E. G. JACKSON and J. K. KILHAM Leeds University, Leeds, England
Heat Transfer from Combustion Products by Forced Convection
THE
problem of heat transfer by forced convection from a stream of gas flowing perpendicular to the axis of a single cylinder has received a considerable amount of attention. Kennelly and coworkers (6) used electrically heated wires in streams of air a t various velocities; Hughes (5) employed steam heated cylinders, and Gibson (3) experimented with water heated cylinders. In all these experiments the technique of passing a stream of cold air over a heated tube was used. But Reiher (73) investigated the converse method of measuring the heat imparted to a cool tube by hot air. The temperature of the air stream varied from 120' to 250' C., and the tubes were water cooled. The heat transfer in all the foregoing experiments was expressed as a function of the air velocity and the tube diameter. An analysis of the process of forced convection was attempted by King (70) who integrated the equation for thermal conduction in a moving fluid to obtain a relationship of the form h D l k = l/a
+ [ Z / T ( G D l p ) (cp/k)l0.5 (1)
where h is the heat transfer coefficient, D is the cylinder diameter, G is the mass velocity of the gases, and k and p are the thermal conductivity and viscosity of the gases, respectively. This equation gave values about 40y0 higher than those found experimentally, which is perhaps not surprising considering the assumptions involved. McAdams (72) has correlated all the available experimental data in terms of dimensionless groups and has shown that the following equation may be used for values of Reynolds' number
**TLR
INLETS
(GD/p) between 0.1 and 1000 hD/k = 0.32 f 0.43 (GD/p)O.62
(2)
This equation only applies for air, where the value of Prandtl number (cp/u/k) = 0.74. For any gas the corresponding equation is hD/k = (cp/k)"' L0.35 4- 0.47 (GD/p)o.6p] (3)
A study of the mechanism of heat transfer when a solid cylinder is immersed in flame gases has been made by Kilham (8). The experimental values of the heat transfer coefficient were compared with those calculated from McAdams' formula and showed remarkably good aggreement for carbon monoxide-air flames. The results obtained for hydrogen-air flames, however, indicated that the experimental heat transfer coefficients were all higher than the calculated values, the discrepancy decreasing as the height of the solid above the burner port increased. Before drawing any conclusions from these experiments-e.g., the possibility of hydrogen atom recombination on the solid surface-it was considered advisable to determine the validity of McAdams' equation at high temperatures. Source of Hot Gases
In view of the difficulty of heating a stream of an inert gas to the desired temperature it was decided to burn a combustible gas-air/oxygen mixture and maintain the combustion products a t a temperature as near as possible to that of the flame by passing them through a
%
heated enclosure which allowed the attainment of thermal equilibrium. The apparatus consisted of a variable annular port, water-cooled burner sealed into the base of a vertical molybdenumwound tube furnace as illustrated in Figure 1. The furnace tube, which was made of recrystallized alumina, was 61 cm. long and 6.3 cm. i.d. The molybdenum wire winding was prevented from oxidizing by an atmosphere of cracked ammonia. Measurement of Heat Transfer
The most suitable experimental arrangement was found to be a rectangular orifice in the top plug of the furnace tube through which the hot gases passed to impinge a t right angles upon a refractory cylinder supported above it. The effect of conduction was rendered negligible by measuring the radiation from a short element of the tube in the center of the hot gas stream. In order to even out the temperature distribution around the perimeter of the tube, it was rotated at about 40 r.p.m. This slow rate of rotation was insufficient to affect the heat transfer, since the tangential velocity of the rotating tube never exceeded 0.001 of the free stream gas velocity. Kilham (9) has also shown experimentally, for a similar case, that the effect of slow rotation of the tube on the convective heat transfer was negligible. The apparatus for measuring the intensity of radiation from a sillimanite tube (0.32 cm. 0.d.) immersed in the hot gas stream is shown diagrammatically in Figures 1 and 2. The thermo-
WATER O U T L l T i
CAI W L r l
Figure 1. General arrangement of the furnace, burner, and thermopile unit
I
Figure 2. Plan view of sillimanite tube, water-cooled screens, and thermopile VOL. 48, NO. 11
NOVEMBER 1956
2077
pile was a 30-element linear, Moll type having a rectangular aperture 0.32 X 1.27 cm. cut in the thin brass cover plate. It was calibrated against a black body furnace and used in conjunction with a moving coil galvanometer. Interposed between the thermopile and the sillimanite cylinder were two water-cooled screens, having rectangular apertures the same size as the thermopile cover plate. The tube, screens, and thermopile were accurately aligned so that the radiation from the full diameter of the tube over the central 1.27-cm. length could be measured. Correlation of the results obtained with those previously published required a knowledge of: Temperature of the gases Surface temperature of the solid Mass velocity of the hot gases
A consideration of the methods available for gas temperature measurement led to the use of a series of decreasing diameter thkrmocouples. The apparent temperature was measured by six platinum :platinum-1 0% rhodium thermocouples of diameters between 0.193 and 0.061 m m O n plotting the indicated temperatures against the square of the
Table 1. Experimental Forced Convective Heat Transfer Coefficients h (Exptl.), Gas Solid Cal./Sq. Temp., Temp., Crn., Sec., Tube Coatino O I
