heat transfer in automoble radiators of the tubular typeDittusBoelter.docx

1、heat transfer in automoble radiators of the tubular typeDittusBoelterINT.COMM.HEAT MASS TRANSFERVol.12, pp.3-22, 1985Printed in the United StatesHeat Transfer In Automobile Radiators Of The Tubular TypeF. W. Dittus and L. M. K. BoelterIntroductionHeat to be dissipated from water-cooled internal comb

2、ustion engines is usually transferred to the atmosphere by means of devices commonly called radiators. The medium conveying heat to the radiator is generally water, the medium conveying heat away is air. In this article it is intended to discuss the fundamentals involve in the transfer of heat from

3、water to the atmosphere in the simplest type of tubular radiator. No attempt will be made to discuss the effect of the rate of heat transfer when using fins, honeycomb section, or any type other than the plain tube. The unit of measure of heat transfer in heat exchange equipment is the “Overall Tran

4、sfer Factor”, which is the heat transferred per unit area of heat transmitting surface per unit time per unit of temperature difference between the hot and cold fluids. Film Transfer Factor On The Liquid Side Of A RadiatorTypes of fluid flour through tubes On the liquid side of a radiator heat is ca

5、rried from the warm water to the colder tube wall by two methods:(1) Convection(2) ConductionIn the region of turbulent flow, most of the heat is transferred from the liquid to the tube wall by forced convection. Because of the low thermal conductivity of fluids, very little heat is transferred from

6、 the center of the stream to the tube wall by conduction. In forced circulation systems the fluid flow through the radiator is turbulent unless the tubes are of very small diameter.In the viscous flow region practically all of the heat is transferred from the interior of the stream to the tube wall

7、by conduction.The rate of heat flow from the water to the air is retarded by (a) Film resistance on the water side of the tube surface,(b) Thermal resistance of tube,(c) Film resistance on the air side of the tube.If we denote the three resistances mentioned above by Rw, Rt, and Ra, respectively, we

8、 may write the following equation:where Ro=overall or total heat flow resistance. Ordinarily, however, the term employed is not thermal resistance but thermal conductance, which is the reciprocal of resistance. Denoting thermal conductance by U we may then write:where Uo=overall transfer factor (BTU

9、/sq.ft././hr.). Uw=film transfer factor on water side (BTU/sq.ft././hr.). Ua=film transfer factor on air side (BTU/sq.ft././hr.). Ut=thermal conductance of separating wall (BTU/sq.ft././hr.).The value of Ut can be readily calculated by the use of the following equation:where t=thickness of separatin

10、g wall (ft.). k=thermal conductivity of separating wall material (BTU/sq.ft././hr.). Equation (2) holds when heat is transferred through a body with parallel heat-transmitting surfaces. In the case of heat flow through curved surfaces, for example, tube walls, a correction should be made for the fac

11、e that the outer surface per unit length of tube is greater than the inner surface for the same length of tube. Equation (2) then becomes:or, referred to the mean diameter of the tube, equation (4) becomes:whereAm=Mean area of heat transfer section based on mean tube diameter (sq.ft). Aa=Area of hea

12、t transfer section on air side (sq.ft). Aw=Area of heat transfer section on water side (sq.ft). R=Ratio of outer tube surface (air) to surface of tube at mean diameter per unit length of tube. R=Ratio of inner tube surface (water) to surface of tube at mean diameter per unit length of tube.R=2D/(D+d

13、).R=2d/(D+d).D=Outside diameter of tube (inches).d=Inside diameter of tube (inches).The value of Ut for a curved separating wall is:Substituting equation (6) for the term Ut and also substituting in equation (5) the equivalent values of R and R, the latter becomes: The type of fluid flow existing wi

14、thin a tube may be determined by calculating “Reynolds criterion”, which is defined as follows:where Cr=Reynolds criterion Cr=Reynolds critical number (see following paragraph) v=mean linear velocity of fluid (ft./sec.) V=mean mass velocity (lbs./sq.ft./sec.) d=inside diameter of tube (inches) u=abs

15、olute viscosity of fluid at mean stream temperature (poises) z=absolute viscosity of fluid at mean stream temperature (centipoises) s=density of fluid (numerically equal to the specific gravity of fluid referred to water at 60.) (gram./cc.)If, upon substitution of the proper values in the above equa

16、tion, the numerical result (Cr) is greater than 40, the flow is turbulent. If, on the other hand, the result is less than 25, the flow is non-turbulent or viscous. In the event that a ratio (Cr) having a value between the just mentioned numbers is obtained, the flow may be either turbulent or viscou

17、s depending to a great extent upon the entrance and exit conditions of the installation in question and roughness of the tube surface.Film transfer factors for turbulent flow Most of the experimental work done on heat transfer covers the turbulent region for fluid flow inside of tubes. McAdams and F

18、rost (1922) correlated all the published data and proposed the following equation for heat transfer existing at turbulent flow:which is a simplified form of the following equation proposed by Nusselt (1910):Where B1=constant c=specific heat of fluid (BTU/lb./) k=thermal conductivity of fluid (BTU/sq

19、.ft./hr././ft.),and all other terms as mentioned above. McAdams and Frost eliminated the third term of equation (10) because the correlated data fell along the same straight line when plotted on logarithmic paper according to equation (9). Most of the data plotted were results of heat transfer tests

20、 conducted with water flowing through tubes. Equation (9) was later modified by McAdams and Frost (1924) to include a correction for the increased heat transfer rate due to turbulence at the entrance of the tube. This modified equation is as follows:where B2=constant N=empirical number r=ratio of tu

21、be length to diameter=l/d u=viscosity of fluid at film temperature (poises) Upon considering the results a number of experiments the equation proposed by the last mentioned authors was: As mentioned above, in most of the experiments performed the fluid used was water and the heat was generally flowi

22、ng from the tube to the liquid, i.e., heating the liquid. Morris and Whitman (1928) conducted a series of experiments in which oils having a wide range of viscosities were used. In addition to this they studied the heat transfer rates for cooling as well as heating of the liquid flowing through the

23、tube. The result of the investigation showed that film transfer factors may be expressed by the following equation:which is of the same form as the Nusselt equation previously mentioned, except that mass velocity (lbs./sq.ft./sec.) is used instead of linear velocity and absolute viscosity expressed

24、in centi-poises instead of poises. The two just mentioned variables are denoted by “V” and “z” respectively. Figure 1 shows the experimental data of these investigators plotted according to equation (13). It will be noted that there are two separate groups of points, one for heating liquids and anot

25、her for cooling liquids. As pointed out by Morris and Whitman, the film transfer factor for cooling a liquid is about 75 per cent of that for heating a liquid when the comparison is made at the same flow conditions. This variation is no doubt due to the fact that the physical properties of the fluid

26、 particles conveying and conducing heat are different for the two conditions, even though the mean fluid temperatures are the same. Perhaps a better procedure would be to plot the film transfer factoes as a function of the various thermal properties of the fluid at the film temperature instead of th

27、e mean stream temperature. The curves obtained when using the physical properties of the fluid at the tube temperature instead of at the mean stream temperature are in no better agreement than those shown by Morris and Whitman, nor is there a better agreement when the physical properties are taken a

28、t a mean temperature between the tube wall and mean stream temperatures. In every case a separate curve was obtained for heating and cooling, in some cases the cooling curve lying above and in some cases lying below the heating curve, depending entirely upon the temperature used to determine the phy

29、sical properties of the liquid. In order to obtain a common curve for heating and cooling, it is suggested to use two different exponents in the term (cz/k)n for each process. Figure 2 shows the plotted results calculated from Morris and Whitmans published data, using n equals 0.4 and 0.3 respective

30、ly for heating and cooling a liquid flowing to a tube. Unfortunately, no other data are available to test the use of two different exponents for heating and cooling. The fluids used by Morris and Whitman in their experiments were water and oils covering a considerable range of viscosities. Neither t

31、hese authors nor McAdams and Frost showed any experimental values for gases flowing through tubes. In order to determine whether or not the Morris and Whitman curve also applies to gases, the published results of a number of investigators using gases in their heat transfer experiments were analyzed

32、and plotted according to the following equations:where n=0.3 for cooling n=0.4 for heatingall other variables as previously defined. The curves thus obtained for gases are shown in figure 3 together with others published by McAdams and Frost for liquids. The curves shown for gas flow cover a range of tube diameters from 1/2 inch to about 6 inches and a temperature range from 60 to 1400. The mass velocities varied from 0.2 to 6.6 lbs. per sq. ft. per second. The pressure