Semi-Analytic Modeling of Laminar Forced Convection in a Rectangular Duct for Arbitrary Boundary Conditions and Inlet Temperature Profile.

Mokhtar, Rawan Y.; Tawfik, Mohamed M.; Sabry, Mohamed Nabil

doi:10.21608/bfemu.2020.109303

Semi-Analytic Modeling of Laminar Forced Convection in a Rectangular Duct for Arbitrary Boundary Conditions and Inlet Temperature Profile.

Document Type : Research Studies

Authors

¹ Reasearcher at Mechanical Power Engineering Dpt., Mansoura University,Mansoura

² Lecturer at Mechanical Power Engineering Dpt.,Mansoura University, Mansoura, Egypt

³ Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, El-Mansoura 35516, Egypt

10.21608/bfemu.2020.109303

Abstract

Modeling the forced convection heat transfer with arbitrary boundary conditions and inlet temperature profile was studied in order to go beyond the classic, but unrealistic cases of imposed uniform heat flux or wall temperature as well as a flat temperature at the inlet. The proposed approach, known as the Flexible Profile Compact Thermal Model (FP-CTM), which has been proposed earlier to treat circular cross-section ducts, is generalized here to treat ducts with a rectangular cross-section. It is applied to the laminar hydrodynamically fully developed flow but thermally developing. It offers significant advantages over the traditional model of convective heat transfer coefficient (HTC), for which correlations only exist for uniform boundary conditions and inlet profile. The proposed approach makes it more efficient when dealing with problems with non-uniform conditions such as conjugate heat transfer problems. A critical advantage of this approach is that it uses a semi-analytic treatment to produce highly accurate results that are comparable to those produced by commercial CFD tools but with significantly less CPU time. Results obtained from the proposed approach, i.e. FP-CTM were compared with that obtained from Ansys Fluent. The comparison has shown that FP-CTM is very reliable. The maximum error compared with Fluent solver results was 0.01 °C for a temperature range between the inlet and outlet of about 50 °C. Based on the preceding comparison, the FP approach was used to solve different problems with different boundary conditions (uniform and linear heating) and inlet profiles (flat and non-flat inlet) using significantly fewer computing resources.

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