Based on recent developments in the so-called Coupled Integral Equation Approach for the approximate solution of heat and mass diffusion problems, the classical lumped-differential formulation for double-pipe heat exchangers is extended and significantly improved in terms of overall accuracy. The energy equation for the outer annular channel is formally integrated and temperature gradients approximately taken into account, in contrast to the conventional lumped system analysis. The resulting partial differential equation for the inner stream, involving a more general type of boundary condition, is analytically handled through the generalized integral transform technique. A critical accuracy analysis is then performed in order to demonstrate the improvement over the plain lumped-differential formulation.

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