This application models the temperature dynamics of a countercurrent double pipe heat exchanger. Three partial differential equations are derived from heat balances across the tube- and shell-side liquids, and the tube wall (accounting for heat flow from the shell- and tube-side liquids, and conduction along the length of the tube). The equations are solved numerically, and the temperature profiles are plotted. The heat exchanger is assumed to be perfectly insulated. Densities, specific heat capacities, heat transfer coefficients, and thermal conductivities are assumed to be constant.