The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer, страница 10

The jets may impinge normally to the heated surface or at an angle.If there is no parallel solid surface close to the heated surface, the jet is said to be free; in the presenceof a parallel surface close to the heated surface, the jet is termed confined. In this section only single,free jets (round or rectangular) impinging normally to the heated surface are considered.FIGURE 4.2.20 Circular jet of diameter d or a rectangular jet of width w.Jets may be submerged with the fluid from the nozzle exiting into a body of a fluid (usually the samefluid), for example, air impinging on a surface surrounded by atmospheric air. In submerged jets entrainedfluid (the part of the surrounding fluid dragged by the jet) has a significant effect on the flow and heattransfer characteristics of the jet, but the effect of gravity is usually negligible. In free-surface jets — aliquid jet in an atmosphere of air is a good approximation to a free-surface jet — the entrainment effectis usually negligible, but the effect of gravity may be significant.A jet is usually divided into three regions, a free-jet region, a stagnation region, and a wall-jet region.In the free-jet region the effect of the target surface on the flow is negligible.

In the stagnation regionthe target surface affects the flow field, and the velocity parallel to the surface increases while the velocitycomponent normal to the surface decreases. At the beginning of the stagnation region, the axial velocityof the fluid is very much greater than the radial component (or the x-component) of the velocity. Thestagnation region is followed by the wall-jet region where the radial component (or the x-component)of the velocity is much greater than the axial velocity.The heat transfer coefficient is a function of H/d (or H/w), Red(rvjd/m) or (rvj2w/m), and Pr anddepends on the region (stagnation or wall jet), whether it is submerged or nonsubmerged and whetherthe flow adjacent to the plate is laminar or turbulent.

Some of the heat transfer correlations suggestedby different researchers are given below. All the correlations are for single jets.Submerged Jets: Single Circular JetsRe d =© 1999 by CRC Press LLC4 m˙p dmNu d =hdkm˙ = mass rate of flow of fluid4-44Section 4Average heat transfer coefficients up to radius r (Martin, 1990):12éæRe 0d.55 ö ù1 - 1.1 d rd0.42Nu d = 2ú PrêRe d ç1 +200 ÷ø úûr 1 + 0.1( H d - 6) d r êëè(4.2.80)Range of validity:2000 £ Re d £ 400, 0002.5 £ r d £ 7.52 £ H d £ 12Local convective heat transfer coefficient at radius r (Webb and Ma, 1995):12Nu d = 1.29Re d Pr0.4-1.07 -17 üìïé tanh(0.88 r d ) ù -8.5 éù ïröæ+íêê1.69è øú ýúrddûïîëëû ïþ-1 17(4.2.81)Submerged Jets: Single Rectangular JetRe w =rv j 2 wm=2 m˙mm˙ = mass rate of flow per unit length of jetNu w =h2 wkAverage heat transfer coefficient (Martin, 1990):Nu w =1.53Pr 0.42 Re mwxH++ 1.392w 2wé x æ H ö 1.33ùm = 0.695 - ê++ 3.06úë 2w è 2w øû(4.2.82)-1Free-Surface Jets: Single Circular Jet.

Correlations are given in Table 4.2.5 (Liu et al., 1991 and Webband Ma, 1995).For more information on jet impingement heat transfer, refer to Martin (1977) and Webb and Ma(1995) and the references in the two papers.BibliographyASHRAE Handbook of Fundamentals, 1993. American Society of Heating, Ventilating and Air Conditioning Engineers, Atlanta, GA.Hewitt, G.F., Ed. 1990. Handbook of Heat Exchanger Design, Hemisphere Publishing, New York.Incropera, F.P. and Dewitt, D.P.

1990. Fundamentals of Heat and Mass Transfer, 3rd ed., John Wiley &Sons, New York.Kakaç, S., Shah, R.K., and Win Aung, Eds. 1987. Handbook of Single Phase Convective Heat Transfer,Wiley-Interscience, New York.Kreith, F. and Bohn, M.S. 1993. Principles of Heat Transfer, 5th ed., PWS, Boston.Suryanarayana, N.V. 1995. Engineering Heat Transfer, PWS, Boston.© 1999 by CRC Press LLC4-45Heat and Mass TransferTABLE 4.2.513Correlations for Free-Surface Jets rn/d = 0.1773 Re dNud0.15 £ Pr £ 3r/d < 0.787Pr > 312(4.2.83)12(4.2.84)0.715Re d Pr 0.40.797Re d Pr 1 3120.787 < r/d < rn /d0.632 Re d Pr 1 3æ döè rø(4.2.85)12130.407Re d Pr 1 3 (d r )rn /d < r/d < rt /dé 0.1713 5.147 r ùêú+2Re d d úêë (r d )û23(4.2.86)23é (r d ) 2ùê+ Cúêë 2úû13where23C = -5.051 ´ 10 -5 Re d12rt ìï s éæ s ö 2 æ p ö 3 ù üï= í- + ê+úè 3 ø ú ýïd ï 2 êëè 2 øû þî133 12üìï s é s 2æ öæ pö ù ï+ í- + êè 3 ø úú ýïïî 2 êëè 2 øû þp=r > rt-2C0.2058Pr - 1Pr < 4.86s=130.00686Re d Pr0.2058Pr - 1(4.2.87)0.251Re d Pré æ rt öê1 - ç ÷êë è r ø22ùæ r öhh+ 0.13 + 0.0371 túddúû è d øwhere ht = h at rt andh 0.1713 5.147 æ r ö=+Re d è d ødrd2ReferencesAchenbach, E.

1978. Heat Transfer from Spheres up to Re = 6 ´ 106, in Proc. 6th Int. Heat TransferConf., Vol. 5, Hemisphere Publishing, Washington, D.C.Burmeister, L.C. 1993. Convective Heat Transfer, Wiley-Interscience, New York.Churchill, S.W. 1976. A comprehensive correlation equation for forced convection from a flat plate,AIChE J. 22(2), 264.Churchill, S.W. and Bernstein, M. 1977.

A correlating equation for forced convection from gases andliquids to a circular cylinder in cross flow, J. Heat Transfer, 99, 300.Churchill, S.W. and Ozoe, H. 1973. Correlations for laminar forced convection with uniform heating inflow over a plate and in developing and fully developed flow in a tube, J. Heat Transfer, 18, 78.Eckert, E.R.G. 1956.

Engineering relations for heat transfer and friction in high-velocity laminar andturbulent boundary-layer flow over surfaces with constant pressure and temperature, Trans. ASME,56, 1273.Eckert, E.R.G. and Drake, M., Jr. 1972. Analysis of Heat and Mass Transfer, McGraw-Hill, New York.Ishiguro, R., Sugiyama, K., and Kumada, T. 1979. Heat transfer around a circular cylinder in a liquidsodium cross flow, Int. J. Heat Mass Transfer, 22, 1041.Jakob, H., 1949.

Heat Transfer, John Wiley and Sons, London.© 1999 by CRC Press LLC4-46Section 4Kays, W.M. and Crawford, M.E. 1993. Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NewYork.Liu, X., Lienhard, v., J.H., and Lombara, J.S. 1991. Convective heat transfer by impingement of circularliquid jets, J. Heat Transfer, 113, 571.Martin, H. 1977. Heat and mass transfer between impinging gas jets and solid surfaces, in Advances inHeat Transfer, Hartnett, J.P. and Irvine, T.F., Eds., 13, 1, Academic Press, New York.Martin, H. 1990.

Impinging jets, in Handbook of Heat Exchanger Design, Hewitt, G.F., Ed., Hemisphere,New York.Morgan, Vincent T., 1975. The overall convective heat transfer from smooth circular cylinders, inAdvances in Heat Transfer, Irvine, T.F. and Hartnett, J.P., Eds., 11, 199, Academic Press, New York.Rose, J.W. 1979. Boundary layer flow on a flat plate, Int. J. Heat Mass Transfer, 22, 969.Schlichting, H. 1979. Boundary Layer Theory, 7th ed., McGraw-Hill, New York.Suryanarayana, N.V. 1995. Engineering Heat Transfer, West Publishing, Minneapolis.Thomas, W.C.

1977. Note on the heat transfer equation for forced-convection flow over a flat plate withan unheated starting length, Mech. Eng. News (ASEE), 9(1), 19.Webb, B.W. and Ma, C.F. 1995. Single-phase liquid jet impingement heat transfer, in Advances in HeatTransfer, Hartnett, J.P. and Irvine, T.F., Eds., 26, 105, Academic Press, New York.Witte, L.C. 1968. An experimental study of forced-convection heat transfer from a sphere to liquidsodium, J. Heat Transfer, 90, 9.Zukauskas, A. 1987. Convective heat transfer in cross flow, in Handbook of Single-Phase ConvectiveHeat Transfer, Kakaç, S., Shah, R.K., and Win Aung, Eds., Wiley-Interscience, New York.Forced Convection — Internal FlowsN.V.

SuryanarayanaIntroductionHeat transfer to (or from) a fluid flowing inside a tube or duct is termed internal forced convection. Thefluid flow may be laminar or turbulent. If the Reynolds number based on the average velocity of thefluid and diameter of the tube (rvd/m) is less than 2100 (Reynolds numbers in the range of 2000 to 2300are cited in different sources), the flow is laminar. If the Reynolds number is greater than 10,000, theflow is turbulent. The flow with a Reynolds number in the range 2100 to 10,000 is considered to be inthe transitional regime.