Experimental and numerical studies on heat transfer enhancement in the silicothermic reduction process

Zhang, Chao; Yan, Weijie; Che, Yusi; He, Jilin; Wang, Xuebin

doi:10.1016/j.egyr.2022.05.103

Cited by 5 publications

(3 citation statements)

References 36 publications

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“…Remark 2. The equation that describes the propagation of heat in an isotropic and homogeneous medium in three dimensions is presented in Equation (6).…”

Section: Methodsmentioning

confidence: 99%

“…Substitution of ( 12) into (6) yields the expression shown in (13), whose identity proves that polynomial given in (11) is a solution to the heat diffusion equation described in (6).…”

mentioning

confidence: 89%

“…A heat diffusion equation is a partial differential equation (PDE) that models the spatial distribution and the time evolution of temperature in a body under specific initial and boundary conditions [1][2][3][4], it is widely used in heat transfer process [5][6][7], and it can be formulated from one to three spatial dimensions and one temporal dimension, in such case it would contain a transient state. It can also be found in rectangular, cylindrical, and spherical coordinates.…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solutions Formulated in the Time Domain for Three-Dimensional Heat Diffusion Equation

Rojas

2022

Processes

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Two different strategies are provided to generate solutions to the three-dimensional heat diffusion equation. The first strategy is inspired by the well-known one-dimensional heat polynomial, which consists of an infinite set of polynomials, which are solutions to the one-dimensional heat diffusion equation. The second strategy is based on an exponential type function. None of the solutions presented here can be obtained by the method of separation of variables. The mathematical developments proving that, indeed, the particular solutions generated with both strategies satisfy the three-dimensional heat diffusion equation are presented. The analytical solutions are validated by generating the corresponding numerical solutions with the method of finite differences. When comparing both analytical and numerical solutions, it is found that they are identical. In addition, as part of the results, it is found that there are exponential solutions that reproduce the behavior of polynomial solutions. Finally, an example of the use of heat polynomials in engineering applications is provided.

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“…Remark 2. The equation that describes the propagation of heat in an isotropic and homogeneous medium in three dimensions is presented in Equation (6).…”

Section: Methodsmentioning

confidence: 99%

“…Substitution of ( 12) into (6) yields the expression shown in (13), whose identity proves that polynomial given in (11) is a solution to the heat diffusion equation described in (6).…”

mentioning

confidence: 89%