2 = 0.25 using 20 eigenvalues. The convective boundary condition allows one to evaluate the effect of external convection cooling including the effect of thermal insulation.