Undeveloped convective heat transfer from an array of cubes in cross-stream direction

Conjugate heat transfer for three-dimensional developing turbulent flows over an array of cubes in cross-stream direction, representing finite heat elements mounted over a surface is studied numerically. Incompressible fluid flow over the cubes is modeled using a fully elliptic form of the Navier-Stokes equations. RNG based k-ɛ turbulent model is incorporated to predict turbulent flow field as well as the recirculating pattern along the blocks. Temperature fields in the blocks and on their outer surfaces were obtained solving heat conduction equation. Finite volume procedure with appropriate boundary conditions is used to solve the coupling between the solid and fluid region. The heat transfer characteristics resulting from recirculating zone around the blocks are presented for a wide range of Reynolds numbers from 4.2×103 to 1×105 (for Pr=0.7) and blockage ratios from 10 to 50%. Numerical computation is validated with experimental studies of Nakamura et al. [Internat. J. Heat Mass Transfer 44 (2001) 3385] and variation of the Nusselt number as well as fin efficiency in terms of flow Reynolds number and blockage ratios are determined. New correlations is developed to predict average Nusselt number as Nu¯=0.11Re0.702(1+0.68Br). Also a new correlation is obtained for fin efficiency such as ηf=126.69Re−0.027(1+Br)−0.035 for an array of inline cubes. The analysis is extended to study the effects of spacing between heat sources for a fixed heat input.