Optimal Distribution of Heat Sources in Convergent Channels Cooled by Laminar Forced Convection

Abstract

The constructal theory is applied to the flow in a convergent channel. The primary goals of this work are to analyze the heat source distribution and generalize the formula concerning such configurations, to study the spacing between consecutive elements, and to verify the analysis by comparing the proposed configuration with numerical simulations. The results show that nonuniform distributions enhance the performance of the system by allowing the heat source element to work near its maximum condition. Furthermore, the optimal distribution occurs when the heat sources are placed closer to each other near the leading edge of the channel. While the literature shows that the spacing between any consecutive element increases as the sources move downstream from the leading edge, the present results proved that such conclusions are restricted, depending on the ratio of outlet to inlet freestream velocity. Accordingly, the spacing has a maximum value when the exit freestream velocity is more than twice that of the inlet. For design issues, the study also addresses the minimum heat required to achieve optimal system performance. The results show that the amount of heat needed by the system to work close to its optimal performance varies exponentially with the convergent angle and increases with the increase in the heating element’s width. The comparison of the present distribution of the heat source elements with a regular one (fixed spacing) is performed numerically to demonstrate the efficiency of the proposed configuration. The results show that the present model forces the system to work more efficiently than the uniform distribution.