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research-article

LAMINAR FORCED CONVECTION IN TRANSVERSELY CORRUGATED MICROTUBES

[+] Author and Article Information
F.Talay Akyildiz

Department of Mathematics and Statistics, Al-Imam University, Riyadh, Saudi Arabia
ftakyildiz@hotmail.com

Dennis A. Siginer

Centro de Investigación en Creatividad y Educación Superior & Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago, Chile; Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Bostwana International University of Science and Technology, Palapye, Bostwana
dsiginer@hotmail.com

1Corresponding author.

ASME doi:10.1115/1.4042331 History: Received March 03, 2018; Revised December 16, 2018

Abstract

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for non-uniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the Spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

Copyright (c) 2018 by ASME
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