Thermal convection in laminar boundary layers III

Abstract

The exact value of the heat loss in laminar thermal convection at the surface of horizontal cylinders and spheres is as yet difficult to calculate explicitly with the aid of the so-called exact boundary layer theory. In this paper we shall therefore calculate the local heat transfer by an approximation method first introduced by S qui r e for a flat plate. The calculations are performed for horizontal cylinders and spheres in first approximation for some values of the Prandtl number between 0.7 and ex» and in second approximation for Pr = co. The results look reasonable in themselves.while the total heat transfer is in rather good agreement with experiment. especially for a horizontal cylinder in air. This more or less justifies the approximations introduced. In the last paragraph we consider some details of the second approximation for large values of the Prandtl number and compare the theoretical results for different shapes of the body. § 1. Two-dimensional case. In our first article, to which we refer as part 1 1 ) , we showed that in the neighbourhood of a stagnation point the solution of the boundary layer equations is "similar". If the stagnation point is a regular point of the surface, the local Nusselt number is a constant, and the maximum tangential velocity component increases linearly as a function of the distance from the stagnation point. In general the solution loses its similarity at some distance from the stagnation point, so that it is then no longer possible to describe the heat transfer with two ordinary differential equations. Expanding sin e in terms of~, we may calculate the heat transfer by means of series in the same way as has been done by B I a s ius and Hie men z for isothermal flow in the boundary layer and by F r 6 s s lin g 7) for forced convection. In that case we have to solve many differential equations. To avoid this we shall use -207-

Numerical investigation of the laminar natural convection heat transfer from two horizontally attached horizontal cylinders

“…What the most important is that no correlations for predicting the heat transfer rate of the horizontal array of cylinders set in contact. The derivation of heat transfer dimensionless correlating equations is a key issue in natural convection, either for a single cylinder [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] or multiple cylinders [24-26,29-33,3 9-41]. Moreover, such extreme case is commonly encountered in electronic cooling device and the various gun barrels, e.g., double-barreled shotgun, antiaircraft gun, rocket artillery and naval gun.…”

“…In the early stage of the field, most of researchers concentrate on the investigations of the flow and heat transfer characteristics for a single cylinder in free space [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], on account of their fundamental significances. They mainly concerned about the correlating equations for the average Nusselt number as a function of Rayleigh number, or both Rayleigh number and Prandtl number, to provide an accurate prediction on the heat transfer coefficients in the process of engineering calculations.…”

Study on heat transfer coefficients during cooling of PET bottles for food beverages

“…This configuration allowed one, during horizontal position cooling, to monitor wall temperature laterally (T3) and simultaneously in the upper side (T4). Indeed, it was shown by many authors that local heat transfer coefficient remarkably changes along the circumference of a horizontal cylinder during natural convection [16]. Holes allowing thermocouples wires passage were sealed with epoxy resin (Loctite 406).…”

“…Operating in horizontal position prevented the air inside the bottle from being confined in the top part of the bottle only. Data collection took place, according to a discontinuous procedure, at certain time intervals, owing to the difficulty Horizontal, spinning [16] to wire a data acquisition device to a rotating bottle. For air cooling, measurement were effectuated after 2, 5, 10 and 20 min.…”

Ice formation in the subcooled brine environment

“…In most cases, N u is a function of the Rayleigh number, Ra, and the Prandtl number, P r, for natural convection only (Gr/Re , N u is a function of Re, Gr and P r; natural and forced convections are in the same order of magnitude (2c) [24][25][26][27].…”