Numerical simulation of heat transfer for pulsating laminar flow in a flat channel
Keywords:
heat transfer, pulsating laminar flow, flat channel, numerical simulationAbstract
A solution of the energy equation for a developed unsteady laminar flow of liquid in a flat channel with a constant heat flux density on the wall is presented. It was assumed that the average velocity over the cross section varied in accordance with a harmonic law with time. The equation was solved using the finite-difference method. The longitudinal velocity appearing in the energy equation was calculated previously by solving the equation of motion. The calculations were performed for the oscillation amplitudes A = 0.1-5 of the velocity averaged over the cross section in a wide range of dimensionless hydrodynamic and thermal oscillation frequencies from a quasi-steady state to a high-frequency mode. In the quasi-steady state mode, the average bulk temperature of liquid and the Nusselt number correspond at each moment of time to the dependences for steady flow on the Reynolds number varying over the oscillation period. In the high-frequency mode, the distributions of wall temperature and bulk liquid temperature over the channel length contain nodal points free from oscillation. The distance between these nodal points is inversely proportional to the square of the dimensionless thermal oscillation frequency. Unlike the vibrations of hydrodynamic variables, the fluctuations of thermal variables are not harmonic in nature, which is especially noticeable in the quasi-steady state mode. Their fluctuations can be characterized only by certain amplitudes and phases, for example, at the points of maximum and minimum. The values of thermal quantities averaged over the oscillation period may differ from their values in steady flow. Variations of the amplitudes and phases of the bulk liquid temperature, wall temperature, and Nusselt number over the length are calculated. A case is considered in which the beginning of heating is preceded by an adiabatic segment, which has an effect on the calculation results at oscillation amplitudes A > 1. The Nusselt number averaged over the oscillation period may be significantly higher than its value for steady flow, which was observed in some experiments. The maximal Nusselt number is located close to the heated portion inlet. A comparison is made between the results of calculations carried out for the cases corresponding to the boundary conditions of the first and second kind. In the first case, the Nusselt number shows a more significant increase, and its maximum is located directly at the heated portion inlet.
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