Nusselt Number as Composite Functions of Aspect Ratio and Wall Inclination in Parallelogram Microchannels with Three Types of Thermal Boundary Conditions

Abstract

AbstractIn this study, attention is focused on the numerical simulations of laminar fluid flow and heat transfer in straight smooth-walled parallelogram channels with various aspect ratios (α) and inclined angles (θ). The Reynolds number (Re), characterized by the channel hydraulic diameter and the working fluid of water, is fixed at 100. The examinedαandθrange from 1 to 10 and 45° to 90°, respectively. Their effects on the thermal fluid features are explored under three thermal boundary conditions: constant wall temperature (TBC), constant axial heat transfer rate with constant peripheral temperature (H1BC), and constant wall heat flux (H2BC). The SIMPLE algorithm is employed for velocity–pressure coupling with the algebraic multigrid method, while the second-order upwind scheme is utilized for spatial discretization in pressure term; the momentum and energy equations are solved with a QUICK scheme; Least Squares Cell-Based Gradient Evaluation is applied for predicting scalar values at the cell faces and for computing secondary diffusion terms and velocity derivatives. One of the new findings is that there exists a critical value ofθ= 70° below which the Nusselt number under H2BC increases with increasingαwhereas beyond which the trend reverses, a result distinct from those computed with TBC and H1BC. Moreover, TBC is found to be a time-saving alternative to H1BC. Furthermore, both Nusselt numbers under the three thermal boundary conditions and friction factor timesReare successfully and compactly correlated with α andθto offer useful reference for designing micro-cooling channels.