Otk 3 Paktann
Otk 3 Paktann
Otk 3 Paktann
7A
Natural convection heat transfer occurs when a solid surface is in contact with a gas or liquid which is at a different temperature from the surface. Density differences in the fluid arising from the heating process provide the buoyancy force required to move the fluid. Free or natural convection is observed as a result of the motion of the liquid. An example of heat transfer by natural convection is a hot radiator used for heating a room. Cold air encountering the radiator is heated and rises in natural convection because of buoyancy forces. The theoretical derivation of equations for natural convection heat-transfer coefficients requires the solution of motion and energy equations. An important heat-transfer system occurring in process engineering is that in which heat is being transferred from a hot vertical plate to a gas or liquid adjacent to it by natural convection. The fluid is not moving by forced convection but only by natural or free convection. In fig. 4.7-1 the vertical flat plate is heated and the free convection boundary layer is formed. The velocity profile differs from that in a forced convection system in that the velocity at the wall is zero and also is zero at the other edge of the boundary layer, since the free stream velocity is zero for natural convection. The boundary layer initially is laminar as shown, but at some distance from the leading edge it starts to become turbulent. The wall temperature is TwK and the bulk temperature Tb. The differential momemtum-balance equation is written for the x and y directions for the control volume (dx dy 1). The driving force is the buoyancy force in the gravitational field and is due to the density difference of the fluid. The momentum balace becomes
Where is the density at the bulk temperature Tb and the density at T. the density difference can be expressed in terms of the volumetric coefficient of expansion and substituted back into Eq. (4.7-1):
For gases,
The solutions of these equations have been obtained by using integral methods of analysis discussed in Section 3.10. Results have been obtained for a vertical plate, which is the simplest case and serves to introduce the dimensionless Grashof number discussed below. However, in
other physical geometries the relations are too complex and empirical correlations have been obtained. These are discussed in the following sections.
4.7B
1. Natural convection from vertical planes and cylinders. For an isothermal vertical surface or plate with height L less than 1 m (P3), the average natural convection heat transfer coefficient can be expressed by the following general equation:
Where a and m are constant from Table 4.7-1. NGr the Grashof number, density in kg/m3 , viscosity in kg/ms, the positive temperature difference between the wall and bulk fluid or vice versa in K, k the thermal conductivity in W/mK, the heat capacity in J/kgK, the volumetric coefficient of expansion of the fluid in 1/K [for gases is 1/(TfK], and g is 9.80665 m/s2. All the physical properties are evaluated at the film temperature Tf = (Tw + Tb)/2. In general, for a vertical cylinder with length L m, the same equation can be used as for a vertical plate. In English units is 2 1/(Tf + 460) in 1/ and g is 32.174 x (3600) 2 F R ft/h
4.10
4.10A Introduction and Basic Equation for Radiation 1. Nature of radiant heat transfer. In the preceding sections of this chapter we have studied conduction and convection heat transfer. In conduction, heat is transferres from one part of a body to another, and the intervening material is heated. In convection, heat is transferred by the actual mixing of materials and by conduction. In radiant heat transfer, the medium through which the heat is transferred usually is not heated. Radiation heat transfer is the transfer of heat by electromagnetic radiation. Thermal radiation is a form of electromagnetic radiation similar to X rays, light, waves, gamma rays, and so on, differing only in wavelength. It obeys the same laws as light. It travels in straight lines, can be transmitted through space and vacuum, and so on. It is an important mode of heat transfer and is especially important where large temperature differences occur, as, example, in a furnace with boiler tubes, in radiant dryers, or in an oven making food. Radiation often occurs in combination with conduction and convection. An elementary discussion of radiant heat transfer will be given here, with a more advanced and comprehensive discussion being given in Section 4.11.
In an elementary sense the mechanism of radiant heat transfer is composed of three distict steps or phases:
1. The thermal energy of a hot source, such as the wall of a furnace at T1, is converted into
T2, such as a furnace tube containing water to be heated. 3. The electromagnetic waves that strike the body are absorbed by the body and converted back to the thermal energy or heat. 2. Absorptivity and black bodies. When thermal radiation (such as light waves) falls upon a body, part is absorbed by the body in the form of heat , part is reflected back into space, and part may actually be transmitted through the body . for most cases in process engineering, bodies are opaque to transmission, so this will be neglected. Hence, for opaque bodies.
Where
A black body is defined as one that absorbs all radiant energy and reflects none. Hence, = 0 and =1.0 for a black body. Actually, in practice there are no perfect black bodies, but a close approximation is a small hole in a hollow body, as shown in Fig. 4.10-1. The inside surface of the hollow body is blackened by charcoal. The radiation enters the hole and impinges on the rear wall; part is absorbed there and part is reflected in all direction. The reflected rays impinge again, part is absorbed and the process continues. Hence, essentially all of the energy entering is absorbed and the area of the hole acts as a perfect black body. The surface of the inside walls is rough and rays are scattered in all directions, unlike a mirror, where they are reflected at a definite angle. As stated previously, a black body absorbs all radiant energy falling on it and reflects none. Such a black body also emits radiation, depending on its temperature, and does not reflect any. The ratio of the emissive power of a surface to that of a black body is called emissivity and is 1.0 for a black body. Kirchhoffs law states that at the same temperature T1, 1 and 1 of a given surface are the same, or
This equation holds for any black or nonblack solid surface. 3. Radiation from a body and emissivity. The basic equation for heat transfer by radiation from a perfect black body with an emissivity =1.0 is
Where is heat flow in W, A is m2 surface area of body, is a constant 5.676 x 10-8 W/m2K4 (0.1714 x 10-8 btu/h.ft2.R4), and T is temperature of the balck body in K (R). For a body that is not a black body and has an emissivity <1.0, the emissive power is reduced by , or
Substance that have emissivities of less than 1.0 are called gray bodies when the emissivity is independent of the wavelength. All real materials have an emissivity <1.0. Since thye emissivity and absorptivity of a body are equal at the same temperature, the emissivity, like absorptivity, is low for polished metal surfaces and high for oxidized metal surfaces. Typical values are given in Table 4.10-1 but do vary some with temperature. Most nonmetallic substance have high values. Additional data are tabulated in Appendix A.3.
4.10B Radiation to a Small Object from Surroundings In the case of small gray object of area A1 m2 at temperature T1 in a large enclosure at a higher temperature T2, there is a net radiation to the small object. The small body emits an amount of radiation to the enclosure given by Eq. (4.10-4) as A11T14. The emissivity 1 of this body is taken at T1. The small body also absorbs an amount of energy from the surrounding at T2 given by A112T24. The 12 is the absorptivity of body 1 for radiation from the enclosure at T2. The value of 12 is approximately the same as the emissivity of this body at T2. The net heat of absorption is then, by the Stefan-Boltzmann equation,
A further simplification of Eq. (4.10-5) is usually made for engineering purpose by using only one emissivity for the small body, at the temperature T2. Thus,
4.10C Combined Radiation and Convection Heat Transfer When radiation heat transfer occurs from a surface, it is usually accompanied by convective heat transfer, unless the surface is in a vacuum. When the radiating surface is at a uniform temperature, we can calculate the heat transfer for natural or forced convenction using the methods described in the previous sections of this chapter. The radiation heat transfer is calculated by the StefanBlotzmann equation (4.10-6). Then the total rate of heat transfer in the sum of convection plus radiation.
As discussed before, the heat-transfer rate by convection and the convective coefficient are given by
Where is the heat-transfer rate by convection in W, hc the natural or forced convection coefficient in W/m2K, T1 the temperature of the surface, and T2 the temperature of the air and the enclosure. A radiation heat-transfer coefficient hr in W/m2K can be defined as
Where is the heat-transfer rate by radiation in W. The total heat transfer is the sum of Eqs. (4.10-7) and (4.10-8),
A convenient chart giving values of in Englisg units calculated from Eq. (4.10-10) with =1.0 is given in Fig. 4.10-2. To use values from this figure, the vakue obtained from the figure should be multiplied by to give the value of to use in Eq. (4.10-9). If the air temperature is not the same as T2 of the enclosure, Eqs. (4.10-7) and (4.10-8) must be used separately and not combined together as in (4.10-9)