Forced and Natural Convection

HEAT TRANSFER BY CONVECTION 9.4.1. Natural and forced convection 

Heat transfer by convection occurs as a result of the movement of fluid on a macroscopic scale in the form of eddies or circulating currents. If the currents arise from the heat transfer process itself, natural convection occurs, such as in the heating of a vessel containing liquid by means of a heat source situated beneath it. The liquid at the bottom of the vessel becomes heated and expands and rises because its density has become less than that of the remaining liquid. Cold liquid of higher density takes its place and a circulating current is thus set up. 

In forced convection, circulating currents are produced by an external agency such as an agitator in a reaction vessel or as a result of turbulent flow in a pipe. In general, the magnitude of the circulation in forced convection is greater, and higher rates of heat transfer are obtained than in natural convection. 

In most cases where convective heat transfer is taking place from a surface to a fluid, the circulating currents die out in the immediate vicinity of the surface and a film of fluid, free of turbulence, covers the surface. In this film, heat transfer is by thermal conduction and, as the thermal conductivity of most fluids is low, the main resistance to transfer lies there. Thus an increase in the velocity of the fluid over the surface gives rise to improved heat transfer mainly because the thickness of the film is reduced. As a guide, the film coefficient increases as (fluid velocity) , where 0.6 n 0.8, depending upon the geometry. 

If the resistance to transfer is regarded as lying within the film covering the surface, the rate of heat transfer Q is given by equation 9.11 as  

When a fluid is heated, the hot less-dense fluid rises and is replaced by cold material, thus setting up a natural convection current. When the fluid is agitated by some external means, then forced convection takes place. It is normally considered that there is a stationary film of fluid adjacent to the wall and that heat transfer takes place through this film by conduction. Because the thermal conductivity of most liquids is low, the main resistance to the flow of heat is in the film. Conduction through this film is given by the usual relation (74), but the value of h is not simply a property of the fluid but depends on many factors such as the geometry of the system and the flow dynamics for example, with tubes there are significant differences between the inside and outside film coefficients. 

Dimensional analysis shows that, in the treatment of natural convection, the dimensionless Grashof number, which represents the ratio of buoyancy to viscous forces, is often important. The definition of the Grashof number, Gr, is 

The characteristic dimension in the Nusselt and Grashof numbers is the length of the plate. 

When free convection occurs from a horizontal cylinder and Gr Pr 10  

In this case, the diameter of the cylinder is the characteristic length used for calculating both the Nusselt and Grashof numbers. 

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Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO9 to develop correlations for mass-transfer coefficients [Lim et al., Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The data were correlated over a wide range of conditions with the following equation for combined natural and forced convection ... 

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

Fand, R.M. and Keswani, K.K., Combined Natural and Forced Convection Heat Transfer from Horizontal Cylinders to Water , Int. J. Heat Mass Transfer, Vol. 16, p. 175, 1973. 

Convection is the transfer of energy by conduction and radiation in moving, fluid media. The motion of the fluid is an essential part of convective heat transfer. A key step in calculating the rate of heat transfer by convection is the calculation of the heat-transfer coefficient. This section focuses on the estimation of heat-transfer coefficients for natural and forced convection. The conservation equations for mass, momentum, and energy, as presented in Sec. 6, can be used to calculate the rate of convective heat transfer. Our approach in this section is to rely on correlations. 

Consider combined natural and forced convection, and assess the relative importance... 

When a surface is subjected to external flow, the problem involves both natural and forced convection. The relative importance of each mode of heat transfer is determined by the value of the coefficient Gr /Ref Natural convection effects are negligible if GiJRel 1, free convection dominates and the forced convection effects are negligible if Gri/Re > 1, and both effects are significant atid must be considered if Grt/Re = 1. 

A plot of the nondimensionalized heal transfer coefficient for combined natural and forced convection on a vertical plate is given in Fig. 9 32 for different fluids. We note from this figure that natural convection is negligible when Gr/Re <0.1, forced convection is negligible when Gr/Re > 10, and neither is negligible when 0.1 < Gr/Re < 10. Therefore, both natural and forced convection must be considered in heal itaiisfer calculations when the Gr and Re are of the same order of magnitude (one is within a factor of 10 times die other). Note that forced convection is small relative to natural convection only in the rare case of extremely low forced flow velocities. 

Variation of the local Nussell number Nu 5 for combined natural and forced convection from a hot isothermal vertical plate. 

When determining heat transfer under combined natural and forced convection conditions, it is tempting to add the contributions of natural and forced convection in assisting flows and to subtract them in opposing flows. However, the evidence indicates differently. A review of experimental data suggests a conelation of the form... 

Both natural and forced-convection oven types can be employed they have been described in the section on drying. The forced-convection oven offers the advantages of uniformity of heat distribution and reduction in lag time in comparison with the natural-convection system. The dry-heat method is reserved almost exclusively for glass or metal as other materials char (cellulose), oxidize (rubber), or melt (plastic) at these temperatures. 

Experimental gas-solid mass transfer data are presented for the well defined supercritical CO 2-naphthalene system at 10-200 atm and 35 C. These data are compared with low pressure gas-solid and liquid-solid systems. It has been found that both natural and forced convection are important under these conditions and that mass transfer rates at near-critical conditions are higher than at lower or higher pressure. 

When both natural and forced convection are important equations 13 and 15 cannot correlate the data successfully Mandelbaum and B5hm (16) suggested the following correlation for combined natural and forced convection. 

A common approach to mixed convection is to compute the Sherwood number as the sum of the powers of pure natural and forced convection (18) ... 

Figure 3. Correlation for combined natural and forced convection in the C02-naphthalene system at 35 C...

At 35 C, the gas-solid mass transfer coefficient increases dramatically near the critical point, has its maximum value near 100 atm, and then decreases gradually as pressure increases. The mass transfer rate under supercritical conditions is much higher than at standard conditions (1 atm and 25 C) for liquid-solid and gas-solid systems, due to strong natural convection effects. Both natural and forced convection are important for supercritical mass transfer. 

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