Optimal search of heat sources location in conjugate natural convection with surface radiation in a two-dimensional enclosure utilizing particle swarm optimization algorithm

In this paper, the numerical analysis of the conjugate natural convection with surface radiation in a two-dimensional enclosure is carried out in order to search the optimum location of the boundary constant flux heat sources to minimize the temperature of the heat sources surface using the particle swarm algorithm. The air is considered as an incompressible fluid and a transparent media inside the enclosure with a steady and laminar flow regime. The surfaces of the enclosure are also considered to be opaque, diffuse and gray. The governing equations are solved using the stream function and vorticity formulation with the finite difference method. The maximum temperature and the location of heat sources are selected as the objective function and design variables, respectively. The results show that the minimum value of the maximum dimensionless temperature of the heat source decreases with the increase of emissivity or Rayleigh number. By increasing the Rayleigh number, the optimal location of heat sources shifts to the bottom for configurations with one or two heat sources. By increasing the emissivity in each Rayleigh number, the optimal value of the heat sources center location approaches to the center and in the configurations with two and three heat sources is close to each other.