Temperature distribution in an oscillatory flow with a sinusoidal wall temperature

The temperature field generated by an oscillatory boundary layer flow in the presence of a wall with a sinusoidal temperature distribution is analyzed. A linear perturbation method is used to find closed form analytical solutions for the temperature field when the amplitude of the velocity oscillation is small. The analytical solutions only consider longtime behavior when the temperature fields oscillate with the frequency of the flow. The structure of the equation that governs the temperature correction due to convection is similar to that of diffusive waves with the solution consisting of traveling or standing waves. The temperature distribution is also solved numerically which allows a description of the transient and periodic temperature fields. At short times, the solution has similarities with the traveling waves, while at long times the solution evolves toward a standing wave. As the amplitude of the solution is increased, beyond the linear approximation, the temperature oscillation remains periodic, but more Fourier modes are incorporated. We find that in all cases, the long-time, time averaged heat transfer from the boundary to the fluid is zero. 2004 Published by Elsevier Ltd.