A heat transfer analysis of laminar flow over a flat plate with unheated starting region for low prandtl number fluids

摘要

In boundary layer analyses involving heat transfer, the Prandtl number (Pr) relates the diffusion of momentum to the diffusion of heat, and can be shown to directly correlate to the ratio of the thermal boundary layer thickness to the velocity boundary layer thickness. For large Prandtl number fluids (i.e., Pr >1) the velcoity boundary layer thickness is larger than the thermal boundary layer thickness, and vice versa. In some applications in the industry heating does not occur over the entire plate, such as in the case of an unheated starting region or spot heating along a finite segment of the plate. For such applications solutions only exist for the simpler case of large Prandtl number fluids where the thermal boundary layer is assumed to be smaller than the velocity boundary layer. The analyses presented in this paper extends the solution to the unheated starting region problem for small Prandtl number fluids, where the thermal boundary layer grows larger and crosses the velocity boundary layer. The solution is based on the integral method approach assuming laminar flow, and both cases of constant wall temperature as well as constant wall heat flux are analyzed.