An alternative to heat transfer coefficient: A relevant model of heat transfer between a developed fluid flow and a non-isothermal wall in the transient regime

•A generalized impedance Z(ω,p) is proposed for modelling the heat transfer between a fluid and a non-isothermal wall.•It appears to be a good alternative to heat transfer coefficient h(x,t).•It can be applied in many cases both in steady-state and transient regimes.•Generalized impedance is intrinsic to the fluid properties and flow characteristics.•Generalized impedance does not depend on the thermal boundaries conditions.

This paper deals with the relevant model that can be proposed for modelling interface heat transfer between a fluid and a wall for thermal boundary conditions varying in space and time. Usually, for a constant and uniform heat transfer (unidirectional steady-state regime), the problem can be solved through the introduction of the notion of a h heat transfer coefficient. This quantity, which is uniform in space and constant in time, links heat flux to a temperature difference (between the wall temperature Tw and an equivalent fluid temperature Tf, where h and Tf both depend on the system geometry) in a linear way.The problem we consider in this work concerns the heat transfer between a dynamically developed steady-state fluid flow and a wall submitted to transient and non-uniform thermal excitations, for instance a steady-state flow over a flat plate submitted to a pulsed and space-reduced heat flux, or a steady-state flow in a duct stimulated by a periodic flux on its outer surface. More generally, we assume that this kind of thermal problem can be described by:-one or several linear partial differential equations with their associated linear boundary and interface conditions;-the coefficients of the homogeneous part of these equations do not depend neither on time nor on the coordinates in the direction parallel to the fluid/solid interface (they may depend on the coordinate in the normal direction);-volume and surface sources (non-homogeneous part of the previous equations) that can depend on space and/or time.We will show that the relevant representation for describing the interfacial heat transfer does not consist in defining a non-uniform and variable heat transfer coefficient h(x,t), as done usually: the corresponding relationship is not really intrinsic because it depends on the thermal boundary conditions. An alternative approach is proposed here. It relies on the introduction of a generalized impedance Z(ω,p), which is a double integral transform of a transfer function z(x,t) in the original space (x)/time (t) domain. This impedance function links heat flux and temperature difference through a convolution product (noted “⊗” here) rather than through a scalar product:Tw(x,t)−Tf(x,t)=z(x,t)⊗φ(x,t)Tw(x,t)−Tf(x,t)=z(x,t)⊗φ(x,t)After a presentation of the generic problem, simple cases, with analytical solutions, will be presented for validation, such as a plug flow, in 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 less academic case will be presented.