The temperature field of an infinite solid containing a cylindrical channel with a thermally thin surface coating

Abstract

The Laplace method of integral transformation is used to find an analytical solution of the problem of unsteady-state heat conduction for an infinite isotropic solid containing a cylindrical channel with a thermally thin surface coating filled with a high-temperature gas.

Nonstationary one-dimensional problem of heat conduction for a cylinder with a thin multilayer coating

“…4, for higher values of Bi , the more the temperature distribution over the thickness of the coating deviates from a uniform distribution. Note that this character of temperature distribution across the thickness of the coating cannot be obtained by the "concentrated capacity scheme" [1].…”

“…Note that, for the case of a plane coating (δ/R = 0) , if the heat capacity of the coating is neglected in (6) (Ω = 0) , we obtain the boundary condition presented in [18], and, if the thermal resistance is neglected (H −1 = 0) , we obtain the generalized boundary condition [1,3].…”

“…In [4], in the investigation of heat transfer in glass coatings on metallic substrates, only the temperature gradient along the thickness of the coating was taken into account, whereas in [1,3], which realize the "concentrated capacity scheme" [22], on the contrary, only its gradient along the thickness of the substrate was taken into account. In [33], the assumption of a constant concentration gradient in the coating was used.…”

“…It can be noted that the approach based on the modeling of coatings by thin shells [20], in contrast to the models presented in [1,3,4], enables one to simultaneously take into account the gradients of the temperature field both in the coating and in the substrate. In [26,36,37], generalized boundary conditions of heat exchange of the body with a medium through a thin multilayer coating were obtained.…”