Effect of Buoyancy on Forced Convection in Vertical Regular Polygonal Ducts

1970 ◽  
Vol 92 (2) ◽  
pp. 237-244 ◽  
Author(s):  
M. Iqbal ◽  
S. A. Ansari ◽  
B. D. Aggarwala
Keyword(s):  
Heat Flux ◽  
Shear Stress ◽  
Nusselt Number ◽  
Pressure Drop ◽  
Forced Convection ◽  
Maximum Shear Stress ◽  
Local Heat ◽  
Buoyancy Effect ◽  
Nusselt Numbers ◽  
Local Heat Flux

Laminar combined free and forced convection through vertical regular polygonal ducts has been studied. All fluid properties are considered constant, except variation of density in the buoyancy term. Heat flux is considered uniform in the flow direction while in the transverse direction two wall conditions have been considered; Case 1—uniform circumferential wall temperature, and Case 2—uniform circumferential heat flux. A solution by point matching method in terms of a series containing Bessel functions has been obtained. Nusselt numbers, local heat flux, local shear stress, and pressure drop have been investigated. The condition of Case 1 results in higher Nusselt number values compared to the condition of Case 2. However, these differences in Nusselt number diminish as the number of sides of the polygon are increased. In each case at higher values of the Rayleigh number, the Nusselt number is less sensitive to the number of sides. When Nusselt numbers against number of sides are considered, in Case 1, the Nusselt numbers reach asymptotic value at lower number of duct sides compared to Case 2. At low values of buoyancy effect, in Case 1, the maximum circumferential heat flux results at the centre of the wall, while at higher values of the same, the local heat flux becomes uniform over a substantial portion of the wall. Under Case 1 buoyancy effect increases the heat flux ratio at the duct corners. In three-sided polygon at higher values of the buoyancy parameter the maximum shear stress is no longer incident at the wall center. As the number of sides is increased, however, the maximum shear stress again takes place at the wall center. The Case 1 produces higher shear stress values near the wall center, while the Case 2 produces higher shear stress values near the duct corner. When the buoyancy parameter is high and the number of sides is not large, Case 2 results in higher values of pressure drop parameter compared to Case 1.

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.

Heat Transfer to Longitudinal Laminar Flow Between Cylinders

1961 ◽  
Vol 83 (4) ◽  
pp. 415-422 ◽  
Author(s):  
E. M. Sparrow ◽  
A. L. Loeffler ◽  
H. A. Hubbard
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Unit Length ◽  
Local Heat ◽  
Bulk Temperature ◽  
Nusselt Numbers ◽  
Spacing Ratio ◽  
Wide Range ◽  
Local Heat Flux

Consideration is given to the fully developed heat-transfer characteristics for longitudinal laminar flow between cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distribution, and from these, Nusselt numbers are derived for a wide range of spacing-to-diameter ratios. It is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 ∼ 2.0 and greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation.

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.

Measurement of Time-Averaged Turbulent Free Convection in a Tall Enclosure Using Interferometry

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
M. E. Poulad ◽  
D. Naylor ◽  
P. H. Oosthuizen
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Free Convection ◽  
Local Nusselt Number ◽  
High Speed ◽  
Local Heat ◽  
Frame Rate ◽  
Time Averaging ◽  
Image Processing Algorithm ◽  
Local Heat Flux

Laser interferometry is combined with high-speed digital cinematography to measure time-averaged transient and turbulent convective heat transfer rates. The method is applied to study free convection in a tall vertical air-filled enclosure. Measurements are made at three wall spacings in the turbulent flow regime (5.2×104≤RaW≤2.8×105). An automated image processing algorithm is used to calculate the instantaneous local heat flux from a sequence of interferograms that is captured by a high-speed camera. The local Nusselt number distributions on the hot and cold walls are obtained by time-averaging the fluctuations in local heat flux. The effects of key experimental parameters, such as the camera frame rate and the total image capture time, are investigated. For the current problem, it is shown that a total capture interval of about 10 s is required to accurately measure the time-average local Nusselt number. Within the measurement uncertainty, the average Nusselt number results are in agreement with a widely used empirical correlation from the literature.

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.

Numerical analysis of local heat flux and thin-slab solidification in a CSP funnel-type mold with electromagnetic braking

2020 ◽  
Vol 117 (6) ◽  
pp. 602
Author(s):  
Heping Liu ◽  
Jianjun Zhang ◽  
Hongbiao Tao ◽  
Hui Zhang
Keyword(s):  
Heat Flux ◽  
Casting Speed ◽  
Shell Growth ◽  
Local Heat ◽  
Operating Conditions ◽  
Thin Slab ◽  
Wide Face ◽  
Slab Width ◽  
Steel Grades ◽  
Local Heat Flux

In this article, based on the actual monitored temperature data from mold copper plate with a dense thermocouple layout and the measured magnetic flux density values in a CSP thin-slab mold, the local heat flux and thin-slab solidification features in the funnel-type mold with electromagnetic braking are analyzed. The differences of local heat flux, fluid flow and solidified shell growth features between two steel grades of Q235B with carbon content of 0.19%C and DC01 of 0.03%C under varying operation conditions are discussed. The results show the maximum transverse local heat flux is near the meniscus region of over 0.3 m away from the center of the wide face, which corresponds to the upper flow circulation and the large turbulent kinetic energy in a CSP funnel-type mold. The increased slab width and low casting speed can reduce the fluctuation of the transverse local heat flux near the meniscus. There is a decreased transverse local heat flux in the center of the wide face after the solidified shell is pulled through the transition zone from the funnel-curve to the parallel-cure zone. In order to achieve similar metallurgical effects, the braking strength should increase with the increase of casting speed and slab width. Using the strong EMBr field in a lower casting speed might reverse the desired effects. There exist some differences of solidified shell thinning features for different steel grades in the range of the funnel opening region under the measured operating conditions, which may affect the optimization of the casting process in a CSP caster.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

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