Archive
Special Issues Volume 4, Issue 1, March 2018, Page: 1-13
Numerical Analysis of Fluid Flow and Heat Transfer Based on the Cylindrical Coordinate System
Mohammad Hassan Mohammadi, Institute of Mathematics, Department of Differential Equations, National Academy of Sciences of Armenia, Marshal Baghramyan Av., Yerevan, Armenia
Received: Oct. 18, 2017;       Accepted: Dec. 8, 2017;       Published: Jan. 15, 2018
Abstract
In this work we will apply the three-dimensional mathematical modelling of fluid flow and heat transfer inside the furnaces based on the cylindrical coordinate system to describe the behavior of the transport phenomena. This modelling is constructed by using the mass, momentum, and energy conservation laws to achieve the continuity equation, the Navier-Stokes equations, and the energy conservation equation. Due to the moving boundary between the solid and melted materials inside of the furnaces we will impose the Stefan condition to describe the behavior of the free boundary between two phases. We will derive the variational formulation of the system of transport phenomena, then we will discrete the domain to complete the finite element method stages and we will obtain the system of nonlinear equations in 256 equations in 256 unknowns. To get the numerical solution of the large-scale system we will prepare a convenient mathematical work and gain some diagrams where they would be applicable in the design process of the furnaces shapes.
Keywords
Fluid Flow, Heat Transfer, Mathematical Modeling, Stefan Condition, Cylindrical Coordinate
Mohammad Hassan Mohammadi, Numerical Analysis of Fluid Flow and Heat Transfer Based on the Cylindrical Coordinate System, Fluid Mechanics. Vol. 4, No. 1, 2018, pp. 1-13. doi: 10.11648/j.fm.20180401.11
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