# HVAC Systems Design Handbook part 18

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## HVAC Systems Design Handbook part 18

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This chapter presents a basic overview of heat transfer fundamentals, particularly as they apply to HVAC. For a detailed, rigorous treatment, the reader should refer to a good college-level text on heat transfer or to the ASHRAE Handbook.

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## Nội dung Text: HVAC Systems Design Handbook part 18

1. Source: HVAC Systems Design Handbook Chapter Engineering Fundamentals: 18 Part 3 Heat Transfer 18.1 Introduction This chapter presents a basic overview of heat transfer fundamentals, particularly as they apply to HVAC. For a detailed, rigorous treat- ment, the reader should refer to a good college-level text on heat trans- fer or to the ASHRAE Handbook.1 18.2 Heat Transfer Modes Heat is transferred between any two bodies by one or more of three modes: conduction, convection, and radiation. Thermal conduction re- fers to the direct transfer of energy between particles at the atomic level. Thermal convection may include some conduction but refers pri- marily to energy transfer by eddy mixing and diffusion, i.e., by ﬂuids in motion. Thermal radiation describes a complex phenomenon which includes changes in energy form: from internal energy at the source to electromagnetic energy for transmission, then back to internal en- ergy at the receiver. Radiation transfer requires no intervening ma- terial, and in fact works best in a perfect vacuum. In accordance with the second law of thermodynamics, net heat transfer occurs in the direction of decreasing temperature. In this text, the Fahrenheit ( F) scale is used, or for absolute temperatures the Rankine ( R) scale: R F 460 . 459 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
2. Engineering Fundamentals: Part 3 460 Chapter Eighteen 18.3 Thermal Conduction For steady-state conduction in one direction through a homogeneous material, the Fourier equation applies: q kA dt/dx (18.1) where q heat transfer rate, Btu/h k thermal conductivity, Btu/(h ft F) A area normal to ﬂow, ft2 dt/ dx temperature gradient, F/ft The minus sign shows that heat ﬂow takes place from a higher to a lower temperature. In HVAC calculations, homogeneous barriers are never encount- ered—even when the solid barrier is homogeneous, there will be ﬁlm resistance at its surface, as shown in Fig. 18.1. The heat transfer equa- tion is then modiﬁed as follows: q UA(T1 T2) (18.2) where U is the overall coefﬁcient of heat transfer per degree of tem- perature difference between the two ﬂuids which are separated by the barrier. Usually, but not always, U is given in Btu per hour per square foot per degree Fahrenheit. The temperatures and the area A must be in units consistent with those of U. Various building materials and combinations thereof have been tested to determine the conductivity k (Btu per hour per square foot per inch or foot of thickness per degree Fahrenheit) or conductance C (for a nonhomogeneous material such as a concrete block, in Btu per hour per square foot per degree Fahrenheit). The tests are made in a Figure 18.1 Conduction heat transfer through a wall. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
3. Engineering Fundamentals: Part 3 Engineering Fundamentals: Part 3 461 ‘‘guarded hot box,’’ designed so that heat transfer through the edges of the material is essentially eliminated. The results of these tests are tabulated and presented, with discussion, in the ASHRAE Handbook.2 The thermal conductivity k of any material is the reciprocal of its resistance R: 1 k (18.3) R For barriers with material combinations which are not tabulated, the U factor may be calculated from the sum of the individual resistances. The general form of the equation is 1 R1 R2 R3 Rn (18.4) U Because resistance is the reciprocal of conductance or conductivity, a more speciﬁc form of the equation is 1 1 x1 xn 1 1 1 (18.5) U fo k1 kn C1 Cn fi where fo outside ﬁlm conductance fi inside ﬁlm conductance x thickness of homogeneous section with conductivity k See Ref. 2 for a more detailed discussion. The incremental tempera- ture drop through each element of the barrier is proportional to the resistance of the element. For example, in Fig. 18.1 if the wall is 6-in- thick perlite concrete with a k value of 0.93 per inch, and if the outside and inside ﬁlm conductances are 4.00 and 1.46, respectively, then the overall U factor is 1 1 6 1 U 4.00 0.93 1.46 0.25 6.45 0.68 7.38 1 U 0.136 7.38 If a temperature difference of 42 F is assumed, based on 72 F inside and 30 F outside, then the temperature gradient can be determined as shown in Table 18.1. This type of calculation is useful in determin- ing the location where moisture condensation or freezing will take Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
4. Engineering Fundamentals: Part 3 462 Chapter Eighteen TABLE 18.1 Temperature Gradient Information place, such as on inside window surfaces. To avoid problems, extra insulation, double glazing, or surface heating may then be used. In HVAC practice, steady-state conduction seldom, if ever, takes place, because the outside air temperature and inside load conditions are constantly changing. The transient heat ﬂow effects which result are functions of several variables, including the mass (storage effect) of the barrier. The sensible heat gain and cooling load factors dis- cussed in Chap. 3 are approximations which allow the designer to compensate for these transients. 18.4 Thermal Convection Thermal convection refers to heat transfer by eddy mixing and diffu- sion, as in a ﬂowing airstream. In the typical airstream heating or cooling process, heat transfer takes place as a result of mixing with, and diffusion through, the air in the conditioned space. The ﬁnal transfer is by conduction between air particles. Convection may be natural or free convection, due to differences in density, or it may be forced by mechanical means such as fans or pumps. An HVAC process illustrating almost pure convective heat transfer is the mixing of two airstreams such as return air and outside air. If complete mixing takes place, the mixed airstream has a temperature (and humidity) resulting from a weighed average of the properties and masses of the two original air-streams. This is a result of convective eddy mixing and diffusion plus conductive heat transfer between par- ticles. A major HVAC application involving a combination of convection and conduction is heat exchange between two ﬂuids such as refriger- ant, water, steam, brine, and air, in many combinations. In general, the two ﬂuids are separated by a barrier, usually the wall of a tube or pipe. Typical examples are the shell-and-tube heat exchanger (see Fig. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
5. Engineering Fundamentals: Part 3 Engineering Fundamentals: Part 3 463 Figure 18.2 Heat transfer through a tube wall. 9.10) and the ﬁnned coil (see Fig. 9.20). In both cases, the barrier is a tube wall, as in Fig. 18.2. Heat transfer takes place within each ﬂuid stream by convection, then by conduction through the wall and the contiguous ﬁlms. The velocity of a ﬂuid stream ﬂowing uniformly in a conduit (tube or duct) is greatest at the center of the conduit and least near the edges (Fig. 18.3). This is due to friction of the ﬂuid particles against the wall and against each other. The ﬁlms of nearly motionless ﬂuids on each side of the wall resist heat transfer, as noted above. Because the tubes in heat exchangers are usually copper, with its high conductivity factor, the ﬁlms provide the major part of the resistance. Additional resistance is provided by the buildup of dirt, oil, or solids deposition on the tube surface. This is known as the fouling factor, and it is usually signiﬁcant. The ﬁlm resistance is a function of the ﬂuid velocity, being highest with laminar ﬂow and lowest with turbulent ﬂow. To estimate the degree of turbulence in a system, the Reynolds number Re is calcu- lated: DV Re (18.6) where D conduit diameter, ft V average ﬂuid velocity, ft/s ﬂuid viscosity, lb/(ft s) density, lb/ft3 The transition value of the Reynolds number is in the range of 2100 Figure 18.3 Velocity pattern for ﬂuid ﬂow in a conduit. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
6. Engineering Fundamentals: Part 3 464 Chapter Eighteen to 3100. Below 2100 ﬂow is assumed to be laminar. Above 3100 tur- bulence is assumed. Between 2100 and 3100 it may be either, depend- ing on various factors such as the roughness of the conduit. From the equation it is evident that laminar ﬂow is equated with low velocities and high viscosities—i.e., other conditions being equal, oil will have a lower Reynolds number than water. The overall heat transfer rate in- creases abruptly as ﬂow changes from laminar to turbulent. For a ﬁnned-coil ﬂuid-to-air heat exchanger, the general equation for heat transfer is Q kA ROWS MED (18.7) where Q total heat transfer, Btu/h k heat transfer coefﬁcient per row per square foot A face area of coil normal to airﬂow direction ROWS number of rows of tubes in direction of airﬂow MED mean temperature difference For a discussion and derivation of MED, see Sec. 9.7.2. The value of k is greatly increased if steam or refrigerant is used in the coil; the effect of two-phase boiling or condensing is to increase the value of k over that obtained with single-phase ﬂow. For a shell-and-tube ﬂuid-to-ﬂuid heat exchanger, the equation for heat transfer is Q kA(MED) (18.8) where k heat transfer coefﬁcient per square foot per degree Fah- renheit and A total outside surface area of tubing in square feet. Again, two-phase ﬂow increases the value of k. In Eqs. (18.7) and (18.8), the value of k must include the ﬁlm and fouling factors. The heat exchanger manufacturer can provide values of k for a range of ﬂow rates and fouling factors. 18.5 Thermal Radiation Radiation heat transfer between two bodies takes place directly, by using electromagnetic energy across the intervening space. It is most efﬁcient through a vacuum, because any intervening medium, even if transparent in the visible spectrum, will absorb some of the radiant energy. Several mechanisms are at work in radiant energy transfer, such as surface emittance and absorptance, absolute temperature differences, and geometry. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.