scholarly journals Modelling of Nonlinear Thermodiffusion for a Spherically Symmetric Case

2021 ◽  
Keyword(s):  
Heat Transfer ◽  
Constant Pressure ◽  
Linear Part ◽  
Average Kinetic Energy ◽  
X Rays ◽  
Transfer Coefficients ◽  
Finite Velocity ◽  
Heat Transfer Coefficients ◽  
Transfer Processes ◽  
Gas Molecules

The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source. In the previous papers A. J. Janavičius proposed the nonlinear diffusion equation which provided a more exact description of impurities diffusion by fast moving vacancies generated by X-rays in Si crystals. This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. Heat transfer in gas must be compatible with the Maxwell distribution function. Heat transfer in gas described by using nonlinear thermodiffusion equation with heat transfer coefficients directly proportional to temperature . The solution of the thermodiffusion equation in gas was obtained by using similarity variables. The equation is solved by separating the linear part of the equation that coincides with Fick's second law. The obtained results coincide with Ya.B. Zeldovich’s previously published solutions of nonlinear equations by changing the respective coefficients.

scholarly journals Nonlinear Thermodiffusion in Gases at Moderate Temperatures

2018 ◽  
Vol 55 (3) ◽  
pp. 34-42
Author(s):  
A.J. Janavičius ◽  
S. Turskienė
Keyword(s):  
Heat Transfer ◽  
Nonlinear Diffusion ◽  
Diffusion Processes ◽  
Average Kinetic Energy ◽  
Transfer Coefficients ◽  
Finite Velocity ◽  
Practical Applications ◽  
Heat Transfer Coefficients ◽  
Approximate Analytical Solutions ◽  
Gas Molecules

Abstract The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the diffusion processes, which occur with a finite velocity. In the previous papers, A. J. Janavičius proposed the nonlinear diffusion equation with the diffusion coefficient directly proportional to the concentration of impurities. This equation provides a more exact description of the profiles of impurities in Si crystals. The heat transfer in gases carries a greater average kinetic energy based on nonlinear diffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. In this case, the heat transfer in gases can be described by using nonlinear thermodiffusion equation with heat transfer and thermodiffusion coefficients directly proportional to temperature T. The obtained approximate analytical solutions are successfully applied in defining temperature profiles and heat transfer coefficients in gases as well as providing opportunities for practical applications. It has been concluded that heat spreading in gases depends on temperature differences and pressure in gases.

Toward the Detailed Simulation of the Heat Transfer Processes in Unsaturated Porous Media

2009 ◽  
Author(s):  
F. A. Jafar ◽  
G. R. Thorpe ◽  
O¨. F. Turan
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Unsaturated Porous Media ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Transfer Processes ◽  
Numerical Predictions ◽  
Three Phase ◽  
Detailed Simulation ◽  
Horizontal Cylinders

Trickle bed chemical reactors and equipment used to cool horticultural produce usually involve three phase porous media. The fluid dynamics and heat transfer processes that occur in such equipment are generally quantified by means of empirical relationships between dimensionless groups. The research reported in this paper is motivated by the possibility of using detailed numerical simulations of the phenomena that occur in beds of irrigated porous media to obviate the need for empirical correlations. Numerical predictions are obtained using a CFD code (FLUENT) for 2-D configurations of three cylinders. Local and mean heat transfer coefficients around these non-contacting horizontal cylinders are calculated numerically. The present results compare well with those available in the literature. The numerical results provide an insight into the cooling mechanisms within beds of unsaturated porous media.

scholarly journals Heat Transfer Process During Filtration Drying of Grinded Sunflower Biomass

2021 ◽  
Vol 15 (1) ◽  
pp. 118-124
Author(s):  
Diana Kindzera ◽  
◽  
Roman Hosovskyi ◽  
Volodymyr Atamanyuk ◽  
Dmytro Symak ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Process ◽  
Biofuel Production ◽  
Design Stage ◽  
Transfer Coefficients ◽  
Number Range ◽  
Velocity Increase ◽  
Heat Transfer Coefficients ◽  
Transfer Processes ◽  
Solid Biofuel

Filtration drying of grinded sunflower stems as the unit operation of the technological line for solid biofuel production has been proposed. Theoretical aspects of heat transfer processes during filtration drying have been analyzed. The effect of the drying agent velocity increase from 0.68 to 2.05 m/s on the heat transfer intensity has been established. The values of heat transfer coefficients have been calculated on the basis of the thin-layer experimental data and equation . Calculated coefficients for grinded sunflower stems have been correlated by the dimensionless expression within Reynolds number range of and the equation has been proposed to calculate the heat transfer coefficients, that is important for forecasting the heat energy costs at the filtration drying equipment design stage.

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