Equipartition principle heat exchanger

Example 5.7 Equipartition principle Heat exchanger For a heat exchanger operating at steady state, the total entropy generation P is obtained by integrating over the surface area 

An average driving force over the surface area is obtained as 

The above equation shows that for a given surface area A and constant L, specification of the duty leads to the average driving force. 

Minimizing the integral in Eq. (5.90) subject to a constraint given in Eq. (5.91) is a variational problem, and the solution by the Euler equation in terms of the force is given by (Tondeur, 1990) 

The above equation implies that the extremum is a minimum. Thus, with a constant transfer coefficient, the distribution of the driving force that minimizes the entropy generation under the constraint of a specified duty is a uniform distribution. The minimal dissipation for a specified duty implies the equipartition of the driving force and entropy generation along the time and space variables of the process. 

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