30079_43b

# 30079_43b - Nu6 = 0.42Ra&lt;P Pr-012(S/#)0-3 for 10 &lt;...

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Nu6 = 0.42Ra<P Pr°-012(S/#)0-3 for 10 < H/d < 40, 1 < Pr < 2 X 104, and 104 < Ras < 107. 43.3.4 The Log Mean Temperature Difference The simplest and most common type of heat exchanger is the double-pipe heat exchanger, illustrated in Fig. 43.15. For this type of heat exchanger, the heat transfer between the two fluids can be found by assuming a constant overall heat transfer coefficient found from Table 43.8 and a constant fluid specific heat. For this type, the heat transfer is given by q=UA &Tm where A72 - A7\ = 2 i_ m ln(Ar2/A7\) In this expression, the temperature difference, A7m, is referred to as the log-mean temperature dif- ference (LMTD); AT^ represents the temperature difference between the two fluids at one end and A72 at the other end. For the case where the ratio A^/AT^ is less than two, the arithmetic mean temperature difference (AT2 + A7\)/2 may be used to calculate the heat-transfer rate without intro- ducing any significant error. As shown in Fig. 43.15, A7\ = ThJ - rc, AT2 - Thf0 - Tc,0 for parallel flow AT; = Thti - Tc^0 A72 = Th^0 - Tci for counterflow Cross-Flow Coefficient In other types of heat exchangers, where the values of the overall heat transfer coefficient, [/, may vary over the area of the surface, the LMTD may not be representative of the actual average tem- perature difference. In these cases, it is necessary to utilize a correction factor such that the heat transfer, q, can be determined by q = UAF AT; Here the value of Arm is computed assuming counterflow conditions, A7\ = Thti — TCti and A72 = Th,0 ~ TCt0. Figures 43.16 and 43.17 illustrate some examples of the correction factor, F, for various multiple-pass heat exchangers. 43.4 RADIATION HEAT TRANSFER Heat transfer can occur in the absence of a participating medium through the transmission of energy by electromagnetic waves, characterized by a wavelength, A, and frequency, v, which are related by c = Xv. The parameter c represents the velocity of light, which in a vacuum is c0 = 2.9979 X 108 m/sec. Energy transmitted in this fashion is referred to as radiant energy and the heat transfer process that occurs is called radiation heat transfer or simply radiation. In this mode of heat transfer, the energy is transferred through electromagnetic waves or through photons, with the energy of a photon being given by hv, where h represents Planck's constant. In nature, every substance has a characteristic wave velocity that is smaller than that occurring in a vacuum. These velocities can be related to c0 by c = c0/n, where n indicates the refractive index. The value of the refractive index n for air is approximately equal to 1. The wavelength of the energy given or for the radiation that comes from a surface depends on the nature of the source and various wavelengths sensed in different ways. For example, as shown in Fig. 43.18 the electromagnetic spectrum consists of a number of different types of radiation. Radiation in the visible spectrum occurs in the range A = 0.4-0.74 /mi, while radiation in the wavelength range 0.1-100 /mi is classified as thermal radiation and is sensed as heat. For radiant energy in this range, the amount of energy given off is governed by the temperature of the emitting body.

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## 30079_43b - Nu6 = 0.42Ra&lt;P Pr-012(S/#)0-3 for 10 &lt;...

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