Optimal design of unequal heat flux elements for optimized heat transfer inside a rectangular duct

When the total amount of thermal energy is fixed in a device, it is important to keep the highest temperatures (hot spots) of the device at the minimum level. The present paper deals with the optimal design of heat flux elements mounted on the outer walls of a rectangular duct. The total amount of heat load is fixed and is transferred by in-duct laminar forced convection. The objective is to minimize the hot spots temperature under the platform of constructal design. A numerical simulation is carried out to calculate the hot spots temperatures. The numerical results suggest that the equal heat flux elements (uniform heating) customarily used in industry must be avoided. By conducting a detailed optimization process, it is shown that there exists an optimum 'descending' distribution for the unequal heat flux elements that minimizes the hot spot temperatures. The influence of Graetz number and the number of unequal heat flux elements on the temperature reduction is studied. For instance, compared with the case of uniform heating, it is shown that the hot spot temperature is reduced up to 25% in the case of four unequal heat flux element under the influence of intermediate values of Graetz number.