A study on the thermal hydraulic characteristics of the Passive Residual Heat Removal(PRHR) system employed in Advanced Light Water Reactors(ALWR) has been performed. A simple one-dimensional lumped parameter model has been developed to predict the time dependent primary system temperature resulting from the heat transfer through the heat exchanger tube to the In-containment Refueling Water Storage Tank. Three time-dependent governing equations and one constitutive equation for the heat exchanger are discretized and a simplified computer program has been developed using Newton-Raphson method. For verification of the developed computer program, the calculation results are compared with the analysis data reported in the Westinghouse Standard Safety Analysis Report(SSAR). Overall results are similar to those of SSAR. The sensitivity analyses for important design parameters of the heat exchanger such as tube wall thickness, tube length, and tube inner diameters are also performed to see the effects on heat transfer rate through the heat exchanger tube.