Many research papers have been published concerning steady-state heat transfers from concentrated heat sources within enclosed spaces. Significant natural-convections occur in such diverse situations as from heaters in ovens, within enclosed micro-electronic component and electrical switch-box enclosures, and during fuel-oil storage-tank heating. Studies (e.g. [10–16]) of heat transfers from horizontal cylinders, in free space or close to adjoining walls, have indicated changes in the rate of natural convection depending upon the spacings between the heaters, between each heater and the wall, and on whether the wall is vertical or horizontal.

The convective currents associated with horizontal, relatively high-temperature single cylinders or wires in free space have been studied intensively: the review by Morgan contains a comprehensive compilation of the pertinent correlations. Eckert and Soehngen considered the effect, on natural convection, of offsetting the middle horizontal cylindrical heater of a vertically-aligned array of three such heaters, each of 22.3 mm diameter (d). Lieberman and Gebhart subsequently investigated the effect of varying the spacing between thin, heated wires (each with d=0·127 mm). Sparrow and Boesneck compared the effects of a range of horizontal and vertical offsets with that for no offset using only two horizontal cylinders, each of 38 mm diameter. These studies concluded that, for the considered circumstances, the Nusselt number of the upper heater decreased to 87% of that of the lower heater, depending upon the vertical separation, because of the warm plume rising from the lower cylinder. However, if the upper heater was offset transversely by 0·5d from the vertical plane passing through the lower heater, the Nusselt number increased by 3%, because the plume from the lower heater entrains cooler air from the surroundings and it approaches the upper heater at a higher velocity.

The effect upon the rate of natural convection from a horizontal cylindrical heater (with d=6.35 mm), of the presence of two confining vertical parallel plates was studied by Marsters. Sparrow and Pfeil carried out a similar study, but employed a larger horizontal cylinder (of 38 mm diameter) situated between two walls which formed a vertical channel. Tokura et al.. examined the behaviours of 3- and 5-cylinder cylindrical arrays, with d=28.5 mm, also confined between vertical parallel plates. These studies achieved rate-of-heat transfer enhancements of up to 40%, as a result of increasing the spacing between the cylinders and the wall. With the aid of flow visualisation, Al-Alusi and Bushnell showed that a chimney effect existed to induce air flows around a 3-cylinder (each with d=25.4 mm) horizontal array situated along a single vertical wall.

Sparrow and Ansari examined the heat-transfer characteristics of three configurations, namely a heated, horizontal cylinder in close proximity to three types of walls: (i) a vertical wall situated to the side of the cylinder; (ii) a horizontal wall situated beneath the cylinder, and (iii) a corner formed by vertical and horizontal walls with the cylinder within its included angle. The geometry has the following effects on the rate of steady-state natural convection. The presence of (i) a closely-positioned side wall (in an otherwise open space) usually reduces the cylinder’s Nusselt number in relation to that occurring when no wall was present, but this value is increased if the horizontal spacing exceeds 0.25 of the cylinder’s diameter (i.e. Nu/Nu_?>1 for S_h/d>0.25); and (ii) a plane horizontal wall beneath the heater always reduces the relative value of the Nusselt number, i.e. Nu/Nu_?<1.0 throughout. When the heater was positioned near the corner, i.e. (iii) the relative rate of natural convection ( / _?) was found to be reduced to as low as 0.6.

Extensive experimental and numerical studies of the heat transfers across various fluid-filled cylindrical annuli exist. Kuehn and Goldstein presented an experimental study, which analysed the effects of annular eccentricity on natural-convection heat transfer through air. The inner object was a relatively-large, 35.6 mm-diameter cylindrical heater in a 92.5 mm-diameter cylindrical enclosure: a non-linear relationship was established between the convective-heat transfer and the heater elevation. Cho et al. also derived numerically corresponing non-linear relationships when the inner cylinder was traversed both horizontally and vertically. Shilston carried out an experimental investigation by traversing a 28 mm-diameter cylindrical heater along the vertical line of symmetry in a 100 mm×100 mm square-sectioned, 600 mm long enclosure. With the aid of a Mach–Zehnder interferometer, the rate of natural convection heat transfer was found to decrease as the heater was moved away from a concentric position towards the upper horizontal wall, although enhancement was noted when it was located just below the central position.

In the experimental studies of Warrington and Powe, particular emphasis was placed on how the rates of heat transfer from a variety of hotter, axi-symmetrical inner bodies (i.e. sphere, cube and cylinder) are influenced by their locations in a cubical (267 mm×267 mm×267 mm) enclosure. When compared with the studies of Weber et al. involving a spherical enclosure, it was revealed that the enclosure size and the gap between the spherical inner body and the enclosure had more significant influences on the rate of natural convection than the shape of the enclosure. The numerical investigation of Deschamps and Desrayaud concerned a cylindrical or line-heat source, situated in a rectangular-sectioned enclosure. At higher values of Ra, there was increased convective activity near the upper horizontal wall (i.e. the ceiling). The experimental and numerical study of Zhao et al., for three uniform-heat-flux emitting cylinders, placed side-by-side near the base of a rectangular enclosure (which served as the heat sink), revealed that the centrally-positioned cylinder was warmest and experienced the lowest mean convective heat-transfer because of the restricted peripheral flows around it.

While many research studies have considered symmetrically-located heaters in enclosures, practical systems, such as encountered in ovens, often require the installation of cylindrical heaters along the enclosure walls. There is a wide variation of the Nusselt number values depending upon the heater location, and even then, there are insufficient experimental data for the intricate and complicated air-flow processes. Thus an attempt is made, in this investigation, to quantify the dependence of the steady-state rate of natural convection from a heater with its location in a rectangular enclosure.

This consisted of a horizontal cylindrical heater located within a metal box with glazed end-plates. This square-sectioned (350 mm×350 mm) enclosure, 750 mm long horizontally, was fabricated from 1.2 mm thick mild-steel sheet, and its inner surfaces finished with a high-temperature matt-black paint (=0.85±0.01). High–temperature glass plates were used to cover the ends of the enclosure. The enclosure was the cold surface, being cooled by the surrounding ambient air, i.e. similar to the experimental method of Zhao et al. The lower horizontal surface will be referred to as the base while the upper horizontal surface is termed the crown.

The first heat-source to be employed in the enclosure was a single cylindrical electric heater, of 9.5 mm diameter and an overall heated length of 590 mm. The maximum power-input flux for the electric element was limited to 990 W/m² of heating surface, so resulting in relatively low heater-temperatures (?363 K), and hence the radiation contribution did not dominate the heat transfers. An automatic a.c. voltage stabiliser and an auto-transformer were employed to provide a stable power supply to maintain steady-state temperature-distributions. The power consumption of the heater was measured with a calibrated wattmeter.