Constructal design of tree-shaped conductive pathways for cooling a heat generating volume

Constructal design is used to study heat removal from a square heated body with a tree shaped high thermal conductivity pathways embedded in the body. The objective is to minimize the defined maximum dimensionless temperature difference for the body. The thermal conductivity of the body is low, and there is a uniform heat generation on it. The volume of the body is fixed. The amount of high conductivity material for building the pathways are also fixed, but their length and diameter are variable. The effect of parameters such as the angle among the pathways, number of pathways, thermal conductivity coefficient, dimensionless area fraction and different length ratios are investigated. The results show that by optimizing the angle among the pathways, the operation of them improves up to %12. By increasing the number of blades, dimensionless temperature difference decreases, but the best heat removal would be achieved when the pathways place along the direction of the diagonal of the square body, since, as the simulations show, the maximum temperature in the body occurs at the corners of the square.