Surface temperature of a multi-layer thermal barrier coated wall subject to an unsteady heat flux

Abstract

A one-dimensional analytical method of determining the surface temperature of a thermal barrier coated plane wall subjected to an arbitrarily time-varying heat flux was developed. The method allows fast computation, enabling it to be embedded in combustion simulation software to correctly calculate wall heat transfer, which is important for reciprocating engine applications with thin, low thermal inertia coatings that have large temperature swings. The method relies on superposition of the response to successive step changes in heat flux, obtained by discretizing the heat flux history, to compile the solution. The embedded problem of a step-change in heat flux is addressed using the one-dimensional heat diffusion equation in conjunction with the matrix method in the Laplace domain, assuming the lateral conduction is neglected. For a two-layer wall (one coating layer on top of the metal wall) in the limit where kρc of the coating is small relative to that for the wall material, an analytical inversion to the time domain can be derived. For modest values of this parameter or for more than one coating layer, the residue theorem is invoked to invert to the time domain, with the poles and residues found numerically. The analytical inversion, however, provided the impetus for defining a set of non-dimensional parameters that uniquely characterize the surface temperature swing for arbitrary periodic heat flux to the wall. Non-dimensional results are given for a sinusoidially varying surface heat flux.