热斗篷结构具有良好的热防护与热隐身效果，在航空、运输和计算机等领域有着广泛的应用。当前的热斗篷研究，主要是利用变换光学的方法实现热流在被保护体表面的绕流。依据稳态过程导热微分方程具有形式不变性，利用变换光学的方法，推导出二维坐标系下，热隐身系统中任意位置的热流偏角的表达式，并通过FLUENT对二维圆形热斗篷材料层边界处的热流偏角进行验证。结果表明，当材料层厚度增大时，热流绕流的偏角减小；当导热系数比值b>1时，热流偏角随着b的增大而增大；当导热系数比值b<1时，热流偏角随着b的增大而减小。据此，设计控制热流的传递路径，并优化热斗篷的防护性能和热隐身效果。
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.
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