Natural convection in a horizontal annular sector containing heat-generating porous medium

Abstract

Purpose The purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. Design/methodology/approach GITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost. Findings The effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium. Originality/value The strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.

Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

“…Recently, hybrid analytical-numerical approaches, the finite integral transform method and the generalized integral transform technique (GITT) (Cotta and Mikhailov, 1997;Cotta, 1998;An and Su, 2014), has been developed to solve the structural mechanics problems (Li et al, 2019;Zhang et al, 2019a;Ullah et al, 2019;An et al, 2020;Li et al, 2020;He et al, 2021), and heat and fluid problems (An et al, 2013;Fu et al, 2018;Lisboa et al, 2018Lisboa et al, , 2019Machado dos Santos et al, 2022). The GITT method essentially preserves the properties of partial differential equations, which is different from the physics-preserving schemes of the finite difference method and the finite element method (Zhao et al, 2017;Shen et al, 2018;Jiang et al, 2021Jiang et al, , 2022.…”