Natural convection in a horizontal channel provided with heat generating blocks: Discussion of the isothermal blocks validity

This work presents a numerical study of air natural convection in a horizontal channel provided with heating blocks periodically distributed on its lower adiabatic surface. 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. Then the calculations are performed using two different models. In the first (denoted Model 1 or M1) the calculations are performed by imposing a uniform volumetric heat generation inside the blocks. In the second model (denoted Model 2 or M2), the blocks are maintained isothermal at the average blocks surface temperature deduced from the Model 1. 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 criteria based on local and mean heat transfer characteristics. It is found that some solutions of the isothermal model do not reproduce correctly the results of the first model even for very large conductivity ratios. The Biot number below which the Model 2 is valid depends strongly on the Rayleigh number and the type of solution.

► We examine the validity of isothermal model for blocks with internal heat generation.
► Criteria based on comparison of total and local quantities are adopted.
► Thermal conductivity and Biot number required for the validity of the isothermal model are dependent on the Rayleigh number.
► The validity conditions are also affected by the multiplicity of solutions.