Inverse conjugate heat conduction and natural convection inside an enclosure with multiple unknown wall heating fluxes

•Conjugate convection problem was investigated regarding of Ra, Rk and body size.•Inverse conjugate convection problem of estimating multiple wall heating fluxes.•Inverse solution accuracy could be influenced by Ra, sensors, and solid body.•Streamlines and heatlines could respectively represent transports of fluid and heat.•General procedures could be applied to inverse conjugate convection in enclosures. Inverse conjugate natural convection problem with multiple unknown heating fluxes is examined in this study by conjugate gradient method based on temperature measurements inside the enclosure. The direct problem, as well as the auxiliary problems, required for the solution of the inverse problem with the CGM is formulated in terms of the Cartesian coordinates. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Some parameters affect the fluid and heat transport significantly, which have been vividly analyzed by streamlines and heatlines, respectively. The effect of thermal Rayleigh number, body size, thermal conductivity of solid-to-fluid, number of blocks, heat flux profiles, measurement errors and the number of sensors on the inverse solution accuracy are respectively addressed. Inverse solutions obtained with simulated temperature measurements reveal that extremely accurate estimations could be obtained for the unknown heat flux functions with the present inverse problem approach. This research could be significant for the design of electronic cooling and enclosed air environment.