A distributed parameter model for a shell and tube heat-exchanger is derived from first principles using the energy conservation law (energy balance) and used for predicting the temperature profiles set up along the length of the equipment. The model is solved numerically using the Runge-Kutta four parameter procedure and analytically and the results show the temperature distribution as being exponentially asymptotic in nature, i.e., the tube fluid temperature (the coolant) rises asymptotically but never equals the shell side fluid temperature (hot fluid) which is in agreement with reality. The tube fluid is water at ambient temperature (31°C) and the shell side fluid, steam in the process of condensing. The model is robust and amenable to a program software package implementable on a desktop/laptop micro-computing facility.

non-dimensionalization, Laplace transformation, distributed parameter model.