Numerical determination of boundary heat fluxes in an enclosure dynamically with natural convection through Fletcher–Reeves gradient method

Abstract

An iterative Fletcher–Reeves conjugate gradient method (CGM) is adopted to estimate the boundary heat fluxes in a fluid-saturated enclosure, where the fluid flow is dynamically coupled with the heat convection. The sets of direct, sensitivity and adjoint equations required for the solution of the inverse problem are formulated in terms of an arbitrary domain in two dimensions. The methodology of conjugate gradient method solves the inverse natural convection problem satisfactorily without any a priori information about the unknown heat fluxes. The pressure-correction method is utilized to solve the continuum direct, sensitivity and adjoint problems by enforcing global mass and energy conservations. Effects of boundary heat flux profile and thermal Rayleigh number on the convective heat transport are investigated. The effects of position and number of temperature sensors on the inverse problem solution are also addressed in this paper. Inverse solutions of noise data are regularized with the Discrepancy Principle of Alifanov; otherwise, the high frequency components of the random noise were reproduced.