Fractal slice model analysis for effective thermal conductivity and temperature distribution of porous crystal layer via layer crystallization

Abstract

A fractal slice model was established based on the reported model to predict the effective thermal conductivity of a porous crystal layer via layer crystallization. The temperature distribution of the crystal layer was obtained by the fractal slice method. The simulation results agreed with the experimental data better than the other theoretical models. The results were helpful to enhance the thermal transport by mitigating the thermal resistance effectively.

Progress in the Application of Fractal Porous Media Theory to Property Analysis and Process Simulation in Melt Crystallization

“…The simulative results of fractal slice model agree with the measured data better than the nonfractal model, which indicates that the porous crystal layer has an extraordinarily complex structure and possesses the fractal properties. 64 Thus, connection between crystal and liquid phase enhances the heat conduction that cannot be simulated by conventional Euclidean geometry model. This conclusion agrees with the result reported by Zhu et al 54 Moreover, the deviation of the fractal model decreases when the setting slice number becomes greater, which indicates that a fractal slice model with thinner slices (closer to the actual situation) can simulate the thermal property of porous crystal layer with better accuracy (the average deviation of the fractal slice model with 20 slices is 3.6%, and the average deviation of the fractal slice model with 2 slices is 4.6%, while that of a nonfractal model is 11.8%).…”

“…This conclusion agrees with the result reported by Zhu et al 54 Moreover, the deviation of the fractal model decreases when the setting slice number becomes greater, which indicates that a fractal slice model with thinner slices (closer to the actual situation) can simulate the thermal property of porous crystal layer with better accuracy (the average deviation of the fractal slice model with 20 slices is 3.6%, and the average deviation of the fractal slice model with 2 slices is 4.6%, while that of a nonfractal model is 11.8%). 64 This result is very important to the thermal balance during the layer growth model development; meanwhile, the thermal effect of fouling layer on the cooling surface can be evaluated by this fractal slice model, rather than the conventional empirical one. 67 In addition, fractal slice analysis also offers the temperature distribution along the crystal layer under a certain cooling curve, which is very helpful for the enhancement of the thermal conduction.…”

“…Meanwhile, the random distribution of pores in the crystal layer is not as “random” as the common FPM: The porosities of the crystal layers are different from the cooling surface to the growing surface of the crystal layers, to simulate the porosity variation of the crystal layer, and then the thermal conductivity of the porous crystal layer is analyzed. The following assumptions had been proposed by Jiang and Wang: Heat transfer from the crystal/liquid (C/L) interface to the cooling surface is an ideal one-dimensional process under the experimental conditions (the experimental setup can be found in ref ). The porous crystal layer is at the phase equilibrium state, which is a principal assumption to calculate the porosity. Thus, the liquid concentration in any cross section corresponds to the saturation concentration at the respective equilibrium temperature. The migration of the entrapped liquid occurs simultaneously with the layer growth.…”

A Discussion on Fractal Models for Transport Physics of Porous Media

“…Several researchers 62-65 applied the fractal scaling laws for pore size distribution and fractal capillary bundle model to study gas diffusion in the porous gas diffusion layer of proton exchange membrane fuel cell. Ng and Kim 66 introduced fractal method to model the permeability of membrane bioreactor for municipal wastewaters, and Othman et al 67 [79][80][81] used the fractal porous media model to simulate the structure of the crystal layer in melt crystallization. They stated that fractal porous media model and fractal theory has potential theoretical value on exploring the relationship between the crystal structure and the fractal porous media and crystal engineering especially on hyperpure product preparation.…”

Porosity Distribution Simulation and Impure Inclusion Analysis of Porous Crystal Layer Formed via Polythermal Process

“…Simultaneously, the theory and research technology development on the structure and transport process analysis of complex porous media have achieved significant progress in recent decades [22,23]. The developed model can simulate the thermal properties [24,25], permeability of porous media [26,27] and the seepage, percolation and imbibition in porous media [28,29]. The application of such research progress covered various chemical engineering research aspects, such as crystallization [3,[30][31][32][33][34][35], drying [36][37][38][39], dropwise condensation [40], etc.…”