Research Article Effects of Wall Confinement and Power-Law Fluid Viscosity on Nusselt Number of Confined Spheres Effects of wall confinement on the heat transfer phenomena of confined spherical particles in power-law fluids are numerically investigated. The spherical particle is held at constant temperature and a power-law fluid is flowing past the particle in a confining tube. Heat transfer takes place from the heated sphere to the sur- rounding fluid. The governing conservation equations of mass, momentum, and energy are solved using computational fluid dynamics-based software. The numeri- cal solver is thoroughly validated by comparing the present average Nusselt num- bers with existing literature values. On the basis of numerical results, an empirical correlation for the average Nusselt number of a confined sphere in Newtonian and power-law fluids is proposed which can be used in new applications. Keywords: Confined sphere, Heat transfer, Nusselt number, Péclet number, Power-law fluid, Wall confinement Received: March 15, 2013; revised: April 15, 2013; accepted: May 17, 2013 DOI: 10.1002/ceat.201300177 1 Introduction Forced convective heat transfer from bluff bodies is often encountered in many industrially important settings. Some applications include fixed and fluidized-bed reactors, heteroge- neous catalytic reactors, mineral processing, pharmaceutical productions, thermal treatment of food stuffs etc. However, in numerous industrial applications, one meets both regular (spherical, cylindrical, cubical etc.) and irregular particles con- tacting with each other, with the container wall, and with the surrounding fluids. Furthermore, many industrial fluids obey non-Newtonian characteristics including shear-thinning, shear-thickening, yield stress, and viscoelastic behavior [1]. Despite these facts, because of simplicity in approach, exten- sive literature has accrued on momentum and heat transfer characteristics of unconfined regular particles such as spheres and cylinders in Newtonian fluids [2–4] and in generalized Newtonian fluids such as power-law and Carreau model fluids [5]. It is readily recognized that the rate of particle settling (or drag coefficient) and the rate of heat transfer (or Nusselt num- ber) are prerequisites for the design of solid-liquid contactors. This information can be conveniently represented by pertinent dimensionless parameters such as the Reynolds (Re) number, Prandtl (Pr) number, wall confinement, and characteristic constants of the non-Newtonian fluid. Although knowledge of the settling velocity and the rate of heat transfer from a single unconfined particle provide insight about the physics of the problem, in most applications the par- ticles are often confined by channels or by the container wall. Some well-known applications of confined particles are fall- ing-ball viscometer, hydrodynamic chromatography, mem- brane transport, coarse particles transport in pipes, microflui- dics etc. In the case of confined transport phenomena when the fluid is a Newtonian fluid, adequate literature is available on drag and Nusselt (Nu) numbers of confined spheres [6–12], whereas the effect of power-law viscosity behavior of a fluid is investigated to a lesser extent. Recently, Dhole et al. [13] numerically examined the heat transfer characteristics of un- confined spherical particles in power-law fluids. Song et al. [10–12] reported effects of the moving wall on the drag and Nu-numbers of confined spheres in Newtonian and shear- thinning fluids only. In our recent work [14], the combined effects of the power-law fluid viscosity and wall retardation along with the Re-number on the flow and drag behavior of confined spherical particles are described. In this work, effects of power-law behavior index and stationary wall confinement on heat transfer characteristics of confined spheres are pre- sented. www.cet-journal.com © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Eng. Technol. 2013, 36, No. 9, 1568–1576 Chinta Rajasekhar Reddy Nanda Kishore Indian Institute of Technology Guwahati, Department of Chemical Engineering, Assam, India. – Correspondence: Prof. N. Kishore (nkishore@iitg.ernet.in), Indian Institute of Technology Guwahati, Department of Chemical Engineer- ing, Assam 781039, India. 1568 C. Rajasekhar Reddy, N. Kishore