Cloaking of heat flux and temperature

Due to equal arc length in different coordinate system, we derive the scaling factor of rectangular Cartesian coordinates and curvilinear orthogonal coordinates; meanwhile, we also derive the equations of heat flux density (or heat flux, or thermal flux) and quantity of heat by means of the transformation relation of vectors in different coordinate system, and thermal conductivity tensor due to temperature scalar field is not changed in the coordinate transformation; we transform thermal conduction equation of rectangular Cartesian coordinate into curvilinear orthogonal coordinates, and draw the conclusion that thermal conductivity equation is covariant when coordinate transforms. As an example, we simulate thermal cloak.