Numerical study of laminar heat transfer with temperature dependent fluid viscosity in a 2:1 rectangular duct

The present study investigates the influence of variable viscosity of temperature-dependent fluids on the laminar heat transfer and friction factor in a 2:1 rectangular duct. The H₁ thermal boundary condition corresponding to axially constant heat flux and peripherally constant temperature was adopted for a top-wall-heated configuration. The governing conservation equations of mass, momentum, and energy were solved using a finite volume method, and the range of the Prandtl number was from 7 to 15000. The present numerical results of local Nusselt numbers for oil showed 70-80% enhancement over those of a constant property fluid and 40-50% enhancement over water, and gave excellent agreement with recent experimental results [Int. J. Heat Mass Transfer 35, 641-648 (1992)]. The heat transfer enhancement from the heated top wall was due to an increased velocity gradient near the wall. The study proposes a new correlation for local Nusselt numbers in the 2:1 rectangular duct, which covers both thermally developing and thermally fully developed regions. Consequently, a temperature-dependent viscous fluid with a non-circular duct is proposed for use in the design of a liquid cooling module for the computer industry and in compact heat exchangers in general.