Multi-source Directional Heat Conduction Method Based on Coordinate Transformation

Abstract Based on the optical transformation theory, the formal invariance of 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, on the basis of 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 that the object was affected by a variety of internal and external heat sources, and the temperature field was uneven, resulting in irregular deformation. Based on translation transformation and compression transformation, the thermal conductivity distribution of directional heat conducting structural materials was derived, and the controllable propagation of heat flow from high temperature region to low temperature region was realized. By analyzing various distributions of multiple heat sources, an applicable directional heat conduction structure with multiple sources and complex boundaries was designed to realize passive control of temperature field. The performance of directional heat conduction in transient state was analyzed by Comsol software simulation.