Entrance effects on low prandtl number convection through a circular duct
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Entrance Effects on Low Prandtl Number Convection through a Circular Duct
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REETA DAS and A.K. MOHANTY
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Fig. 13--Schematic diagram showing the anodic and cathodic regions in a metal displacement reaction.
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Figure 14--X-ray pattern of the cementation product.
REFERENCES 1. F.H. Habashi: Extractive Metallurgy, Gordon and Breach Science Publishers, Inc., New York, NY, 1969, pp. 227-41. 2. R.D. Pehlke: Unit Process of Extractive Metallurgy, American Elsevier Publishing Co., New York, NY, 1975, pp. 224-25. 3. G.W. Castellan: Physical Chemistry, 2nd ed., Addison-Wesley Publishing Co., Reading, MA, 1972, pp. 711-12. 4. David R. Gaskell: Introduction to Metallurgical Thermodynamics, McGraw-Hill Kogakusha Ltd., 1973, pp. 471-74. 5. F.H. Habashi: Extractive Metallurgy, Gordon and Breach Science Publishers, Inc., New York, NY, 1969, pp. 51-53. 6. E. Gileadi: lnterfacial Electrochemistry, Addison Wesley Publishing Co., Reading, MA, 1975, pp. 138-51. 7. E.C. Lee, F. Lawson, and K. Han: Trans. IMM, 1975, vol. 84, pp. 87-90. 8. E.A. Von Han and J.R. Ingraham: Trans. TMS-A1ME, 1967, vol. 239, pp. 1066-71. METALLURGICAL TRANSACTIONS B
Convection in low Prandtl number fluids is characterized by a thermal boundary layer significantly thicker than its hydrodynamic counterpart. Prominent among low Pr fluids are the liquid metals, typically Pr = 0.02 for mercury and 0.01 for sodium. Since these fluids are often used as coolants in nuclear reactors, especially the fastbreeder types, the importance of relevant heat-transfer studies is obvious. A low Pr fluid has low viscosity and high thermal conductivity. The first factor results in turbulent flow condition at moderate velocities. On the other hand, a high thermal conductivity value reflects through thermal transport rates, which are controlled by molecular considerations. It is for such reasons that we observe a pattern of Nu = A + B Pe ~ where nominal values are: A = 5.8 for lighter metals and 3 for heavier ones and B = 0.02. U'21 This nature of variation of Nu also indicates that increasing flow rate only moderately enhances heat transfer. The above discussion has been presented to emphasize that accuracy of Nu value is controlled by A. It is also recalled that a constant Nusselt number is a characteristic of developed laminar flows. In other words, laminar flow analyses are practically useful. Such a flow would be developing if the duct length were short. Furthermore, since the thermal conductivity is very high for low Pr fluids, moderate inaccuracies in the Nu value can reflect through large uncertainties in the value of the heat-transfer coefficient. The objectives and justifications of the present study stem from the foregoing. The study aims to derive heattransfer results in the entry region, such as are applicable to circular pipes of short lengths, considering laminar flow. Combined entry length solutions are generated for the two thermal boundary conditions of uniform heat flux (UHF) and
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