Experimental and numerical study of inverse natural convection-conduction heat transfer in a cavity with a fin

The computational fluid dynamics (CFD) method along with the least squares method and overdetermined experimental data is used to investigate inverse 3D turbulent natural convection-conduction heat transfer in a cavity with a horizontal conduction fin on the vertical hot wall. The main purpose of this study is to predict the unknown heat transfer rate Q_h, the heat transfer coefficient on the solid wall, and fluid flow and heat transfer characteristics. To verify the accuracy of an appropriate flow model selected, the root mean square error between the CFD results for temperature obtained from it and all experimental data needs to be the smallest among the selected flow models. The Nusselt numbers obtained also need to be closer to existing correlations or results than those obtained by other flow models. The validation tests through various flow models show that the appropriate flow model for dimensionless distance S_p = H_fp/L_w = 7/24 is the standard k-ε model with dimensionless fin length L_p = L/L_w = 1/4 and Ra = 4.59 × 10⁶ and the zero-equation model with L_p = 2/3 and Ra = 2.33 × 10⁶, respectively. This means that an appropriate flow model may be related to L and Ra. Compared to the isothermal wall assumption, the present results are more accurate, and less experimental temperature data are required.