Analytical solutions of heat transfer for laminar flow in rectangular channels

Archives of Thermodynamics

Jaros?aw MikielewiczThe Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gda?sk, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹  Witold Rybi?skiCorresponding authorThe Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gda?sk, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] The Szewalski Institute of Fluid-Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gda?sk, Poland

关键词: Keywords: Analytical solution;    Heat transfer;    Rectangular channel;    Laminar flow;    Fully developed;   

DOI  :  10.2478/aoter-2014-0031

学科分类：能源（综合）

来源: Polska Akademia Nauk * Oddzial w Gdansku, Instytut Maszyn Przeplywowych / Polish Academy of Sciences, Institute of Fluid-Flow Machinery

【 摘 要 】

The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

【 授权许可】

Unknown