Inverse determination of boundary heat fluxes in a porous enclosure dynamically coupled with thermal transport

The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy–Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher–Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated.