1. Introduction

The flow and heat transfer past bluff bodies of various cross-sectional geometries is important because of advances in heat exchanger technology, cooling of electronic components and chips

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

of different shapes and sizes. Although the majority of these studies have focused on studying the cross-flow past bluff bodies such as cylinders of circular [1–6], elliptic [7–10], rectangular [11–15] and square cross-sections [16–20], there are fewer studies on the semicircular cylinder geometry [21–24]. Gode et al. [25] studied numerically the momentum and heat transfer characteristics of a two-dimensional (2D), incompressible and steady flow over a semicircular cylinder and pointed out that the wake ceases to be steady somewhere in the range of 120 ≤Re ≤ 130. Boisaubert and Texier [26] performed solid tracer visualizations to assess the effect of a splitter plate on the near-wake development of a semicircular cylinder for Reynolds numbers of Re ¼ 200 and 400 and three splitter plate configurations. Their results show that for Re ¼ 400, the splitter plate causes an increase in near-wake length, a decrease in near-wake maximum width, a secondary vortex formation and a decrease of the maximum velocity in the recirculating zone, while for Re ¼ 200, the near-wake keeps its symmetry and vortex shedding is inhibited. Nalluri et al. [27] solved numerically the coupled momentum and energy equations for buoyancy-assisted mixed convection from an isothermal hemisphere in Bingham plastic fluids and reported results for streamline and isotherm contours, local and mean Nusselt number as a function of the Reynolds, Prandtl, Richardson and Bingham numbers. Bhinder et al. [28] studied numerically the wake dynamics and forced convective heat transfer past an unconfined semicircular cylinder at incidence using air as the working fluid for Reynolds numbers in the range of 80 ≤ Re ≤ 180 and angles of incidence in the range of 0<sup>o</sup> ≤ α ≤ 180<sup>o</sup> . Based on the flow pattern and the angle of incidence, they identified three flow distinct zones and proposed a correlation for the Strouhal and averaged Nusselt number as a function of Re and α. Chandra and Chhabra [29] performed a numerical study to assess the flow and thermal characteristics from a heated semicircular cylinder immersed in power-law fluids under laminar free and mixed convection for the case of buoyancy-assisted flow. Their results show that as the value of the Richardson and Reynolds numbers increase, the drag coefficient shows a monotonic increase and that the average Nusselt number increases with an increase in the value of the Reynolds, Prandtl and Richardson numbers.

The foregoing survey of literature reveals that although the great majority of research for the flow and heat transfer past a heated hemisphere in cross-flow has been made for an unbounded domain, there are relatively few studies that deal with the investigation of the blockage constraints present in the confined hemisphere problem. Kumar et al. [30] performed a numerical analysis to investigate the forced convection of power-law fluids (power-law index varying from 0.2 to 1.8) around a confined heated semicircular cylinder for Reynolds numbers between 1 and 40 and Prandtl number of 50. They assessed the effects of blockage ratios ranging from 0.16 to 0.50 and found that for a fixed value of Re, the length of the recirculation zone decreased with an increase in the value of n and that the drag coefficients and the averaged Nusselt number increased with increasing blockage ratio for any value of n.

From the foregoing discussion, it is clear that no prior results are available on the flow and heat transfer characteristics past a confined tandem hemisphere array under buoyancy-assisted and buoyancy-opposing conditions. This study aims to fill this void in the existing literature. In this work, we numerically investigate the transient fluid flow and thermal characteristics in the mixed convection regime around two isothermal semicylinders of the same diameter in tandem arrangement confined inside a vertical channel of finite length using fixed Reynolds and Prandtl numbers, fixed blockage ratio and gap width and several values of the buoyancy parameter (Richardson number).
