Spheres natural convection

Garner and Keey(52 53) dissolved pelleted spheres of organic acids in water in a low-speed water tunnel at particle Reynolds numbers between 2.3 and 255 and compared their results with other data available at Reynolds numbers up to 900. Natural convection was found to exert some influence at Reynolds numbers up to 750. At Reynolds numbers greater than 250, the results are correlated by equation 10.230 ... 

Experimental data on heat transfer from spheres to an air stream are shown in Fig. 5.20. Despite the large number of studies over the years, the amount of reliable data is limited. The data plotted correspond to a turbulence intensity less than 3%, negligible effect of natural convection (i.e., Gr/Re <0.1 see Chapter 10), rear support or freefloating, wind tunnel area blockage less than 10%, and either a guard heater on the support or a correction for conduction down the support. Only recently has the effect of support position and guard heating been appreciated a side support causes about a 10% increase in Nu... 

The details of natural convective flows over surfaces other than flat plates have only recently been studied experimentally (A7, Jl, P3, SI2). We consider a heated sphere in an infinite, stagnant medium. Flow is directed toward the surface over the bottom hemisphere and away from the surface over the top hemisphere with a stagnation point at each pole (P3, S12). The lower pole is considered the forward stagnation point. 

In Fig. 10.4 the sphere diameter, terminal velocity, and temperature difference each appear in only one dimensionless group. The effect of natural convection on is smaller at Pr = 10 because the region over which the buoyancy force acts is much thinner than for Pr = 1. As Pr oo the effect should disappear altogether. For Pr = 0, numerical solutions (W7) show effects about 50% larger than for Pr = 1. 

Consideration of the available data for spheres indicates that forced flow correlations are accurate to about 10% for Gq/Re < 0.2. The analogous limit for natural convection is not so well defined, being about 10 at Pr = 0.7 and increasing with Pr. Additional studies of mixed convection are needed to elucidate the physical phenomena and provide correlations. Simultaneous mass... 

Equations (10-65) and (10-66) give a good fit to data of Takao (Tl) for heat transfer from a brass sphere to air with = 0.8. Natural convection at low pressures has been studied for cylinders and spheres (D9, K12). 

The slip-velocity theories are based on the correlations of steady state transfer to particles fixed in space, with the average slip velocity used to calculate the Reynolds number. When natural convection effects are absent and when the Reynolds number is greater than 1, the transfer rate for single spheres is given by the semitheoretical equation (Harriot, 1962)... 

Spalding (51, 55, 60) presents, in dimensionless form, data on natural convection for kerosine, gas oil, petrol, and heavy naphtha burning from a 1.5-inch sphere. He suggests the following empirical relation (see Equation 8) for a range of transfer numbers, B, of 0.25 to 3 ... 

Equation (4.15) indicates that, for an isolated, isothermal solid sphere in an infinite fluid, Nup approaches 2 in the limit of negligible forced or natural convection. This relationship was confirmed experimentally by Ranz and Marshall (1952). 

Bishop, E. N., L. R. Mack.andJ. A. Scanlan Heat Transfer by Natural Convection between Concentric Spheres, Int. J. Heat Mass Transfer, vol. 9, p. 649, 1966. 

M. Other objects, including prisms, cubes, hemispheres, spheres, and cylinders forced convection jD=omzN ,NMr = -M- Terms same as in 5-20-J. [E] Used with arithmetic concentration difference. Agrees with cylinder and oblate spheroid results, 15%. Assumes molecular diffusion and natural convection are negligible. 500 < Nfo p < 5000. Turbulent. [88] p. 115 [141] p. 285 [111][112]... 

Natural Convection over Surfaces 510 Vertical Plates (Fj = constant) 512 Verbeal Plates (4 = constant) 512 Vertical Cylinders 512 Inclined Plates 512 Horizontal Plates 513 Horizontal Cylinders and Spheres 513... 

Mass How Rate ttirougn ttie Space beLV, een Plates 519 9-5 Natural Convection Inside Enclosures 521 effective Thermal Conductivity 522 Horizontal Rectangular Enclosures 523 Inclined Rectangular Enclosures 523 Vertical Rectangular Enclosures 524 Concentric Cylinders 524 Concentric Spheres 525 Combined Natural Convection and Radiation 525... 

The two concentric spheres of diameters D, = 20 cm and D = 30 cm shown in Ftgt 9-30 are separated by air at 1 atrn pressure. The surface temperatures of the tv/o Spheres enclosing the air are T, - 320 K and T - 280 K, respectively. Determine the rate of heat transfer from the inner sphere to the outer sphere by natural convection. 

Discussion Note that the air in the spherical enclosure acts like a stationary fluid whose thermal conductivity is Aif/k = 0.1105/0.02566 = 4.3 times that of air as a result of natural convection currents. Also, radiation heat transfer 1 between spheres is usually significant, and should be considered in a complete 1 analysis. 

For a spherical enclosure, the rate of heat transfer through the space between the spheres by natural convection is expressed as... 

Calderbank and Moo-Young also confirmed the classical correlation for mass and heat transfer through natural convection in dispersions of fine droplets or fine gas bubbles for so-called rigid spheres" ... 

Under conditions of laminar flow, the usual natural convection equations can be used. Reference (K2) gives a table of heat transfer equations for spheres and cylinders recommended for use when molecular conduction is a factor, and a second table applicable to natural convection under laminar flow conditions. 

Enclosure problems (Fig. 4.1c) arise when a solid surface completely envelops a cavity containing a fluid and, possibly, interior solids. This section is concerned with heat transfer by natural convection within such enclosures. Problems without interior solids include the heat transfer between the various surfaces of a rectangular cavity or a cylindrical cavity. These problems, along with problems with interior solids including heat transfer between concentric or eccentric cylinders and spheres and enclosures with partitions, are discussed in the following sections. Property values (including P) in this section are to be taken at Tm = (Th+ TC)I2. 

R. J. Kee, C. S. Landram, and J. C. Miles, Natural Convection of a Heat Generating Fluid Within Closed Vertical Cylinders and Spheres, J. Heat Transfer (98) 55-61,1976. 

J. H. Min and F. A. Kulacki, Transient Natural Convection in a Single-Phase Heat Generating Pool Bounded From Below by a Segment of a Sphere, Nucl. Eng. Des. (54) 267-278,1979. 

N. Weber, R. E. Powe, E. H. Bishop, and J. A. Scanlan, Heat Transfer by Natural Convection Between Vertically Eccentric Spheres, /. Heat Transfer (95) 47-52,1973. 

Natural convection to blunt bodies such as cylinders (2-dimensional) and spheres (3-dimensional) has been studied by Acrivos (9) and from his analysis one can show that these configurations are characterized by constant boundary-layer thicknesses. For 2-dimensional bodies,... 

Natural convection is caused by density differences Ap, which result from temperature differences or from concentration differences. The characteristic length is the contact length, i.e., the height of a vertical wall, half of the circumference of a vertical cyhnder or half of the circumference of a sphere. The volume related buoyancy energy, that is caused by the density difference Ap in the gravity field of the earth, is transformed into kinetic energy ... 

Fig. 4.3-4 Nusselt number depending on the product Gr Pr for the sphere and the cylinder at natural convection. The illustrated straight line gives a theoretical solution (by Schmidt and Beckmann 1930) for a Prandtl number of 0.73...

---