Technical Brief

Critical Biot numbers of periodic arrays of fins

[+] Author and Article Information
Marios M. Fyrillas

Department of Mechanical Engineering, Nazarbayev University, Astana 010000, Republic of KazakhstanDepartment of Mechanical Engineering, Frederick University, 1303 Nicosia, Cyprus

Sayat Ospanov

Department of Mechanical Engineering, Nazarbayev University, Astana 010000, Republic of Kazakhstan

Ulmeken Kaibaldiyeva

Department of Chemical Engineering, Nazarbayev University, Astana 010000, Republic of Kazakhstan

1Corresponding author.

ASME doi:10.1115/1.4035971 History: Received August 25, 2016; Revised January 11, 2017


We consider the heat transfer problems associated with a periodic array of triangular, longitudinal, axisymmetric and pin fins. The problems are modeled as a wall where the flat side is isothermal and the other side, which has extended surfaces/fins, is subjected to convection with a uniform heat transfer coefficient. Hence our analysis differs from the classical approach because (i) we consider multi-dimensional heat conduction and (ii) the wall, that the fins are attached, is included in the analysis. The latter results in a non-isothermal temperature distribution along the base of the fin. The Biot number (Bi=h~t/k) characterizing the heat transfer process is defined with respect to the thickness/radius of the fins (t). Numerical results demonstrate that the fins would enhance the heat transfer rate only if the Biot number is less than a critical value which, in general depends on the geometrical parameters, i.e. the thickness of the wall, the length of the fins and the period. For pin fins, similar to rectangular fins, the critical Biot is independent of the geometry and is approximately equal to 3.1. The physical argument is that, under strong convection, a thick fin introduces an additional resistance to heat conduction.

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