Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure : heat flow visualization through energy flux vectors

Venkatadri, K; Beg, OA; Rajarajeswar, P; Prasad, VR

Abstract

A theoretical and numerical study of natural convection intwo-dimensional laminar
incompressible flow in a trapezoidal enclosurein the presence of thermal radiation is conducted,
motivated by energy systems applications. Heat flow visualization via the method of energy flux
vectors (EFVs) is also included. The trapezoidal cavity has an inclined top wall which in addition to the bottom wall is maintained at constant temperature, whereas the remaining (vertical side)
walls are adiabatic. The governing partial differential conservation equations are transformed
using a vorticity-stream function formulation and non-dimensional variables and the resulting
nonlinear boundary value problem is solved using a finite difference method with incremental time
steps. EFVs provide abundant details of the heat flow at the core of the enclosure. The larger
energy flux vectors indicate high temperature gradient zones and the sparse EFVs correspond to
low temperature gradient zone. Heat flow distribution in the trapezoidal enclosure can be clearly
elaborated via energy flux vectors and provides a deeper insight into thermal characteristics. A
comprehensive parametric study is performed to evaluate the impact of Rayleigh number
(buoyancy parameter) and radiation parameter on transport phenomena. The computations indicate
that local Nusselt number and velocity are increasing functions of the Rayleigh number and
radiation parameter. Significant changes in streamlines, temperature contours and energy
streamlines for high Rayleigh number are observed. The energy flux vectors show that a large eddy
is formed within the enclosure which migrates towards the cold wall. Greater thermal buoyancy
force accelerates the primary flow whereas it decelerates the secondary flow. The simulations are
relevant to solar collector systems, enclosure fire dynamics, electronic cooling and fuel cell
systems. Furthermore, the computations furnish a good benchmark for more general computational
fluid dynamics (CFD) analysis with commercial software e.g. ANSYS FLUENT.

Citation

Venkatadri, K., Beg, O., Rajarajeswar, P., & Prasad, V. (2020). Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure : heat flow visualization through energy flux vectors. International Journal of Mechanical Sciences, 171, https://doi.org/10.1016/j.ijmecsci.2019.105391

• Journal Article Type: Article
• Acceptance Date: Dec 12, 2019
• Online Publication Date: Dec 23, 2019
• Publication Date: Apr 1, 2020
• Deposit Date: Dec 12, 2019
• Publicly Available Date: Dec 23, 2020
• Journal: International Journal of Mechanical Sciences
• Print ISSN: 0020-7403
• Publisher: Elsevier
• Volume: 171
• DOI: https://doi.org/10.1016/j.ijmecsci.2019.105391
• Publisher URL: https://doi.org/10.1016/j.ijmecsci.2019.105391
• Related Public URLs: https://www.sciencedirect.com/journal/international-journal-of-mechanical-sciences