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Laminar natural convection in a water filled square enclosure containing at its center a horizontal hexagonal cylinder is studied by the lattice Boltzmann method. The hexagonal cylinder is heated while the walls of the cavity are maintained at the same cold temperature. Two orientations are treated, corresponding to two opposite sides of the hexagonal cross-section which are horizontal (case I) or vertical (case II). For each case, the results are presented in terms of streamlines, isotherms, local and average convective heat transfers as a function of the dimensionless size of the hexagonal cylinder cross-section (0.1≤B≤0.4), and the Rayleigh number (103≤Ra≤106).

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This paper presents a detailed numerical study, in steady state regime, of the interaction between two dimensional heat transfers by conduction, natural convection and radiation in double hollow bricks formed by two honeycomb walls separated by an air layer. The air motion in all cavities of the system is laminar. The left and right vertical sides of the hollow bricks are considered isothermal and maintained at different constant temperatures. The top and bottom horizontal sides are assumed to be adiabatic. The governing equations are solved using the finite volume method (FVM) and the SIMPLE algorithm. The impact of the thickness of the air layer on the global heat flux through the structure is discussed. The simulation results show that the variation of the overall heat flux through each hollow brick as a function of the temperature difference ΔT between the vertical sides of the system is almost linear for the different types of double hollow bricks considered.This linear thermal behaviour allowed the generation of appropriate overall heat exchange coefficients that permit fast and accurate prediction of heat transfers through the hollow bricks without solving the complex system of equations governing the coupled heat transfers. Comparison of the performance of different types of double hollow bricks is made.