An approximate method for transient behavior of finned-tube cross-flow heat exchangers

A closed, approximate, analytical approach is obtained for transient behavior of finned-tube, liquid/gas cross flow heat exchangers for the step change in the inlet temperature of the hot fluid. In this two-solid heat capacity approach, the heat capacities of the hot and cold fluids and the heat capacity of the wall and the fins are lumped separately. The temperature variation of both fluids between inlet and outlet is assumed to be linear. It is also assumed that flow rates and inlet conditions remain fixed for both fluids, except for the step change imposed on the inlet temperature of the hot fluid. Energy equations for the hot and cold fluids, fins and walls for both approaches are derived and solved analytically. The variation of the exit temperatures of both fluids with time are obtained for a step change in the inlet temperature of the hot fluid. The dynamic behavior of the heat exchanger is characterized by time constant, delay time and gain. This approach is easier to apply and can easily be modified for other heat exchanger types. Results are compared with the experimental and numerical results given in the literature.