I am solving the user-defined transport equation for potential in fluent. A more detailed explanation of my question is mentioned in ppt file, please open that file. Kindly help me.
My confusion in diffusion material property (unit) and source term. If I use dimensionless value as diffusivity then the left-hand side unit( [kg/ms]*[scalar/m^2]) and right-hand side unit ( [C/m^3]/[C^2 N^-1 m^-2]) which is not equal.
On Quantum Theory of Transport Phenomena: Steady Diffusion
Sadao Nakajima
Progress of Theoretical Physics, Volume 20, Issue 6, December 1958, Pages 948–959, https://doi.org/10.1143/PTP.20.948
Article historyPublished:01 December 1958
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Abstract
A general formulation is given to the quantum theory of steady diffusion. In seeking for a steady solution of Liouville's equation, the boundary condition is taken into account by requiring that the solution should lead to a given distribution of average density. The distribution is to be determined by macroscopic law of diffusion and macroscopic boundary condition.The basic equation thus obtained has a form similar to Bloch's kinetic equation and reduces to the latter in the limit of a system of weakly interacting particles. This is shown by generalizing a demping theoretical expansion of Kohn and Luttinger.It is found that the Einstein relation is valid only for the symmetric part of diffusion- and electric conductivity tensors, in agreement with Kasuya's suggestion.
Modeling of heat transport phenomena using the equations of mathematical physics
C Nolasco Serna1, N Afanador Garcia2 and G Guerrero Gómez3
Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 2102, IV International Seminar on Pedagogical Practice (IV ISPP) 26-27 August 2021, San José de Cúcuta, Colombia Citation C Nolasco Serna et al 2021 J. Phys.: Conf. Ser. 2102 012016 DOI 10.1088/1742-6596/2102/1/012016
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Abstract
The study of physical phenomena that include conservative principles is part of the research field of the equations of mathematical physics. To deepen in methods to solve the equations of mathematical physics is a contribution in understanding the modeling of applications in different areas. This research studies the physical phenomenon of heat transport with convection from the viewpoint of modeling with differential equations. The advantage of working with equations is to apply the techniques of mathematical analysis and numerical methods to obtain the temperature function. In the research, the solution of the heat transport model is computed according to the analytical method of separable variables in order to represent the temperature function as a trigonometric series. With the help of a simple numerical method, it is possible to derive a scheme of calculation of the temperature function. By performing a case study, the methods are compared, and their fit is verified by simulation.
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