流体力学与传热课件Heat Transfer and Its Applications

1、流体力学与传热课件流体力学与传热课件Heat Transfer Heat Transfer and Its Applicationsand Its Applications4.1.1 Nature of heat flow When two objects at different temperature are brought into thermal contact , heat flow from the object at the higher temperature to that at the lower temperature. The net flow is always in

2、 the direction of the temperature decrease.Steady-State Heat Transfer The heat transfer occurs in the control volume where the rate of accumulation of heat is zero and the temperatures at various points in the system do not change with time it is called as steady-state heat transfer. Basic Mechanism

3、s of Heat Transfer The mechanisms by which the heat flows are three: vConductionvConvectionv Radiation4.1.2 Conduction If a temperature gradient exists in a continuous substance, heat can flow unaccompanied by any observable motion of matter.According to Fouriers law, the heat flux is proportional t

4、o the temperature gradient and opposite to it in sign. For one-dimensional heat flowdxdtkdAdq In metals, thermal conduction results from the motion of free electrons.Thermal conduction for various materialsIn solids that are poor conductor of electricity and in most liquids, thermal conduction resul

5、ts from momentum transfer between adjacent vibrating molecules or atoms. In gases, conduction occurs by the random motion of molecules.4.1.3 Convection When a current or macroscopic particle of fluid crosses a specific surface, such as the boundary of a control volume, it carries withit a definite q

6、uantity of enthalpy. Such a flow of enthalpy is called a convective flow of heat. The convection flux is usually proportional to the difference between the surface temperature and temperature of the fluid, as stated in Newtons law of cooling)(fwtthAq(4.1-2) Note that the linear dependence on the tem

7、perature driving force tw-tf is the same as that for pure conduction in a solid of constant thermal conductivity. The heat-transfer coefficient is not an intrinsic property of the fluid, but depends on the flow patterns determined by fluid mechanics as well as on the thermal properties of the fluid.

8、The forces used to create convection currents in fluids are of two types:l natural convection l and force convectionNatural convection If the currents are the result of buoyancy forces generated by differences in density and the differences in density are in turn caused by temperature gradients in t

9、he fluid mass, the action is called natural convection. forced convectionIf the currents are set in motion by the action of a mechanical device such as a pump or agitator, the flow is independent of densitygradients, and is called forced convection.4.1.4 RadiationRadiation is a term given to the tra

10、nsfer ofenergy through space by electromagnetic waves. If radiating is passing through empty space, it is not transformed to heat or any other form of energy, nor is it diverted from its path.If , however, matter appears in its path, the radiation will be transmitted, reflected, or absorbed. It is o

11、nly the absorbed energy that appears as heat. The energy emitted by a black body is proportional to the fourth power of the absolute temperature.4TWb=stefan-boltzmann constant T=absolute temperature4.2 Heat Transfer by Conduction Conduction is most easily understood by considering heat flow in homog

12、eneous isotropic solids because in these there is no convection and the effect of radiation is negligible.The basic relation for heat flow by conduction is the proportionality between heat flux and the temperature gradient.dqTkdAn It can be writtenThe partial derivative calls attention to the fact t

13、hat the temperature may vary with both location and time. The negative sign reflects the physical fact that heat flow occurs from hot to cold and the sign of the gradient is opposite that of the heat flow. In using equation it must be clearly understood that the area A is that of a surface perpendic

14、ular to the flow of heat and distance n is the length of path measured perpendicularly to area A.For steady one-dimensional flow. Equationmay be written dxdtkdAdqWhere q= rate of heat flow in direction normal to surface x=distance measured normal to surface k= thermal conductivityThermal Conductivit

15、y The proportionality constant k is a physical property of the substance.It , like the viscosity , is one of the so-called transport properties of material. k vary over a wide range. They are highest for metals and lowest for finely powdered materials from which air has been evacuated.Fouries law st

16、ates that k is independent of the temperature gradient. Experiment does confirm the independence of k for a wide range of temperature gradients except for porous solids. For small ranges of temperature, k may be considered constant. On the other hand, k is a function of temperature, but not a strong

17、 one.For larger temperature ranges, the thermalconductivity can usually be approximated by an equation of the formkabT4.2-5 1. Gases Theories to predict thermal conductivities of gases are reasonably accurate and are given elsewhere. The thermal conductivity increases approximately as the square roo

18、t of the absolute temperature and is independent of pressure up to a few atmospheres. 4.2-6Gases have the smallest thermal conductivities, with values as low as 0.007 W/m.C.For air at 0C, k is 0.024 W/m.C.The thermal conductivity decreases with increasing molecular weight or with decreasing temperat

19、ure because of changes in the molecular velocity and energy distribution.2. Liquids Since an adequate molecular theory of liquids is not available, most correlations to predict the thermal conductivities are empirical. For most liquid k is lower than that for solids and higher than that of gases, wi

20、th typical values of about 0.17, and k decreases by 3 to 4 percent for a 10 C rise in temperature.3. Solids The thermal conductivity of homogeneous solids varies quite widely, as may be seen for some typical values in Tablek of metals cover a wide range of values, from about 17W/m.C for stainless st

21、eel and 45 for mild steel, to 380 for copper and 415 for silver. The conductivity of alloys is less than that of pure metals.k of metals are generally nearly constant or decrease slightly as the temperature is increased. For glass and most nonporous materials, the thermal conductivities are much low

22、er, from about 0.35 to 3.5.4.2.2 Steady-State Conduction Conduction Through a Flat Slab or Wall For the simplest case of steady-state conduction,consider a flat slab like that shown in figure. l k is constant;l The area of the wall is very large in comparison with its thickness;l The external surfac

23、es are at right angles to the plane.assumingtxqSince in steady state there can be neitheraccumulation nor depletion of heat within theslab, q is constant along the path of heat flow. If x is distance from the hot side.qdtkAdx (4.2-7) Since the only variables are x and t, direct integration givesWhen

24、 k varies linearly with temperature, Eq.(4.2-8 ) still can be used rigorously by taking an average value k.4.2-8 btkxxttkAq1221If the thermal conductivity is not constant but varies linearly with temperature, thenbttkttxttbaAqm2121122This means that the mean value of km is the value of k evaluated a

25、t the linear average of t1 and t2 Equation (4.2-8) can be written in the form4.2-9 Where R=b/Ak is thermal resistance between points 1 and 2.RtkAbtqEquation (4.2-9) equates a rate to the ratio of a driving force to a resistance.Conduction Through a Hollow Cylinder In the process industries, heat is

26、being transferred through the walls of cylinder. Consider the hollow cylinder in figure with an inside radius of r1, where the temperature is t1, an outside radius of r2 having a temperature of t2, and a length of L. Heat is flowing radially from the inside surface to the outside. LThe inside radius

27、 of the cylinder is r1, r2the outside radius is r2,and the length of the cylinder is L. r1It is desired to calculate the rate of heat flow outward for this case.The rate of heat flow through an arbitrary cylinder, concentric with the main cylinder, is given2dtqkrLdr Since the area perpendicular to t

28、he heat flow is 2rL,and thickness of the wall of this cylinder is dr. Rearranging equation and integrating between limits gives21212ttrrdtkrdrLq4.2-13 It can be put in a more convenient form by expressing the rate of flow of heat as4.2-14 2112ln2ttrrLkqMultiplying numerator and denominator by (r2 -

29、r1) 122112211212ln)(2rrttkArrttrrrrLkqmlet1212ln22rrrrLLrAmm4.2-16 4.2-15RtkAbtrrttkAqmm1221Equation(4.2-16) is known as the logarithmic mean area. The logarithmic mean is less convenient than the arithmetic mean, and the latter can be used without appreciable error for thin-walled tubes, where r2/r

30、1 is nearly 1. The ratio of the logarithmic mean to the arithmetic mean is a function of r2/r1 Thus when r2/r1 =2. The logarithmic mean is 0.96 , and the error in the use of the arithmetic mean is 4 percent.arr2/r1Plane Walls in Series CONDUCTION THROUGH SOLIDS IN SERIESConsider a flat wall construc

31、ted of a series of layers, as shown in figure. Assume that the layers are in excellent thermal contact, so that no temperature difference exists across the interfaces between the layers. Then, if t is the total temperature drop across the entire wallt= t1+ t2+ t3In heat flow through a series of laye

32、rs the overall thermal resistance equals the sum of the individual resistancesR=R1+R2+R3 The rate of heat flow through several resistance in series is analogous to the current flowing through several electric resistances in series. In an electric circuit the potential drop over any one of several re

33、sistances are to the total potential drop in the circuit as the individual resistances are to the total resistance. In the same way the potential drop in the thermal circuit, which are the temperature differences, are to the total temperature dropas the individual thermal resistances are to the tota

34、l thermal resistance.312312123123tttttttqRRRRRRR The rate of heat flow through several resistance in series isMultilayer Cylinders Figure Radial heat flow through multiple cylinders in series In the process industries, heat transfer often occurs through multilayers of cylinders, as for example when

35、heat is being transferred through the walls of an insulated pipe. Figure shows a pipe with two layers of insulation around it, that is, a total of three concentric hollow cylinders.The temperature drop is T1 - T2 across material AThe heat-transfer rate q will be the same for each layer. Writing an equation similar to Eq. (4.2-15) for each concentric cylinder.CCBBAAAkrrttA