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The irreversibility of heat conduction in porous media, its relation to effective thermal conductivities (ETCs), and the optimization of thermal conduction process are investigated in this work based on the concept of entransy dissipation. Two more new concepts of reference entransy dissipation and nondimensional entransy dissipation are first introduced. Then it is showed that the nondimensional entransy dissipation rate (NER) can be employed as an objective function to evaluate the efficiency of a thermal transfer process in a porous material. By using this criterion and a newly developed structure growth algorithms, different porous structures were generated and the corresponding values of both ETC and NER were derived to illustrate the usefulness and power of using NER to assess the thermal performance of the materials. The results show that the effective thermal conductivity not only influences the heat transfer ability of porous media, but also reflects the irreversibility of heat conduction in porous media, which is a dissipation coefficient for heat transfer. Meanwhile, decreasing the structural particle size will increase the contact points, i.e. more heat bridges, decrease the temperature gradient nearby the contact points, and hence significantly increase the effective thermal coefficient of porous media. Essentially, decreasing the particle size will result in a more uniform distribution of both temperature gradient and local entransy dissipation rate along the heat flow direction, and consequently lead to a larger effective thermal conductivity.

Irreversibility of Heat Conduction in Complex Multiphase Systems and Its Application to the Effective Thermal Conductivity of Porous Media