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

• Published in: European journal of mechanics, B, Fluids B, Fluids, 2018-09, Vol.71, p.77-91
• Main Author: Jafarimoghaddam, Amin
• Format: Article
• Language: English
• Subjects: Adiabatic surface; Closed form solutions to thermal characteristics of wall jet flows; Convective surface; Glauert type flows; Prescribed temperature and heat flux conditions
• ISSN: 0997-7546; 1873-7390
• DOI: 10.1016/j.euromechflu.2018.04.002

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