Oscillating heat transfer is a fundamental phenomenon occurring in Stirling machines and IC engines. A group of relevant dimensionless numbers which characterize this problem is identified by dimensional analysis. The convective heat transfer coefficient, or Nusselt number, is a function of the Reynolds number, the Prandtl number, plus the dynamic Reynolds number and the dimensionless amplitude, when compressibility is not considered. The case for compressible fluid is more complicated. An experiential study confirms above analysis and results in a nonlinear longitudinal fluid temperature distribution in the pipe. The history effect is found to affect the heat transfer rate remarkably. A correlation equation for Nusselt number is obtained by multivariate analysis.