The comparison of a discrete-continuous approach and a method of finite differences in solving the problem of unsteady-state heat and moisture transfer in the building envelope

This article is devoted to the development of methods for calculating heat and humidity regime in the building envelope. The equation of steady-state thermal conductivity with boundary conditions of the third kind and the formula for calculating heat losses of a building based on the heat transfer equation have been considered. The equation of unsteady-state thermal conductivity as well as its solution using the discrete-continual approach has also been studied. The solution of the unsteady-state heat conductivity problem with invariable over time boundary conditions using the discrete-continuous approach was proposed by A.B. Zolotov and P.A. Akimov. The subsequent modernization of the solution was conducted by V.N. Sidorov and S.M. Matskevich. The unsteady-state equation of moisture transfer based on Fick’s second law using the theory of moisture potential is derived. The solution of the unsteady-state moisture transfer equation using the finite difference method according to an explicit difference scheme as well as the solution of the unsteady-state moisture transfer equation using the discrete-continuous approach is demonstrated. To prove the effectiveness of using the discrete-continuous approach in the area of the unsteady-state humidity conditions we compared the calculation results of the distribution of moisture in a single-layer enclosing structure made of aerated concrete using two methods of moisture potential theory. It was found that the difference in the results of calculation by the discrete-continual formula and by the method of finite differences does not exceed 3.2%.

Heat and Mass Transfer Modeling to Predict Temperature Distribution during Potato Frying after Pre-Treatment with Pulsed Electric Field

Based on unsteady state heat conduction, a mathematical model has been developed to describe the simultaneous heat and moisture transfer during potato frying. For the first time, the equation was solved using both enthalpy and Variable Space Network (VSN) methods, based on a moving interface defined by the boiling temperature of water in a potato disc during frying. Two separate regions of the potato disc namely fried (crust) and unfried (core), were considered as heat transfer domains. A variable boiling temperature of the water in potato discs was required as an input parameter for the model as the water is evaporated during frying, resulting in an increase in the soluble solid concentration of the potato sample. Pulsed electric field (PEF) pretreatment prior to frying had no significant effect on the measured moisture content, thermal conductivity or frying time compared to potatoes that did not receive a PEF pretreatment. However, a PEF pretreatment at 1.1 kV/cm and 56 kJ/kg reduced the temperature variation in the experimentally measured potato center by up to 30%. The proposed heat and moisture transfer model based on unsteady state heat conduction successfully predicted the experimental measurements, especially when the equation was solved using the enthalpy method.

The Debye theory of solid-state heat capacities

“The Debye theory of solid-state heat capacities” gives a careful account of the Debye cut-off. We start by looking at a monatomic linear chain, leading to degrees of freedom and the equipartition of energy at the high-temperature (classical) limit. Reasonable approximations lead more naturally to the Born–von Karman model than to Debye, but Debye follows via a further reasonable step.