Laminar-transitional micropipe flows: Energy and exergy mechanisms based on Reynolds number, pipe diameter, surface roughness and wall heat flux

Abstract

Energy and exergy mechanisms of laminar-transitional micropipe flows are computationally investigated by solving the variable fluid property continuity, Navier-Stokes and energy equations. Analyses are carried for wide ranges of Reynolds number (Re = 10-2,000), micropipe diameter (d = 0.50-1.00 mm), non-dimensional surface roughness (epsilon* = 0.001-0.01) and wall heat flux (q '' = 1,000-2,000 W/m(2)) conditions. Computations revealed that friction coefficient (C-f) elevates with higher epsilon* and Re and with lower d, where the rise of epsilon* from 0.001 to 0.01 induced the C-f to increase by 0.7 -> 0.9% (d = 1.00 -> 0.50 mm), 3.4 -> 4.2%, 6.6 -> 8.1%, 9.6 -> 11.9% and 12.4 -> 15.2% for Re = 100, 500, 1,000, 1,500 and 2,000, respectively. Earlier transition exposed with stronger micro-structure and surface roughness at the descriptive transitional Reynolds numbers of Re-tra = 1,656 -> 769 (epsilon* = 0.001 -> 0.01), 1,491 -> 699 and 1,272 -> 611 at d = 1.00, 0.75 and 0.50 mm; the corresponding shape factor (H) and intermittency (gamma) data appear in the narrow ranges of H = 3.135-3.142 and gamma = 0.132-0.135. At higher Re and lower d, epsilon* is determined to become more influential on the heat transfer rates, such that the Nu(epsilon*=0.01)/Nu(epsilon*=0.001) ratio attains the values of 1.002 -> 1.023 (d = 1.00 -> 0.50 mm), 1.012 -> 1.039, 1.025 -> 1.056 and 1.046 -> 1.082 at Re = 100, 500, 1,000 and 2,000. As e * comes out to cause minor variations in the cross-sectional thermal entropy generation rates (S'(Delta T)), q '' is confirmed to augment S'(Delta T), where the impact becomes more pronounced at higher Re and d. Frictional entropy generation values (S'(Delta P)) are found to be motivated by lower d, higher Re and epsilon*, such that the S'(Delta Pd=0.50mm)/S'(DPd=1.00mm) ratio is computed as 4.0011 -> 4.0014 (epsilon* = 0.001 -> 0.01), 4.002 -> 4.007, 4.006 -> 4.027 and 4.023 -> 4.102 at Re = 100, 500, 1,000 and 2,000. As the role of q '' on total entropy generation (S') turns out to be more remarkable at higher d and lower Re, the task of epsilon* becomes more sensible at higher Re.