ALTERNATIVE AND RELEVANT REPRESENTATION TO HEAT TRANSFER COEFFICIENT FOR MODELING THE HEAT TRANSFER BETWEEN A FLUID AND A NON-ISOTHERMAL WALL IN TRANSIENT EGIME
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 T_w and an equivalent fluid temperature T-f . The problem we consider inthis 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 thermalboundary 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 timedomain 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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