Analytical solution of thermodynamic control-volume energy equation with periodic heat-transfer and enthalpy flow

An analysis of a stationary control volume with periodically varying temperature streams of constant mass flow has been made. The heat-transfer rate, at the conducting boundary of the control volume, is an interdependent function of time, while the work-transfer rate to the control volume is assumed to be constant. Using a global approach, the outlet temperature history of the streams is predicted analytically when the frequency of the sinusoidally varying inlet temperature is relatively small. The analysis and results are pertinent to a wide range of practical engineering applications involving periodic heat transfer, and in particular those where relatively slow climatic or seasonal temperature variations must be catered for. As a demonstration of the method, a calculation for the temperature in a large ventilated underground void is presented for the situation when the variation of the temperature takes place annually. Such an example is commonplace in civil and building engineering.