Abstract: Thermal cloak provides good behaviors of thermal protecting and cloaking, which leads to wide applications in the fields of aviation, transport, and computer. Currently, the design and study of thermal cloak are based on transformation optics, forcing the heat flux bypassing the protected obstacle. In this work, the heat flux, bending at random position of the thermal cloaking system in 2D domain, was obtained using transformation optics based on the form invariance of differential equations of heat conduction after coordinate transformation. FLUENT was employed to verify the bending angle of heat flux on the material layer boundaries. The results indicated that the thicker material layer led to the smaller bending angle. The bending angle increased with the ratio of conductivities b if b>1, and it reduced with the ratio of conductivities b if b<1. Hence, the heat flux path can be regulated with these findings, and the cloaking and protecting performances can be optimized.

Key words: heat flux bending, thermal cloaking, transformation optics, regulation