Entranspy And Its Applications In Heat Transfer Optimization

Many motions in nature take the easiest or minimum paths, which are described in physics by the principles of least action. The subject of heat transfer is to investigate the nature of heat transport phenomena, especially the heat transfer rate. Therefore, the principle of least action in heat transfer is studied and new principles are developed. Based on the principles, the heat transfer process is optimized to maximize the heat transfer rate, so that the heat flux is controlled to flow along the easiest or quickest path for the given conditions.Firstly, two extremum principles in non-equilibrium thermodynamics, the principle of least dissipation of energy and the principle of minimum entropy production, are analyzed. The linear phenomenological law for heat flux and temperature is found to be different from the Fourier Law because entropy and entropy production are the thermodynamic properties to measure the conversion efficiency of heat to work. The entropy production corresponds to the loss of available energy. Therefore, based on the conception of entropy, principle of least dissipation of energy and the principle of minimum entropy production are unavailable for the analysis or the optimization of the heat transfer rate. For the heat transfer process following the Fourier Law, a new special word, "entranspy", is created to define a new physical property, which means the overall capability of heat transport. In reversible process, there is the entranspy conservation, that is, no loss of capability of heat transport. However, in irreversible process where the heat flows from high temperature to low temperature, the entranspy should be dissipated and the heat transport capability should be reduced. Based on the concept of entranspy, the principle of extremum entranspy is developed by the weighted residual method, which includes the principle of minimum entranspy in the temperature representation and the principle of minimum entranspy in the heat flux representation. The principle of extremum entranspy renders the heat transfer process completely, that is, the principle is equivalent to the Fourier Law, energy conservation equation and the boundary conditions. According to the principle of extremum entranspy, the principle of extremum entranspy dissipation is presented for heat transfer enhancement. The principle of extremum entranspy dissipation includes two principles, which correspond to the two goals of heat transfer enhancement respectively. When the enhancement aims to minimize the temperature difference for given heat flux, the optimization follows the principle of minimum entranspy dissipation in temperature representation. Alternatively, when the enhancement maximizes the heat flux for given temperature difference, the optimization follows the principle of maximum entranspy dissipation in heat flux representation. Then, the principle of extremum entranspy dissipation is applied to optimize the volume-to-point problem. Both the theoretical and numerical results show higher heat transfer rate than those obtained by the method of entropy generation minimization. The comparison shows that the principle of extremum entranspy dissipation is to maximize the heat transfer rate, while the entropy generation minimization is to minimize the loss of available energy. At the same time, the result of the principle of extremum entranspy dissipation is characterized by the uniform temperature-gradient, which is exactly the principle to optimize the distribution of high conductivity material in bionic optimization method. Finally, the weighted residual method is also applied to modify and complete the principle of least dissipation of energy to represent the transport process of available energy. Then the relation between the principle of least dissipation of energy and the principle of minimum entropy production is analyzed. The result shows that the minimum entropy production is not an independent principle but a reformulation of the principle of least dissipation of energy for special cases.