Wall jet flows of Glauert type: Heat transfer characteristics and the thermal instabilities in analytic closed forms

Abstract

Heat transfer characteristics of the traditional wall jet flows subject to various thermal boundary conditions including isothermal surface, prescribed temperature, constant heat flux, prescribed heat flux, adiabatic surface and thermally convective surface are documented in analytic closed forms. Heat dissipation has been also included where the similarity energy equation could structurally adjust to this specific term (for the adiabatic case, this term has been necessarily included). In all the studied cases, both the transpiration velocity and moving wall conditions are allowed to exist (where applicable) in such a way, being consistent with the Glauert integral constraint and subject to the context of exponentially decaying wall jet flows.In particular, it is analytically proved (even without having the closed form solutions) that for the Glauert original case, a surface with a prescribed temperature in the form of Tw(x)=mx−14+T∞ serves zero contribution to heat transfer at the wall (the Induced Heat Shield). More precisely, the value −14as the prescribing parameter is the Surface Heat Transfer Stopping Point and below this point, heat transfer phenomenon falls from a usual physical interpretation, expressing spectrums of thermal instabilities through a hyper geometric function. Furthermore, it is argued that a normalized similarity temperature in the form of θ(η)=T−T∞mxn<−14 results in the appearance of an uninterruptable singularity within the heat transfer phenomenon for the Glauert case subject to a rigorous physical ground; and as an immediate practical consequence, there is no physically-valid similarity solution for an adiabatic surface or more precisely, for energy equation with heat dissipation consideration.It should be mentioned that the concept of Induced Heat Shield is discussed in here for the first time (to our knowledge) which may inspire a concealed fact regarding the restrictions of the thermal similarity solutions.Therefore, it is hopeful that heat transfer phenomenon in the Glauert type wall jet flows and the associated physical representations can be better understood by the present research.