The ecological optimization of a generalized irreversible Carnot heat pump for a generalized heat transfer law, Journal of the Energy Institute, 78 (1), 2005, pp 5 - 10

The optimal ecological performance of an irreversible Carnot heat pump with the losses of heat
resistance, heat leak and internal irreversibility, in which heat transfer between the working fluid
and the heat reservoirs obeys a generalized heat transfer law q3(DT)n, is derived by considering
an ecological optimization criterion as the objective function, which consists of maximizing a
function representing the best compromise between the exergy output rate and exergy loss rate
(entropy production rate) of the heat pump. Some special examples are discusses. A numerical
example is given to show the effects of heat transfer law, heat leakage and internal irreversibility
on the optimal performance of the generalized irreversible heat pump. The results can provide
some theoretical guidance for the design of practical heat pumps.