Immersed volume method for solving natural convection, conduction and radiation of a hat‐shaped disk inside a 3D enclosure

Abstract

Purpose

The purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.

Design/methodology/approach

The incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.

Findings

In the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.

Originality/value

The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

Citation

Hachem, E., Digonnet, H., Massoni, E. and Coupez, T. (2012), "Immersed volume method for solving natural convection, conduction and radiation of a hat‐shaped disk inside a 3D enclosure", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 6, pp. 718-741. https://doi.org/10.1108/09615531211244871