Conjugate mixed convection in the entrance region of a symmetrically heated vertical channel with thick walls G. Yang, J.Y. Wu * Institute of Refrigeration and Cryogenics, Key Laboratory for Power Machinery and Engineering of M.O.E, Shanghai JiaoTong University, Shanghai, 200240, China article info Article history: Received 29 June 2014 Received in revised form 17 July 2015 Accepted 17 July 2015 Available online 10 August 2015 Keywords: Mixed convection Conjugate heat transfer Flow reversal Vertical channel abstract Conjugate mixed convection with buoyancy assisted laminar flow in the entrance region of a vertical channel is considered numerically. The problem is solved by a finite volume method for a thick walled, two-regional channel which has constant and uniform outside wall temperatures. The effects of wall thermal conduction as well as assisted buoyancy force on the flow and heat transfer are discussed in detail. Results are presented for a Prandtl number of 0.7, solid-to-fluid thermal conductivity ratios of 1  k* < ∞, wall thickness-to-channel length ratios of 0  l*  5, Reynolds numbers of 200  Re  1000, and for various Grashof numbers. The critical buoyancy parameter (Gr/Re), above which the flow reversal occurs, increases linearly with the increasing l*/k*, while it is independent on the Reynolds number. © 2015 Elsevier Masson SAS. All rights reserved. 1. Introduction Mixed convection heat transfer in vertical pipe and channel flows has been extensively studied in the past few decades due to its importance in industrial and engineering applications, such as heat exchanger systems, nuclear reactors, electronic cooling, fluid transport, building works and so on. It has been recognized that, when the flow velocity is low and the temperature difference be- tween the channel wall and the fluid is large, the direction and magnitude of the buoyancy force may significantly affect the flow structure and heat transfer characteristics in the channel. Most of the previous literatures concerned with the mixed convection flow and heat transfer in a vertical channel with imposed heat flux or temperature at the channel wall, neglected wall thermal conduction [1,2]. The flow reversal, which occurs when the buoyancy parameter exceed a threshold value, was one of the most extensively investigated subjects, as it determined the flow structure in the channel and, consequently, heat transfer, pressure drop, fluid friction and entropy generation, etc. The regime of such buoyancy induced reversed flow has been presented comprehensively by researchers for fully developed or developing flow, accounting for cases of symmetric or asymmetric heated boundary conditions [3e10]. In a recent study, Desrayaud and Lauriat [11] numerically investigated the flow reversal phenome- non for laminar mixed convection of air in a vertical parallel-plate channel. The effects of the assisted buoyancy on the flow pattern and temperature profiles were discussed in detail, and the regime of reversed flow was identified for high values of the P eclet number in a Pe-Gr/Re map. Their study was thereafter extended to three dimensional mixed convection flow by the present authors [12,13], who investigated the flow reversal and heat transfer in a three dimensional symmetrically heated rectangular duct. However, in most practical situation, such as for hot/cold fluid transport and heat exchangers, the boundary conditions of the fluid zone are not known initially but depend on the coupling between convection and wall conduction at the fluidesolid interface, and the effect of wall conduction is even pronounced in the thermal entrance region [14]. The earlier studies of conjugate heat transfer problems were mainly concerned with the coupling of wall con- duction and pure forced convection flow or the coupling of wall conduction with natural convection. For laminar convection flows in parallel plates or in circular pipes, the effect of axial wall con- duction was examined by many authors such as Davis and Gill [15], Mori et al. [16,17], Faghri and Sparrow [18], etc. The wall conduction was considered as one dimensional in these studies. Bilir [19] numerically analyzed the conjugate heat transfer problem within thermal developing laminar pipe flow, involving two dimensional (axial and radial) wall and axial fluid conduction. Adelaja et al. [20] * Corresponding author. Tel./fax: þ86 21 34206776. E-mail addresses: y_g@sjtu.edu.cn (G. Yang), jywu@sjtu.edu.cn (J.Y. Wu). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts http://dx.doi.org/10.1016/j.ijthermalsci.2015.07.023 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved. International Journal of Thermal Sciences 98 (2015) 245e254