Numerical Investigation of the Thermally Developing Flow in a Curved Elliptic Duct With Internal Fins

2006 ◽  
Vol 129 (6) ◽  
pp. 759-762 ◽  
Author(s):  
P. K. Papadopoulos ◽  
P. M. Hatzikonstantinou
Keyword(s):  
Aspect Ratio ◽  
Low Friction ◽  
Cross Sectional ◽  
Transfer Rates ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Temperature Boundary ◽  
Prandtl Numbers ◽  
Internal Fins ◽  
Temperature Boundary Condition

The hydrodynamically fully developed and thermally developing flow inside a curved elliptic duct with internal longitudinal fins is studied numerically. The duct is subjected to the uniform temperature boundary condition on its wall and fins. The local and mean Nusselt numbers are examined for various values of the Dean and Prandtl numbers, the cross-sectional aspect ratio, and the fin height. The characteristics of the optimum duct, which achieves enhanced heat transfer rates combined with low friction losses, are determined in terms of the aspect ratio and the fin height.

Heat Transfer With Film Cooling Within and Downstream of One to Four Rows of Normal Injection Holes

1976 ◽  
Author(s):  
D. E. Metzger ◽  
P. A. Kuenstler ◽  
D. I. Takeuchi
Keyword(s):  
Heat Transfer ◽  
Film Cooling ◽  
Mass Velocity ◽  
Experimental Measurements ◽  
Transfer Rates ◽  
Uniform Wall Temperature ◽  
Temperature Boundary ◽  
Uniform Wall ◽  
Line Patterns ◽  
Temperature Boundary Condition

Results are presented from experimental measurements of heat-transfer rates on surfaces which are cooled by injection through one to four rows of evenly spaced, flush, normal injection holes arranged in staggered and in-line patterns with hole spacings of 4.8 dia. Film cooling performanc is evaluated in both the injection and downstream recovery regions from transient tests which provide a uniform wall temperature boundary condition. Both the film and mainstream fluids are air, and film-to-mainstream mass velocity ratios of 0.1, 0.2, 0.3, and 0.5 are covered.

Laminar Heat Transfer in the Entrance Region of Internally Finned Square Ducts

2001 ◽  
Vol 123 (6) ◽  
pp. 1030-1034 ◽  
Author(s):  
V. D. Sakalis ◽  
P. M. Hatzikonstantinou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
High Heat ◽  
Axial Distance ◽  
High Heat Transfer ◽  
Developing Flow ◽  
Temperature Boundary ◽  
Internal Fins ◽  
High Heat Transfer Coefficient ◽  
Square Ducts

The laminar, incompressible, hydrodynamically fully developed and thermally developing flow is studied in straight ducts of square cross section, containing four equal, symmetrical, straight, thin and with 100 percent efficiency internal fins. Both the duct wall and the fins are subjected successively to constant temperature boundary condition. Numerical results are obtained using an iterative ADI scheme for the friction number, the temperature distribution and the Nusselt number for the thermally developing and developed regions as functions of axial distance and fin height. Results obtained are in good agreement with the corresponding literature values. In the thermally developing region a high heat transfer coefficient is obtained. Friction number and Nusselt number in the thermally developed limit increase as the fin height increases until they reach their critical values at fin heights near 0.85 and 0.73 respectively.

Convection at the Entrance of Micropipes With Sudden Wall Temperature Change

2002 ◽  
Author(s):  
Gokturk Tunc ◽  
Yildiz Bayazitoglu
Keyword(s):  
Wall Temperature ◽  
Integral Transform ◽  
Velocity Slip ◽  
Viscous Heating ◽  
Developing Flow ◽  
Heating Effects ◽  
Temperature Boundary ◽  
The Laplace Transform ◽  
Circular Microchannel ◽  
Temperature Boundary Condition

Transient heat convection in a circular microchannel for hydrodynamically fully developed and thermally developing flow conditions is analytically solved by the integral transform and the Laplace transform techniques. A prescribed wall temperature boundary condition is assumed. The effects of velocity slip, temperature jump, and viscous heating are investigated. The results confirm that the viscous heating effects increase the Nusselt number for the specified conditions.

Developing Convective Heat Transfer in Multiport Microchannel Flat Tubes

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Qin Sun ◽  
Yanhua Diao ◽  
Yaohua Zhao ◽  
Sheng Tang ◽  
Ji Zhang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Cross Sectional ◽  
Turbulent Transition ◽  
Developing Flow ◽  
Flat Tubes ◽  
Heat Transfer Capacity ◽  
High Reynolds

An experimental investigation of fluid flow friction and heat transfer coefficient in simultaneously developing flow through a multiport microchannel flat tube (MMFT) was presented. The cross-sectional geometries of five tubes were rectangular with hydraulic diameters of 0.8–1.33 mm and aspect ratio of 0.44–0.94. The working fluid was water, and the Reynolds number was in the range 150–4500. The experiment result showed that friction factor was successfully predicted by classical correlation in laminar regime, whereas the laminar–turbulent transition in the developing flow was not as obvious as in the completely developed flow. The greater aspect ratio produced stronger heat transfer capacity in the developing flow, although the effect of the aspect ratio decreased at increased Reynolds numbers for heat transfer characteristics. Moreover, the scale effect improved the heat transfer performance of MMFTs, especially at high Reynolds numbers.

Laminar Convection in Circular Tubes With Developing Flow

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
T. D. Bennett
Keyword(s):  
Circular Tube ◽  
Constant Heat Flux ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Wide Range ◽  
Extended Range ◽  
Prandtl Numbers ◽  
Laminar Convection ◽  
Heat And Momentum Transfer ◽  
Historical Range

Abstract The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number ZH≥10−6 and for a wide range of Prandtl numbers 0.1≤Pr≤500. For the historical range of ZH≥5×10−4 and 0.7≤Pr≤50, earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr≥0.5. In contrast, legacy correlations typically had a 10–20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5–10%.

scholarly journals Numerical Solution of Natural Convection on a Vertical Stretching Surface with Suction and Blowing

2021 ◽  
Vol 39 (5) ◽  
pp. 1469-1474
Author(s):  
Shankar Goud Bejawada ◽  
Yanala Dharmendar Reddy ◽  
Kanti Sandeep Kumar ◽  
Epuri Ranjith Kumar
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Three Dimensions ◽  
Surface Mass ◽  
Transfer Rates ◽  
Nusselt Numbers ◽  
Surface Mass Transfer ◽  
Prandtl Numbers ◽  
Primary Focus ◽  
Energy And Momentum

In this paper, the natural convective heat transfer from a stretching sheet oriented vertically involving surface mass transfer is of primary focus. A similarity solution in three dimensions is described for energy and momentum. The transformed equations are answered by using MATLAB in-built numerical programmer solver bvp4c. For a range of Prandtl numbers and surface mass transfer rates, friction factor and Nusselt numbers are tabulated. The heat transfer mechanism is observed to influence surface mass transfer. Heat transfer rate increases and thermal boundary layer thickness decreases with an increase of Prandtl values. In addition, the current results are compared with the previously published results and initiate to be a successful agreement.In this paper, the natural convective heat transfer from a stretching sheet oriented vertically involving surface mass transfer is of primary focus. A similarity solution in three dimensions is described for energy and momentum. The transformed equations are answered by using MATLAB in-built numerical programmer solver bvp4c. For a range of Prandtl numbers and surface mass transfer rates, friction factor and Nusselt numbers are tabulated. The heat transfer mechanism is observed to influence surface mass transfer. Heat transfer rate increases and thermal boundary layer thickness decreases with an increase of Prandtl values. In addition, the current results are compared with the previously published results and initiate to be a successful agreement.

Thermally developing forced convection flow through porous concentric pipes annular duct

2021 ◽  
pp. 095440622110022
Author(s):  
Farhan Ahmed
Keyword(s):  
Flow Region ◽  
Axial Direction ◽  
Darcy Number ◽  
Convection Flow ◽  
Axial Distance ◽  
Cross Sectional ◽  
Developing Flow ◽  
Annular Sector ◽  
Flow Through ◽  
The Cross

This article shows the thermally developing flow through concentric pipes annular sector duct by describing the Darcy Brinkman flow field. The cross sectional convection-diffusion terms are transformed in power law discretized form by integrating over the differential volume, whereas backward difference scheme is used in the axial direction of heat flow. With the help of semi implicit method for pressure linked equations-revised ( SIMPLE-R), we get the solution of the governing problem. The graphs of velocity profiles against R and average Nusselt number against axial distance are plotted for different values of Darcy number and geometrical configuration parameters. It has been pointed out that velocity and thermal entrance length decrease, when we decrease the value of Darcy number. By decreasing the cross section of the concentric pipes annular sector duct in the transverse direction, thermally fully developed flow region develops earlier.

scholarly journals Microcrystal alignment in drawn fiber over sub-meter to kilometer length scales

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Laurel Tauzer ◽  
Ann Mescher
Keyword(s):  
Aspect Ratio ◽  
Composite Fiber ◽  
Polymer Surfaces ◽  
Crystal Length ◽  
Cross Sectional ◽  
Length Scales ◽  
Grapeseed Oil ◽  
The Mean ◽  
Width Reduction ◽  
Uniform Reduction

AbstractThis paper describes a method for aligning stiff, high-aspect-ratio microcrystals over macro-length scales using a polymer fiber drawing process. A composite preform was constructed with an interfacial, liquid shell layer of grapeseed oil suspending ytterbium-doped potassium lutetium fluoride microcrystals (30% Yb:K2LuF5, KLF) between adjacent cylindrical surfaces of acrylic (polymethyl methacrylate, PMMA). The mean length of synthesized KLF microcrystals was 67 microns, and the mean aspect ratio, equivalent to crystal length divided by diameter, was eight. The acrylic-host preform was drawn into fiber, resulting in uniform reduction of all cross-sectional dimensions by a factor of approximately 20 in the final fiber. A corresponding width reduction of the interstitial liquid-filled gap, containing microcrystals between the polymer surfaces, constrains the microcrystals and causes alignment of the crystal long axes parallel to the axis of the drawn composite fiber. Alignment was best for clearly separated microcrystals and improved even further with the longest lengths, or highest aspect-ratio microcrystals.

The Graetz Problem for the Ellis Fluid Model

2018 ◽  
Vol 74 (1) ◽  
pp. 15-24 ◽  
Author(s):  
N. Ali ◽  
M.W.S. Khan
Keyword(s):  
Energy Equation ◽  
Fluid Model ◽  
Separation Of Variables ◽  
Surface Heat ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Graetz Problem ◽  
Developing Flow ◽  
Sturm Liouville

AbstractThe determination of temperature and auxiliary quantities such as local and average Nusselt numbers for thermally developing flow is referred as the Graetz problem. In the classical Graetz problem, the fluid entering the tube or channel is Newtonian in nature. Here, an extension of the classical Graetz problem is presented by assuming that the fluid entering the tube or channel obeys the Ellis constitutive equation. The energy equation for the considered problem is solved using the separation of variables technique supplemented with the MATLAB routine bvp4c for computation of the eigenvalues and numerical solution of the associated Sturm-Liouville boundary value problem. The problem is solved for two types of thermal boundary conditions, namely, uniform surface temperature and uniform surface heat flux for both flat and circular geometries. Expressions for bulk mean temperature and local and average Nusselt numbers are presented and discussed through tables and graphs.

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