NDLI: A New Nusselt Number for Complicated Configurations

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Tom, I.-Ping Shih Sathyanarayanan, Srisudarshan Krishna
Copyright Year	2013
Abstract	Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.
Sponsorship	Heat Transfer Division
File Format	PDF
ISBN	9780791855492
DOI	10.1115/HT2013-17114
Volume Number	Volume 3: Gas Turbine Heat Transfer; Transport Phenomena in Materials Processing and Manufacturing; Heat Transfer in Electronic Equipment; Symposium in Honor of Professor Richard Goldstein; Symposium in Honor of Prof. Spalding; Symposium in Honor of Prof. Arthur E. Bergles
Conference Proceedings	ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology
Language	English
Publisher Date	2013-07-14
Publisher Place	Minneapolis, Minnesota, USA
Access Restriction	Subscribed
Subject Keyword	Turbine cooling Heat transfer in the entrance region of ducts Heat-transfer coefficient Heat-transfer correlations Entrance region Temperature Cooling Computational fluid dynamics Ducts Flow separation Reynolds number Fins Convection Heat flux Wall temperature Heating Reynolds-averaged navier–stokes equations Shear stress Compressible flow Heat transfer Turbines
Content Type	Text
Resource Type	Article

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