Heat Transfer in the Initial Hydrodynamic Section of a Flat Channel with Boundary Conditions of the Second Kind in a Laminar Pulsating Flow

A method for solving the problem of heat transfer in a pulsating quasi-stationary flow in a channel is proposed, based on the use of calculation results for a stationary flow. This approach is applicable at low relative oscillation frequencies (for Womersley numbers less than one). The solution to the system of stationary equations of motion, continuity, and energy in the initial section of a flat channel is carried out by the finite difference method using an iterative implicit unconditionally stable scheme. Two methods for calculating the average Nusselt number over the oscillation period are considered. It is proposed to divide the oscillation period into two parts, in the first of which the fluid flows from the inlet to the channel to its outlet (direct flow), and in the second part of the period, in the opposite direction (reverse flow), which is appropriate when using the calculation results in practical applications. It is shown that an enhancement of heat transfer when flow pulsations are superimposed on a laminar flow is observed only for large values of the amplitude of the oscillation of the cross-section average velocity greater than one. The influence of the regime parameters—the dimensionless channel length and Prandtl number—on the Nusselt number is investigated. It is found that for relatively short channels, the Nusselt numbers averaged over the length and period of oscillations can exceed these values up to 1.5 times for a steady flow. It is shown that the results of heat transfer calculations under boundary conditions of the first and second kind are close to each other.