Free and Forced Convective Heat Transfer

In Chapter 5 we derived the Equation of Energy and then applied it to various cases as, for example, in static systems (no flow). These situations were essentially cases of conduction or conduction together with heat generation. The flow cases that were treated were restricted to laminar flow and simplified geometries and boundary conditions. 

Situations that involve either turbulent flow, complex geometries, or difficult boundary conditions make it extremely difficult to obtain solutions of the Equation of Energy. For these cases, we must instead take a semiempirical approach which uses the concept of the heat transfer coefficient h. The defining equation for h is given as 

Using first principles and dimensionless forms, we will derive the basic format describing the heat transfer coefficient. Next, we will use experimental data or combination of analytical solutions of the Energy Equation and experimental data to obtain equation for h. 

Furthermore, because the heat flow can be defined by radial conduction at the wall, the total heat flow is given as 

The above assumes heat is added in the (—r) direction. Substituting for q gives 

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H. Miyazaki, Combined Free and Forced Convective Heat Transfer and Fluid Flow in a Rotating Curved Circular Tube, Int. J. Heat Mass Transfer (14) 1295-1309,1971. 

Acrivos, A. 1958. Combined laminar free and forced convection heat transfer in external flows. AIChE Journal. 4. 285-289. 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

In all flows involving heat transfer and, therefore, temperature changes, the buoyancy forces arising from the gravitational field will, of course, exist. The term forced convection is only applied to flows in which the effects of these buoyancy forces are negligible. In some flows in which a forced velocity exists, the effects of these buoyancy forces will, however, not be negligible and such flows are termed combined- or mixed free and forced convective flows. The various types of convective heat transfer are illustrated in Fig. 1.5. 

Maitra, D. and Sabba Raju, K., Combined Free and Forced Convection Laminar Heat Transfer in a Vertical Annulus". J. Heat Transfer Vol. 97. pp. 135-137. 1975. 

Depew, C.A. and August, S.E., Heat Transfer Due to Combined Free and Forced Convection in a Horizontal and Isothermal Tube , J. Heat Transfer Vol. 93, pp. 380-384, 1971. 

Yousef, W.W. and Tarasuk, J.D., Free Convection Effects on Laminar Forced Convective Heat Transfer in a Horizontal Isothermal Tube , J. Heat Transfer, Vol. 104, pp. 145-152, 1982. 

Conduction is treated from both the analytical and the numerical viewpoint, so that the reader is afforded the insight which is gained from analytical solutions as well as the important tools of numerical analysis which must often be used in practice. A similar procedure is followed in the presentation of convection heat transfer. An integral analysis of both free- and forced-convection boundary layers is used to present a physical picture of the convection process. From this physical description inferences may be drawn which naturally lead to the presentation of empirical and practical relations for calculating convection heat-transfer coefficients. Because it provides an easier instruction vehicle than other methods, the radiation-network method is used extensively in the introduction of analysis of radiation systems, while a more generalized formulation is given later. 

The third chapter covers convective heat and mass transfer. The derivation of the mass, momentum and energy balance equations for pure fluids and multi-component mixtures are treated first, before the material laws are introduced and the partial differential equations for the velocity, temperature and concentration fields are derived. As typical applications we consider heat and mass transfer in flow over bodies and through channels, in packed and fluidised beds as well as free convection and the superposition of free and forced convection. Finally an introduction to heat transfer in compressible fluids is presented. 

Convection is modeled using classical heat transfer relationships for free and forced convection. Normalized to naked body area, and using the temperature difference between the clothing and the ambient as the driving potential ... 

J. A. Sabbagh, A. Aziz, A. S. El-Ariny, and G. Hamad, Combined Free and Forced Convection in Inclined Circular Tubes, J. Heat Transfer (98) 322-324,1976. 

S. B. Memory, V. H. Adams, and P. J. Marto, Free and Forced Convection Laminar Film Condensation on Horizontal Elliptical Tubes, Int. J. Heat Mass Transfer, 40, pp. 3395-3406,1997. 

At an interface between gas and liquid or solid or between liquid and solid, convective heat transfer can take place when those media have a temperature difference. It can be in the form of free convection, such as in the case of a central heating radiator, or it can be forced convection, for example, an air flow from a blower. Owing to the resistance to heat transfer, a heat gradient will occur. In the model that describes this interface transfer, it is assumed, as shown in Fig. 2.8, that the temperature gradient restricts itself to a boundary layer. The bulk outside this boundary layer has a uniform temperature as a result of convection or mixing. Fig. 2.8 shows two possibilities. 

It is the purpose of this paper, therefore, to present experimental data which show the effect of frost on heat transfer for a variety of free and forced convection conditions and the applicability of certain existing heat transfer correlations to the low temperature case. 

Mixed free and forced convection. In this mass transfer situation, a free convection process driven either by thermal and/or concentration Ap differences is present in the boundary layer formed by forced convection flow parallel to the surface. The situation of pesticide evaporation from a hot soil surface into a light wind moving across is a good example. An empirical combination mle adapted from the heat transfer is proposed it is... 

It is not certain whether h2 is significant at this point. Using Eqs. 5.123 and 5.124 for forced convection heat transfer involving flow over a fiat plate and the conditions given in the problem, we estimate h2 = 2.8 W/m K, which is quite small. For free or natural convection from a vertical flat plate we use Eq. 5.132 to find = 3.87 W/m K, which again is small. Hence, we consider only the heat transfer at the film-drum surface and Eq. 5.190 becomes... 

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be... 

As explained in Chapter 1, natural or free convective heat transfer is heat transfer between a surface and a fluid moving over it with the fluid motion caused entirely by the buoyancy forces that arise due to the density changes that result from the temperature variations in the flow, [1] to [5]. Natural convective flows, like all viscous flows, can be either laminar or turbulent as indicated in Fig. 8.1. However, because of the low velocities that usually exist in natural convective flows, laminar natural convective flows occur more frequently in practice than laminar forced convective flows. In this chapter attention will therefore be initially focused on laminar natural convective flows. 

Eckert, E. and Diaguila, A.J., Convective Heat Transfer for Mixed. Free, and Forced Flow Through Tubes , Trans. ASME, Vcl. 76. pp. 497-504, 1954. 

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