Effect of aiding-buoyancy on mixed-convection from a heated cylinder in Bingham plastic fluids A. Bose a , N. Nirmalkar b , R.P. Chhabra a,⇑ a Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India b Department of Chemical Engineering, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli 229316, India article info Article history: Received 19 March 2014 Received in revised form 29 May 2014 Accepted 4 June 2014 Available online xxxx Keywords: Mixed convection Bingham fluid Cylinder Richardson number Prandtl number abstract Mixed convection heat transfer from a heated horizontal circular cylinder in Bingham plastic fluids has been studied numerically over wide ranges of the governing parameters as follows: Reynolds number, 0.1 6 Re 6 40; Prandtl number, 1 6 Pr 6 100; Richardson number, 0 6 Ri 6 2 and Bingham number, 0 6 Bn 6 10. Extensive results on the flow and heat transfer characteristics are presented in terms of the streamlines and isotherm contours in the close proximity of the cylinder and the distribution of pres- sure and the Nusselt number over the surface of the cylinder. The gross behavior is described in terms of the drag coefficient and average Nusselt number as functions of the above-noted influencing parameters. In addition, the morphology of the flow domain in terms of the size and shape of (and their dependence on the governing parameters) the yielded- and unyielded regions separated by the so-called yield sur- faces is also analyzed. The momentum and thermal boundary layers progressively thin with the increas- ing values of each of Re, Pr, Bn and Ri. Thus, it stands to reason that the rate of heat transfer should bear a positive dependence on each of these parameters. The results reported herein elucidate this fundamental dependence. Finally, the heat transfer results are consolidated by choosing a slightly modified velocity and viscosity scales thereby enabling a satisfactory correlation between the modified Nusselt number and Reynolds number. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction It is readily acknowledged that many multiphase and/or struc- tured fluids like foams, emulsions and suspensions encountered in a range of engineering applications display visco-plastic flow behav- ior [1–3]. Typical examples include processed foods and chocolates [4], toiletries and cosmetics [5], drilling muds and lubricating greases [6], building materials [7], etc. Other examples can be found in Refs. [1–3,8,9]. A visco-plastic substance is characterized by its dual nature, i.e., when the externally applied stress is below its yield stress, it deforms like an elastic solid. Once the magnitude of the applied stress exceeds the value of the fluid yield stress, it deforms like a fluid with constant (Bingham plastic) or shear-thinning (Herschel–Bulkley) viscosity [8,9]. Naturally, such a dual nature makes convective transport in these fluids rather difficult, for only molecular transport occurs in the solid-like unyielded regions which may form a substantial part of the flow domain. This, in turn, can limit the overall rate of convective transport in such fluids. Thus, for instance, not only their mixing in batch systems tends to be rather difficult [9,10], heat transfer also is severely impeded in these fluids during their heating or cooling in numerous process engineer- ing applications. In spite of their frequent occurrence in a range of settings, very little is known about their heat transfer characteris- tics. A cursory inspection of the available body of information clearly reveals that the bulk of the literature pertains to duct flows [11,12], porous media flows [8,13]. Indeed, very little information is avail- able on heat transfer in visco-plastic fluids in the so-called external boundary layer-type of flows such as that over a sphere and a circu- lar cylinder. Depending upon the prevailing flow conditions, heat transfer may occur in the forced- or free- or the mixed-convection regimes. In the mixed-convection regime, the relative importance of the forced- and free-convection contributions is expressed using the familiar Richardson number, Ri, which is defined as Ri = Gr/Re 2 . Thus, the two limiting cases of Ri ? 1 and Ri ? 0 correspond to the pure free- and forced-convection flow regimes respectively. On the other hand, the values of the Richardson number of order unity correspond to the mixed-convection regime where the exter- nally imposed velocity is comparable to that due to the buoyancy effects. Therefore, under such conditions, both free- and forced con- vection contributions must be considered in a given application. Additional complications arise in the case of mixed convection depending upon the direction of the forced flow with reference to the direction of gravity. Thus, both flows may be in the same http://dx.doi.org/10.1016/j.jnnfm.2014.06.006 0377-0257/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +91 512 2597393; fax: +91 512 2590104. E-mail address: chhabra@iitk.ac.in (R.P. Chhabra). Journal of Non-Newtonian Fluid Mechanics xxx (2014) xxx–xxx Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: http://www.elsevier.com/locate/jnnfm Please cite this article in press as: A. Bose et al., Effect of aiding-buoyancy on mixed-convection from a heated cylinder in Bingham plastic fluids, J. Non-Newtonian Fluid Mech. (2014), http://dx.doi.org/10.1016/j.jnnfm.2014.06.006