scholarly journals Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

2017 ◽  
Vol 53 (11) ◽  
pp. 9960-9979 ◽  
Author(s):  
Quanlin Zhou ◽  
Curtis M. Oldenburg ◽  
Jonny Rutqvist ◽  
Jens T. Birkholzer
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Multidimensional Diffusion ◽  
Fundamental Analytical Solutions

scholarly journals Heat and mass transfer in the process of heat treatment and drying of natural leather with the convective method of energy supply

2021 ◽  
Vol 66 (1) ◽  
pp. 84-92
Author(s):  
A. O. Ol’shanskii ◽  
A. M. Gusarov ◽  
S. V. Zhernosek
Keyword(s):  
Heat Transfer ◽  
Heat Treatment ◽  
Mass Transfer ◽  
Heat Conduction ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Unsteady Heat Conduction

In the work, the authors investigated the possibility of using the results of analytical solutions of the linear differential equations of unsteady heat conduction with constant heat transfer coefficients to calculate the temperature of the material during heat treatment of leathers. Heat treatment of natural leathers as heat-sensitive materials is carried out under mild temperature conditions and high air moisture contents, the temperature does not undergo significant changes, and the heat transfer coefficients change almost linearly. When using analytical solutions, the authors made the assumptions that for small temperature gradients over the cross section of a thin body, the thermal transfer of matter can be neglected and for values of the heat and mass transfer Biot criteria less than unity, the main factor, limiting heat and mass transfer, is the interaction of the evaporation surface of the body with the environment; so, in solving the differential heat equation we can restrict ourselves to one first member of an infinite series. In this case, a piecewise stepwise approximation of all thermophysical characteristics with constant values of these coefficients at the calculated time intervals was applied, which made it possible to take into account the change in the transfer coefficients throughout the entire heat treatment process. Processing of experimental data showed that in low-intensity processes with reliable values of the transfer coefficients, it is possible to use the results of solutions of differential equations of unsteady heat conduction in heat transfer calculations. The results of the study of heat transfer during drying of leather confirm the laws of temperature change established experimentally. Together with experimental studies of drying processes, analytical studies are of great practical importance in the development of new methods for calculating heat and mass transfer in wet bodies.

scholarly journals New explicit analytical solutions of equations for heat and mass transfer in a cooling tower energy system

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989614
Author(s):  
Qianjian Guo ◽  
Xiaoni Qi ◽  
Peng Sun ◽  
Pengjiang Guo
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Solutions ◽  
Cooling Tower ◽  
Mass Transfer Process ◽  
Energy System ◽  
Transfer Model ◽  
Elementary Functions ◽  
Solutions Of Equations ◽  
The One

The aim of this article is to develop an accurate and fast analytical method for heat and mass transfer model in a cooling tower energy system. Some algebraic explicit analytical solutions of the one-dimensional differential equation sets describing the coupled heat and mass transfer process in a cooling tower are derived. The explicit solutions have not yet been published before. The explicit equations of heat and mass transfer are expressed in elementary functions. By solving these differential equations in a cooling tower, the temperature distribution of liquid and gas, the moisture content in the air can be obtained in each section over the vertical height of the tower. A comparison of analytical and experimental results was given in this article, and good agreements were shown for the typical cases studied. The analytical solutions can serve as a benchmark to check the results of numerical calculation.

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