A New Nusselt Number for Complicated Configurations

2013 ◽  
Author(s):  
Tom I-Ping Shih ◽  
Srisudarshan Krishna Sathyanarayanan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Local Heat ◽  
Negative Slope ◽  
Test Problems ◽  
Rectangular Duct ◽  
Circular Duct ◽  
Flow And Heat Transfer ◽  
Local Heat Flux

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.

scholarly journals Experimental Investigation to Evaluate the Effectiveness of Air and Co2 in Impingement Cooling of Electronic Equipment

2013 ◽  
pp. 203-208
Author(s):  
Syed Zakrea ◽  
Siddiq Ali ◽  
Mohammed Ayaz Ahmed ◽  
M. Anwarullah
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Experimental Investigation ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Local Heat ◽  
Graphical Form ◽  
Wide Range ◽  
Local Heat Flux

Experimental investigation is conducted to examine the characteristics of forced convective heat transfer from electronic components, subjected to a confined impinging circular jet of Air and CO2. Parameters such as Heat transfer coefficient, Jet velocities, Nozzle-to-chip spacing (aspect ratio) (H/d) have been studied. Nozzle diameter ranged from 2mm to 8mm. Local heat flux measurements are made with different diameters of jet in the range of Reynolds numbers from 5,000 to 44,000 for CO2 and 2,500 to 23,000 for air. H/d is varied from 3 to 45 for both air and CO2. Variations both in the local heat transfer coefficient and Nusselt number are determined as function of Re. Variations of average Nusselt number and local heat flux with time are obtained in a wide range of Re and H/d ratios. The results of the investigation are presented in graphical form and a comparative study of Air and CO2 as coolant is made.

Conjugate Heat Transfer Study of Turbulent Slot Impinging Jet

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
A. Madhusudana Achari ◽  
Manab Kumar Das
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Nusselt Number ◽  
Conjugate Heat Transfer ◽  
Local Heat ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Impingement Plate ◽  
Local Heat Flux

Conjugate heat transfer in a two-dimensional, steady, incompressible, confined, turbulent slot jet impinging normally on a flat plate of finite thickness is one of the important problems as it mimics closely with industrial applications. The standard high Reynolds number two-equation k–ε eddy viscosity model has been used as the turbulence model. The turbulence intensity and the Reynolds number considered at the inlet are 2% and 15,000, respectively. The bottom face of the impingement plate is maintained at a constant temperature higher than the jet exit temperature and subjected with constant heat flux for the two cases considered in the study. The confinement plate is considered to be adiabatic. A parametric study has been done by analyzing the effect of nozzle-to-plate distance (4–8), Prandtl number of the fluid (0.1–100), thermal conductivity ratio of solid to fluid (1–1000), and impingement plate thickness (1–10) on distribution of solid–fluid interface temperature, bottom surface temperature (for constant heat flux case), local Nusselt number, and local heat flux. Effort has been given to relate the heat transfer behavior with the flow field. The crossover of distribution of local Nusselt number and local heat flux in a specified region when plotted for different nozzle-to-plate distances has been discussed. It is found that the Nusselt number distribution for different thermal conductivity ratios of solid-to-fluid and impingement plate thicknesses superimposed with each other indicating that the Nusselt number as a fluid flow property remains independent of solid plate properties.

Taylor-Heat Flux Effect on Fluid Flow and Heat Transfer in a Curved Rectangular Duct with Rotation

2021 ◽  
Vol 7 (4) ◽  
Author(s):  
Ratan Kumar Chanda ◽  
Mohammad Sanjeed Hasan ◽  
Md. Mahmud Alam ◽  
Rabindra Nath Mondal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Rectangular Duct ◽  
Flow And Heat Transfer

Effect of Water Temperature on Spray Cooling Heat Transfer on Hot Steel Plate

2010 ◽  
Author(s):  
Jungho Lee ◽  
Cheong-Hwan Yu ◽  
Sang-Jin Park
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Water Temperature ◽  
Steel Plate ◽  
Cooling Water ◽  
Local Heat ◽  
Spray Cooling ◽  
Transfer Coefficients ◽  
Cooling Water Temperature ◽  
Local Heat Flux

Water spray cooling is an important technology which has been used in a variety of engineering applications for cooling of materials from high-temperature nominally up to 900°C, especially in steelmaking processes and heat treatment in hot metals. The effects of cooling water temperature on spray cooling are significant for hot steel plate cooling applications. The local heat flux measurements are introduced by a novel experimental technique in which test block assemblies with cartridge heaters and thermocouples are used to measure the heat flux distribution on the surface of hot steel plate as a function of heat flux gauge. The spray is produced from a fullcone nozzle and experiments are performed at fixed water impact density of G and fixed nozzle-to-target spacing. The results show that effects of water temperature on forced boiling heat transfer characteristics are presented for five different water temperatures between 5 to 45°C. The local heat flux curves and heat transfer coefficients are also provided to a benchmark data for the actual spray cooling of hot steel plate cooling applications.

High-Temperature Heat Transfer Investigations Using Heterogeneous Gradient Sensors

2010 ◽  
Author(s):  
Sergey Z. Sapozhnikov ◽  
Vladimir Yu. Mityakov ◽  
Andrey V. Mityakov ◽  
Andrey A. Snarskii ◽  
Maxim I. Zhenirovskyy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
High Temperature ◽  
Power Plant ◽  
Thermal Power ◽  
Local Heat ◽  
Working Temperature ◽  
Metal Metal ◽  
Flux Measurements ◽  
Local Heat Flux

The local heat flux measurements are limited by low working temperature of the gradient heat flux sensors (GHFS) [1–3]. The novel heterogeneous sensors (HGHFS) made from metal-metal or metal-semiconductor layered composites (so-called anisotropic thermoelements) have high temperature level of 1300 K and more. Theory of the HGHFS allows to choose thickness and angle of inclination for the layers of composite, and to forecast volt-watt sensitivity. The sensitivity of metal-metal sensors is typically on the order of 0.02 to 0.5 mV/W, and it is much beyond when semiconductors are used. HGHFS are used for a first time for heat flux measurements in the furnace of the industrial boiler which is in operating of the Thermal Power Plant (fossil fuel power plant) in the city of Kirov (Russia). The local heat flux at the surface of refractory-faced water wall is measured in different regimes of operating. It is also shown that HGHFS may be used as indicator of furnace slugging. Small sizes (minimally 2×2×0.1 mm) and high working temperature of the HGHFS are useful for heat transfer investigations.

Radiative Transfer From a Gray, Absorbing-Emitting, Isothermal Medium in a Conical Enclosure

1989 ◽  
Vol 111 (4) ◽  
pp. 324-329 ◽  
Author(s):  
Deborah A. Kaminski
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Monte Carlo ◽  
Radiative Heat ◽  
Control Volume ◽  
Local Heat ◽  
Exact Results ◽  
Differential Approximation ◽  
Isothermal Medium ◽  
Local Heat Flux

Radiative heat transfer from an isothermal participating medium in a truncated, conical enclosure is investigated numerically. Two methods of solution are employed: the Monte-Carlo technique and the P1 differential approximation. The solution to the P1 representation is obtained from a control-volume-based discretization of the governing equation. The medium is assumed to be gray and nonscattering, and the absorption coefficient and temperature are uniform throughout the medium. Overall and local heat flux rates at the walls predicted by the P1 method are compared to the quasi-exact results of the Monte-Carlo solution. Results are obtained for a variety of optical thicknesses and cone shapes.

Effects of spatially varying roof cooling on thermal convection at high Rayleigh number in a fluid with a strongly temperature-dependent viscosity

2009 ◽  
Vol 629 ◽  
pp. 109-137 ◽  
Author(s):  
A. M. JELLINEK ◽  
A. LENARDIC
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Surface Area ◽  
Large Scale ◽  
Local Heat ◽  
Temperature Gradients ◽  
Local Heat Flux ◽  
Transfer Properties ◽  
Lateral Temperature

We investigate the effects of an insulating lid of variable spatial extent on convection in the stagnant-lid regime under thermally steady-state conditions. Using a combination of laboratory experiments, numerical simulations and scaling analyses we characterize the qualitative structure and quantitative heat transfer properties of flows in terms of the fractional extent L of an insulating lid applied at the cold boundary, the thermal resistance of the lid, the magnitude of the temperature dependence of the fluid viscosity Λ and the effective Rayleigh number Rae for the composite system. A partial insulating lid has two main effects: (i) To increase the mean interior temperature and reduce the average viscosity of the system, which enhances fluid motions, and (ii) to impart a lateral asymmetry to the thermal structure of the cold boundary that leads, in turn, to lateral temperature gradients that drive an overturning flow. Consequently, whereas flow in the uninsulated stagnant-lid regime is in the form of ‘small-scale’ rising and sinking thermals, there is an additional ‘large-scale’ circulation in the presence of partial insulation. The structure, wavelength and heat transfer properties of this large-scale stirring depends on L, Λ and Rae. For given Rae – Λ conditions we find optimal values of L at which there occur well-defined maxima in the rate of overturn, the local heat flux carried into the uninsulated part of the cold boundary and in the global average heat flux Nu carried across the system. Whereas both the rate of overturning and local heat flux are associated with the largest lateral temperature gradients, the optimal basal heat flux depends also on a tradeoff with the fractional surface area of the lid. Remarkably, maximal values of the global heat flux can significantly exceed that of the uninsulated stagnant-lid case. The occurrence of such maxima is insensitive to the mechanical boundary conditions applied and is not strongly influenced by lid shape. However, the magnitude and location of optimal heat fluxes depends in a complicated way on the lid surface area and shape, as well as the structure of the hot and cold boundary layers and the wavelength of the large-scale flow.

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