Controlling and maximizing effective thermal properties by manipulating transient behaviors during energy-system cycles

Transient processes generally constitute part of energy-system cycles. If skillfully manipulated, they actually are capable of assisting systems to behave beneficially to suit designers needs. In the present study, behaviors related to both thermal conductivities ($kappa$) and heat capacities ($c_{v}$) are analyzed. Along with solutions of the temperature and the flow velocity obtained by means of theories and simulations, three findings are reported herein: $(1)$ effective $kappa$ and effective $c_{v}$ can be controlled to vary from their intrinsic material-property values to a few orders of magnitude larger; $(2)$ a parameter, tentatively named as nonlinear thermal bias, is identified and can be used as a criterion in estimating energies transferred into the system during heating processes and effective operating ranges of system temperatures; $(3)$ When a body of water, such as the immense ocean, is subject to the boundary condition of cold bottom and hot top, it may be feasible to manipulate transient behaviors of a solid propeller-like system such that the system can be turned by a weak buoyancy force, induced by the top-to-bottom heat conduction through the propeller, provided that the density of the propeller is selected to be close to that of the water. Such a turning motion serves both purposes of performing the hydraulic work and increasing the effective thermal conductivity of the system.

Entropy variation rate divided by temperature always decreases

For an isolated assembly that comprises a system and its surrounding reservoirs, the total entropy ($S_{a}$) always monotonically increases as time elapses. This phenomenon is known as the second law of thermodynamics ($S_{a}geq0$). Here we analytically prove that, unlike the entropy itself, the entropy variation rate ($B=dS_{a}/dt$) defies the monotonicity for multiple reservoirs ($ngeq2$). In other words, there always exist minima. For example, when a system is heated by two reservoirs from $T=300,K$ initially to $T=400,K$ at the final steady state, $B$ decreases steadily first. Then suddenly it turns around and starts to increases at $387,K$ until it reaches its steady-state value, exhibiting peculiar dipping behaviors. In addition, the crux of our work is the proof that a newly-defined variable, $B/T$, always decreases. Our proof involves the Newtons law of cooling, in which the heat transfer coefficient is assumed to be constant. These theoretical macro-scale findings are validated by numerical experiments using the Crank-Nicholson method, and are illustrated with practical examples. They constitute an alternative to the traditional second-law statement, and may provide useful references for the future micro-scale entropy-related research.