Numerical Simulation

International Communications in Heat and Mass Transfer 37 (2010) 1535–1545

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International Communications in Heat and Mass Transfer
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t

Numerical simulation of steady natural convection heat transfer in a 3-dimensional single-ended tube subjected to a nanofluid☆Mina Shahi a,c,⁎, Amir Houshang Mahmoudi a,b, Farhad Talebi a
a b c

Department of Mechanical Engineering, Faculty of Engineering, Semnan University, Semnan, Iran R&D department of Oghab Afshan Company, Semnan, Iran R&D department of Semnan Water &Waste Water Company, Semnan, Iran

a r t i c l e

i n f o

a b s t r a c t
In this paper, 3-dimensional numerical simulation of steady naturalconvective flow and heat transfer are studied in a single-ended tube with non-uniform heat input. Apart from some other applications, it serves as a simplified model of the single-ended evacuated solar tube of a water-in-glass evacuated tube solar water heater. It is assumed that the sealed end of tube to be adiabatic and also the tube opening to be subjected to copper–water nanofluid. Governingequations are derived based on the conceptual model in the cylindrical coordinate system. The governing equations have been then approximated by means of a fully implicit finite volume control method (FVM), using SIMPLE algorithm on the collocated arrangement. The study has been carried out for solid volume fraction 0 ≤ φ ≤ 0.05 and maximum heat flux 100 ≤ qm ≤ 700. Considering that the driven flow in thetube is influenced by the dimensions and the inclination angle of the solar tube, the flow patterns and temperature distributions are presented on different cross sectional planes and longitudinal sections, when the tube is positioned at different orientations. © 2010 Elsevier Ltd. All rights reserved.

Available online 26 August 2010 Keywords: Single-ended tube Evacuated tube solar collectorNatural convection heat transfer Non uniform heat input Nanofluid Solid concentration Numerical method

1. Introduction Natural convection inside cylindrical enclosures is the most often encountered phenomena in solar energy systems such as evacuated tube collectors. In high temperature operation, Evacuated tube collectors have higher efficiency and better performance than flatplate collectors, becauseevacuated tube minimizes the convective heat loss by the vacuum envelope placed around the absorber surface. These types of collector can be usually used in solar water heaters [1,2]. A schematic scheme of water-in-glass evacuated tube solar water heater is shown in Fig. 1 [3]. The tube is heated by direct exposure to the light of the sun and the reflected solar radiation from the back plate(reflector plate). The heat transfer in these types of solar water heater is driven purely by natural circulation of water through the single-ended tube into the storage tank. Water in the tubes is heated by circumferential heat input which then rises along the top of the tube to the tank and is replaced by colder one from the tank which is entering into the bottom of the tube [4,5]. In contrast to thenumerous experimental, numerical and analytical studies performed on natural convection in rectangular enclosures [6–13], just few literatures can be found about the three-

☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. University of Semnan, Central organization, Molavi Blvd, Saadi Sq., Semnan, Iran. E-mail addresses: mina.shahi@gmail.com (M. Shahi), amirhoshangm@gmail.com (A.H.Mahmoudi). 0735-1933/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2010.08.005

dimensional convection heat transfer in the cylindrical tube. However, most of the previous investigations have been done in two-ended tube and based on uniform wall temperature or uniform heat input condition [14–17]. In all of mentioned researches, the study is...