Heat transfer from sphere

Kramers. H. Physica 12 (1946) 61. Heat transfer from spheres to flowing media. 

Kramers, H., Heat Transfer from Spheres to Flowing Media, Physica, 12 61 (1946)... 

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... 

Yuge, T., Experiments on Heat Transfer from Spheres Including Combined Natural and Forced Convection , J. Heat Transfer, Vol. 82, pp. 214-220. I960. 

McAdams [10] recommends the following relation for heat transfer from spheres to a flowing gas ... 

Kowalski, G. J. Mitchell, J. W. "Heat Transfer from Spheres in the Naturally Turbulent, Outdoor Environment" J. Heat Transfer, p. 649-653, 1976. 

A226 [26] E. Ackenbach. Heat transfer from spheres up to Re = 6 x 10s, In Proc. 6th Int. Heat Trans Conf., vol. 5. Hemisphere, Washington, DC,1978. 

Dhir, V.K., and Purohit, G.P., "Subcooled Film-Boiling Heat Transfer from Spheres," American Institute of Chemical Englneers/Amerlcan Society of Mechanical Engineers Heat Transfer Conf., Salt Lake City, UT, 1977. 

Temperatures at off-centre locations within the solid body can then be obtained from a further series of charts given by Heisler (Figures 9.17-9.19) which link the desired temperature to the centre-temperature as a function of Biot number, with location within the particle as parameter (that is the distance x from the centre plane in the slab or radius in the cylinder or sphere). Additional charts are given by Heisler for the quantity of heat transferred from the particle in a given time in terms of the initial heat content of the particle. 

I I. Tayi.or, T.D. Physics of Fluids 6 (1963) 987. Heat transfer from single spheres in a low Reynolds number slip flow. 

DeBortoli, R. A., and R. Masnovi, 1957, Effect of Dissolved Hydrogen on Burnout for Water Flowing Vertically Upward in Round Tubes at 2000 psia, USAEC Rep. WAPD-TH-318, Pittsburgh, PA. (5) Ded, J., and J. H. Lienhard, 1972, The Peak Pool Boiling Heat Transfer from a Sphere, AIChE J. 18(2)331-342. (2)... 

Cornish, A. R. H. Trans. Inst. Chem. Eng. 43 (1965) T332. Note on minimum possible rate of heat transfer from a sphere when other spheres are adjacent to it. 

Fig. 5.17 Local Nusselt number for heat transfer from a sphere to air (Pr = 0.71). Experimental results of Galloway and Sage (Gl). Dashed lines are predictions of boundary layer theory by Lee and Barrow (LIO).

Fig. 5.20 Nusselt number for heat transfer from a sphere to air (0.70 < Pr < 0.73). Lines calculated from Eqs. A and B of Table 5.4 and Eq. (5-25).

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). 

Hatim (H2) obtained numerical solutions for heat transfer from a sphere of constant temperature accelerating from rest. The trajectory was calculated from Eq. (11-33), and the time-dependent Navier-Stokes and energy equations... 

The analytical solution for convective heat transfer from an isolated particle in a Stokes flow can be obtained by using some unique perturbation methods, noting that the standard perturbation technique of expanding the temperature field into a power series of the Peclet number (Pe = RepPr) fails to solve the problem [Kronig and Bruijsten, 1951 Brenner, 1963]. The Nup for the thermal convection of a sphere in a uniform Stokes flow is given by... 

Example 4.2 Show that the convective heat transfer from a sphere in a flowing medium at low Reynolds number can be expressed by Eq. (4.42). It is assumed that the sphere is kept at a constant temperature Tp and the temperature inside the sphere is uniform. The flow is uniform with velocity of Uco and temperature of Too at infinity. All the thermal properties are constant. 

Hughmark, G. A. (1967). Mass and Heat Transfer from Rigid Spheres. AIChE J., 13, 1219. 

Witte [32] has measured the heat transfer from a sphere to liquid sodium during forced convection, with the data being correlated by... 

Vliet.G. C.,andG. Leppert Forced Convection Heat Transfer from an Isothermal Sphere to Water, J. Heat Transfer, serv. C. vol. 83, p. 163, 1961. 

Witte, L. C. An Experimental Study of Forced-Convection Heat Transfer from a Sphere to Liquid Sodium, J. Heat Transfer, vol. 90, p. 9, 1968. 

Amato, W. S., and C. V. Tien Free Convection Heat Transfer from Isothermal Spheres in Water, Int. J. Heat Mass Transfer, vol. 15, p. 327, 1972. 

In the same article Treybal utilizes information on mass transfer from solids and heat transfer to spheres, to arrive at a procedure for making rough estimates of extraction stage efficiencies for baffled vessels agitated with flat-blade turbine impellers. Results from this calculation procedure are in general agreement with the experimental results of Flynn and Treybal and of Overcashier et al. 

Figure 17.37. Some measured and predicted values of heat transfer coefficients in fluidized beds. 1 Btu/hr(sgft)(°F) = 4.88 kcal/(hr)(m )(°C) = 5.678 W/(m )(°C). (a) C o mp arisen of correlations for heat transfer from silica sand with particle size 0.15 mm dia nuiaized in air. Conmtions are identified in Table 17.19 Leva, 1959). (b) Wall heat transfer coefficients as function of the superficial fluid velocity, data of Varygin and Martyushin. Particle sizes in microns (1) ferrosilicon, i 82.5 (2) hematite, d = 173 (3) Carborundum, d = 137 (4) quartz sand, d = 140 (5) quartz sand, d = 198 (6) quartz sand, d = 216 (7) quartz sand, d = 428 (8) quartz sand, d = 51.5 (9) quartz sand, d = 650 (10) quartz sand, d = 1110 (11) glass spheres, d= 1160. Zabrqdskystal, 1976,Fig. 10.17). (c) Effect of air velocity and particle physical properties on heat transfer between a fluidized bed and a submerged coil. Mean particle diameter 0.38 mm (I) BAV catalyst (II) iron-chromium catalyst (III) silica gel (IV) quartz (V) marble Zabrodsky et at, 1976, Fig. 10.20).

We stait this chapter with one-dimensional steady heat conduction in a plane wall, a cylinder, and a sphere, and develop relations for thennal resistances in these geometries. We also develop thermal resistance relations for convection and radiation conditions at the boundaries. Wc apply this concept to heat conduction problems in multilayer plane wails, cylinders, and spheres and generalize it to systems that involve heat transfer in two or three dimensions. We also discuss the thermal contact resislance and the overall heat transfer coefficient and develop relations for the critical radius of insulation for a cylinder and a sphere. Finally, we discuss steady heat transfer from finned surfaces and some complex geometries commonly encountered in practice through the use of conduction shape factors. 

When the lumped system analysis is not applicable, the variation of temperature with position as well as time can be determined using the transient temperaiure charts given in Figs, 4-15,4-16, 4 17, and 4-29 for a large plane wall, a long cylinder, a sphere, and a semi-infinite medium, respectively. These charts are applicable for one-dimensional heal transfer in those geometries. Therefore, their use is limited to situations in which the body is initially at a uniform temperature, all surfaces are subjected to the same thermal conditions, and the body docs not involve any heat geiieiation. Tliese charts can also be used to determine the total heat transfer from the body up to a specified lime I. 

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. 

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