Constructal optimization of heat conduction with minimum entransy dissipation rate for leaf-shaped quadrilateral heat-generating body

Abstract

<p indent=0mm>In this work, a constructal study of a leaf-shaped quadrilateral heat-generating body based on the bionic quadrilateral of the common leaf vein shape was performed by combining the constructal and entransy theories, thus allowing the optimal construct of the leaf quadrilateral heat-generating body to be derived. The effect of the number of intervals, i.e., the number of branches containing high thermal conductivity materials, <italic>n</italic>, and angle <italic>θ</italic> between the high thermal conductivity material in the branch and the center, on the optimal construction of the heat-generating body was also studied. The constructal differences of the heat-generating body were compared under the minimum entransy dissipation rate and minimum temperature difference. The results show that the mean heat transfer temperature difference of the heat-generating body is the smallest in the optimal constructal when the entransy dissipation rate is the lowest. With the increase in the number of intervals (<italic>n</italic>≥20), the optimal aspect ratio and minimum mean temperature difference of the heat-generating body decreased slightly. Therefore, increasing the complexity of the high heat conduction passage in the heat-generating body can decrease the mean heat transfer temperature difference. Different optimal constructs of the heat-generating body were obtained using the entransy dissipation rate and maximum temperature difference as the optimization objective; both provide more optimal solutions when the high thermal conductivity material of the branch and center are perpendicular. Furthermore, minimizing the entransy dissipation rate allowed for a smaller mean temperature difference to be obtained. Therefore, using the minimum entransy dissipation rate as the optimization objective can reduce the mean heat transfer temperature difference more effectively in a leaf-shaped quadrilateral heat-generating body.