Multi-source directional heat conduction method based on coordinate transformation

Abstract

Based on the optical transformation theory, the formal invariance of the heat conduction equation was used to realize the transformation of constitutive parameters of heat conducting materials through coordinate transformation, so as to control the distribution of heat flow in physical space. In addition, based on the research on the control method of heat flow propagation path, a multi-heat source directional heat conduction method with complex boundary was studied for the case where the object is affected by a variety of internal and external heat sources, and the temperature field is uneven, resulting in irregular deformation. Based on translation transformation and compression transformations, the thermal conductivity distribution of the material was derived for the directional heat conduction structure. And the controllable propagation of heat flow from high temperature region to low temperature region was realized. By analyzing three distributions of multiple heat sources, applicable directional heat conduction structures with multiple sources and complex boundaries were designed to realize passive control of temperature field. The performance of directional heat conduction structures in transient state was analyzed by Comsol software simulation, where the direction of the heat flow is observed through the temperature cloud. Then, from the comparison graph of the average temperature of different sides of the heat conduction structure after 60 min, it can be concluded that the difference between the average temperature of different areas decreases, and the temperature field of the structure becomes more uniform.