Heat transfer in the initial hydrodynamic section of a flat channel with boundary conditions of the first kind on the walls in laminar pulsating flow

The problem of heat transfer in a laminar developing pulsating flow in a channel in a quasi-steady mode is solved using the calculation results for a steady flow. A system of stationary equations of motion, continuity, and energy in the initial section of a flat channel is solved by the finite difference method using an iterative implicit unconditionally stable scheme. Two methods for calculating the oscillation-period-averaged Nusselt number are considered. The effect of the relative cross-sectional average amplitude $A$ of velocity oscillations, the dimensionless channel length, and the Prandtl number on the heat flux rate on the wall and the mass averaged temperature of the fluid is studied. Nusselt numbers are calculated in two different ways. It is found that, for relatively short channels, with values of $A$ greater than one, the length- and oscillation-period-averaged Nusselt numbers are noticeably higher than for a steady flow. It is shown that, for long channels, the ratio of the oscillation period-averaged Nusselt number to its steady-state value near the channel entrance has a maximum, the value of which increases with $A$.