Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects

Beg, OA; Venkatadri, K; Prasad, VR; Beg, TA; Kadir, A; Leonard, HJ

Abstract

We present a mathematical and numerical study of the transient Marangoni thermo-convection flow of an
electrically conducting Newtonian fluid in an isotropic Darcy porous rectangular semiconductor melt
enclosure with buoyancy and internal heat generation effects, in an (x, y) coordinate system. The
governing equations comprising the mass conservation, x-direction momentum, y-direction momentum
and energy equation are formulated subject to a quartet of boundary conditions at the four walls of the
enclosure. The upper enclosure wall is assumed to be “free” with an appropriate surface tension dynamic
boundary condition. A series of transformations are implemented to render the mathematical model
dimensionless and into a vorticity form. The governing thermophysical parameters are shown to be the
Marangoni number for surface tension (thermocapillary) effects (Ma), Prandtl number (Pr), Grashof
number for buoyancy effects (Gr), enclosure aspect ratio (A), Hartmann hydromagnetic number (Ha),
Darcy number for bulk porous resistance (Da), and the internal heat generation parameter () the latter
being a function of the internal (RaI) and global Rayleigh numbers (Ra). An efficient finite difference
numerical method is employed to solve the boundary value problem. Validations with earlier purely fluid
solutions (Da →) are included. A mesh-independence test is included with further validation with other
published studies. Isotherms and isovels (streamlines) are computed as are Nusselt numbers at selected
boundaries. Solutions for the case of Pr = 0.054 (semiconductor melt) are also compared with earlier
studies showing excellent correlation. The model finds applications in the bulk crystal growth of
semiconductors, electromagnetic materials processing control and also hybrid fuel cells.

Citation

Beg, O., Venkatadri, K., Prasad, V., Beg, T., Kadir, A., & Leonard, H. (2020). Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects. Materials Science and Engineering: B, 261, 114772. https://doi.org/10.1016/j.mseb.2020.114722

• Journal Article Type: Article
• Acceptance Date: Aug 14, 2020
• Online Publication Date: Sep 10, 2020
• Publication Date: Nov 1, 2020
• Deposit Date: Aug 21, 2020
• Publicly Available Date: Mar 10, 2022
• Journal: Materials Science and Engineering B
• Print ISSN: 0921-5107
• Publisher: Elsevier
• Volume: 261
• Pages: 114772
• DOI: https://doi.org/10.1016/j.mseb.2020.114722
• Publisher URL: https://doi.org/10.1016/j.mseb.2020.114722
• Related Public URLs: http://www.journals.elsevier.com/materials-science-and-engineering-b/