This paper deals with the relevant model that can be proposed for modeling the interfacial heat transfer between a fluid and a wall in the case of space and time varying thermal boundary conditions. Usually, for a constant and uniform heat transfer (unidirectional steady-state regime), the problem can be solved introducing a heat transfer coefficient h, uniform in space and constant in time that linearly links the surface heat flux and the temperature difference between the wall temperature Tw and an equivalent fluid temperature Tf. The problem we consider in this work concerns the heat transfer between a steady-state fluid flow and a wall submitted to a transient and non uniform thermal solicitations, as for instance a steady-state flow on a flat plate submitted to a transient and space reduced heat flux. We will show that the more interesting representation for describing the interfacial heat transfer is not to define as usually done a non-uniform and variable heat transfer coefficient h(x,t) because as it depends on the thermal boundary conditions, it is not really intrinsic. We propose an alternative approach, which consists in introducing a generalized impedance Z(ω,p) that links in space and time domain the heat flux and the temperature difference through a double convolution product instead of a scalar product. After the presentation of the general problem, the simple case of a stationary piston flow that can be solved analytically will be considered for validation both in thermal steady-state and transient regimes. To conclude and show the interest of our approach, a comparison between a global approach and a numerical simulation in a more complex and realistic case taking into account the thermal coupling with a flat plate will be presented.

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