Effect of velocity non-uniformity on heat transfer in oscillating flow

Effect of velocity non-uniformity on heat transfer in oscillating flow is numerically investigated. The spectral method is used to solve the energy equation of the fluid. Both the Chebyshev polynomials and the Fourier series are utilized to suppose the form of the solution. A sinusoidal temperature profile, which is a basis of a Fourier series, is utilized at the wall. The results show that the Nusselt number is greatly affected by velocity profiles because heat transfer in oscillating flow is related to both conduction and advection. Heat is transferred from the channel wall to fluid center by conduction, then axially transferred by advection. Therefore, heat transfer in oscillating flow is governed by two non-dimensional parameters: the kinetic Reynolds number and the Peclet number, which are related to velocity profiles and the transverse conduction, respectively. When the Womersley number is small, the parabolic velocity profile is observed. In this case, there is no advection near the wall so that it is hard to transfer heat by advection in that region. On the other hand, axial heat transfer near the wall is increased as the kinetic Reynolds number increases. This is because the fluid motion near the wall is active when the kinetic Reynolds number is large. If we assume the uniform velocity profile, the Nusslet number is significantly overestimated because that assumption is identical to the infinitely large kinetic Reynolds number. In order to visualize the effect of velocity non-uniformity on heat transfer, time-averaged heatlines are proposed. Time-averaged heatlines give a better understanding of heat transfer in oscillating flow. From the present study, it is revealed that heat transfer in oscillating flow is affected by the velocity profiles and velocity non-uniformity should be accounted for to avoid the overprediction.