The limits of isothermal model validity in the case of natural convection cooling of heating blocks in a horizontal channel

Numerical simulations are conducted to study natural convection in a horizontal channel provided with heating blocks mounted on its lower wall. The blocks are submitted to a uniform heat generation and the channel upper surface is maintained at a cold constant temperature. The main objective of this study is to examine the validity of the model with isothermal blocks for the system under consideration. The controlling parameters of the present problem are the thermal conductivity ratio of the solid block and the fluid (0.1 ≤ k* = ks/ka ≤ 200) and the Rayleigh number (104 ≤ Ra ≤ 107). The validity of the isothermal model is examined for various Ra by using different criteria based on local and mean heat transfer characteristics.