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

Purpose This work aims to investigate two-dimensional transient natural convection in a horizontal annular sector containing heat-generating porous medium. Design/methodology/approach The generalized integral transform technique (GITT) was used to solve the governing equations in stream-function formulation and in log-polar coordinates. Double integral transforms are carried out in the azimuthal and radial directions, with the resulting system of nonlinear ordinary differential equations in time solved numerically. The GITT solutions are validated by comparison with fully numerical solutions by a 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, while less significant for temperature. To simplify calculations and remove variable interdependence, an auxiliary log-polar transformation was introduced, which effectively removed the need to compute Bessel functions associated with the eigenfunctions and eigenvalues in cylindrical coordinates, contributing to a significant increase in computational efficiency. Originality/value The use of log-polar transformation simplifies the calculations and decouples variables. An approach not previously found in the literature, this transformation eliminated the need to compute Bessel functions and significantly improved computational efficiency. The present hybrid analytical–numerical approach can be extended to solve other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in nuclear and other industries.