Control and design heat flux bending in thermal devices with transformation optics

We propose a fundamental latent function of control heat transfer and heat flux density vectors at random positions on thermal materials by applying transformation optics. The expressions for heat flux bending are obtained, and the factors influencing them are investigated in both 2D and 3D cloaking schemes. Under certain conditions, more than one degree of freedom of heat flux bending exists corresponding to the temperature gradients of the 3D domain. The heat flux path can be controlled in random space based on the geometrical azimuths, radial positions, and thermal conductivity ratios of the selected materials.