The Nonlinear Increase of Nusselt Number With Friction Factor in Fully Developed Laminar Duct Flow

2004 ◽  
Vol 126 (5) ◽  
pp. 840-842 ◽  
Author(s):  
E. Van den Bulck
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Constant Heat Flux ◽  
Duct Flow ◽  
Parallel Plates ◽  
Physical Explanation ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Nonlinear Increase

This paper deals with heat transfer in fully developed laminar flow in cylindrical ducts. For this type of flow, the product of friction factor with Reynolds number f Re and the Nusselt number are both constants. It is known that the Nusselt number increases with the shift of boundary condition from constant wall temperature to constant heat flux. Also, the ratio of the Nusselt number to f Re increases when the convexity of the duct is reduced, e.g., a cylinder visavis parallel plates. This paper gives a simple physical explanation for these two phenomenona.

scholarly journals EFFECT OF CAVITY RATIO ON HEAT TRANSFER BY FREE LOAD FROM HEATED PLATES UPWARD WITH CONSTANT HEAT FLUX

2021 ◽  
Vol 9 (12) ◽  
pp. 686-695
Author(s):  
Waleed Abdulhadiethbayah ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Free Convection ◽  
Electronic Devices ◽  
Experimental Studies ◽  
Constant Heat Flux ◽  
Rate Of Change ◽  
Constant Heat ◽  
The Difference

Many engineering and industrial applications always seek to find ways to dissipate heat from heated surfaces used in these industries. As it is involved in the cooling of electronic parts and electrical transformers, as well as the design of solar collectors, in addition to being a process of heat exchange between hot surfaces and the fluids in contact with them. Since most electronic devices or their parts are cooled by removing the heat generated inside them by using air as a heat transfer medium and in a free convection way, and the fact that heat transfer by free convection occurs in many fields, so there were many studies that dealt with this topic. The free load is generated by the buoyant force (Bouncy force) As a result of the difference in the density of the fluid adjacent to the heated surface due to the difference in temperatures between the fluid and the surface. The laminar flow along surfaces has been extensively studied analytically [1,2,3,4] In the horizontal, inclined and vertical case, whether by constant heat flux or constant surface temperature, there are also many experimental studies of heat transfer by free convection from horizontal, inclined and vertical surfaces with constant heat flux or constant surface temperature [5,6,7,8]. Some experimental studies have also been conducted on heat transfer by convection from heated surfaces in the form of a disk (ring)The outcome of these studies was to extract an exponential mathematical relationship between the average of Nusselt number and the Kirchhoff number or Rayleigh number and the following formula: (Nu=C(Ra) n It is one of the most suitable formulas for heat transfer by free convection from heated surfaces in all its forms and over a wide range of Rayleigh number . It is noted that not all of these studies dealt with the study of the effect of the cavity ratio on heat transfer by free convection from square-shaped surfaces, which is the form that is more applied in electronic devices. Therefore, the current research means studying the rate of change in the average of Nusselt number, which represents a function of the rate of change in the rate of heat transfer by convection, as well as studying the thermal gradient above the surface, and this was done through using three hollow surfaces in proportions (0.25,0.5,0.75) of the total area.

Laminar Slug Flow: Heat Transfer Characteristics With Constant Heat Flux Boundary

2009 ◽  
Author(s):  
P. A. Walsh ◽  
E. J. Walsh ◽  
Y. S. Muzychka
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Heat Transfer Performance ◽  
Constant Heat Flux ◽  
Transfer Performance ◽  
Segmented Flow ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Flow Heat

The problem of elevated heat flux in modern electronics has led to the development of numerous liquid cooling devices which yield superior heat transfer coefficients over their air based counterparts. This study investigates the use of liquid/gas slug flows where a liquid coolant is segregated into discrete slugs, resulting in a segmented flow, and heat transfer rates are enhanced by an internal circulation within slugs. This circulation directs cooler fluid from the center of the slug towards the heated surface and elevates the temperature difference at the wall. An experimental facility is built to examine this problem in circular tube flow with a constant wall heat flux boundary condition. This was attained by Joule heating a thin walled stainless steel tube. Water was used as the coolant and air as the segregating phase. The flow rates of each were controlled using high precision syringe pumps and a slug producing mechanism was introduced for segmenting the flow into slugs of various lengths at any particular flow rate. Tube flows with Reynolds numbers in the range 10 to 1500 were examined ensuring a well ordered segmented flow throughout. Heat transfer performance was calculated by measuring the exterior temperature of the thin tube wall at various locations using an Infrared camera. Nusselt number results are presented for inverse Graetz numbers over four decades, which spans both the thermally developing and developed regions. The results show that Nu in the early thermally developing region are slightly inferior to single phase flows for heat transfer performance but become far superior at higher values of inverse Gr. Additionally, the slug length plays an important role in maximizing Nusselt number in the fully developed region as Nu plateaus at different levels for slugs of differing lengths. Overall, this paper provides a new body of experimental findings relating to segmented flow heat transfer in constant heat flux tubes without boiling. Put abstract text here.

Heat Transfer Enhancement With Vortex Generators

2019 ◽  
Author(s):  
Md. Islam ◽  
L. Guangda ◽  
S. Ainane ◽  
S. Bojanampati
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Constant Heat Flux ◽  
Vortex Generators ◽  
Cfd Simulations ◽  
Circular Pattern ◽  
Delta Winglet

Abstract In this research, heat transfer and pressure drop from a tube with vortex generators (VGs) insert are numerically investigated. The effects of heights, attack angles of VGs inside a tube on heat transfer and flow behavior are investigated. CFD simulations, with and without VGs insert, are done for an air flow range (Reynolds numbers 6000 to 33000) and for a constant heat flux on the tube model surface. Four VGs are fitted in a circular pattern on the inner surface of the tube. We studied the characteristics of the delta winglet VGs for different attack angles and blockage ratios. The Nusselt number and friction factor results show the influence of the VGs insert on heat transfer and frictional factor. The maximum Nusselt number increment (Nu/Nu0) was achieved to be 1.75 while the maximum friction factor increment (f/f0) was 3.21. In order to understand the flow behavior and different vortices, path lines released by the VGs surface and details of the vortices are also studied.

Investigation of the convective heat transfer and friction factor of magnetic Ni nanofluids within cylindrical pipes

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
M. Abdelkader ◽  
H. Ameur ◽  
Y. Menni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Constant Heat Flux ◽  
Particle Volume ◽  
Number Range

The current paper reports the results of numerical research on the magnetic Ni nanofluid flowing in a tube, developing turbulent flows under constant heat flux conditions. The numerical investigations are conducted for a Reynolds number range from 3,000 to 22,000, and a particle concentration range of 0% to 0.6%. The effects of the Reynolds number on the friction factor and Nusselt number are computed and compared satisfactorily with the experimental results of the literature. The classical correlations of Gnielinski, Notter – Rouse, and Pak and Cho are verified by predicting the Nusselt number of the Ni nanofluid. The obtained results revealed an enhancement in the heat transfer with the increase of magnetic Ni particle volume fraction and Reynolds number.

scholarly journals Numerical Studies on Thermo-Hydraulic Characteristics of Turbulent Flow in a Tube with a Regularly Spaced Dimple on Twisted Tape

CFD letters ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 20-31
Author(s):  
Birlie Fekadu ◽  
Harish H.V ◽  
Manjunath. K
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Thermal Performance ◽  
Numerical Study ◽  
Constant Heat Flux ◽  
Twisted Tape ◽  
Performance Factor ◽  
Thermal Performance Factor

Heat transfer augmentation is an important concern due to the increase in heat management problems in thermal systems. There are many techniques for enhancement of heat transfer, by active and passive techniques. A commonly used passive technique to enhance heat transfer is by inserting twisted tapes in tubes. This work presents a numerical study on Nusselt number, friction factor, and thermal performance characteristics through a circular pipe built-in with/without dimples on twisted tape. The analysis results for a turbulent flow range of 4500≤Re≤20000 are obtained with a twist ratio of the strip is 3.0. The analysis is carried for full-length tape with constant heat flux. The governing equations are numerically solved by a finite volume method using the RNG κ–ε model. The simulation results of Nusselt number versus Reynolds number of the plain, plain twisted tape and dimple twisted tape tube with the experimental data give a variation of 4.15%, 3.89%, and 7.65%. The friction factor of the dimple twisted tape tube is 60 to 70% higher than that of the plain twisted tube at different Reynolds numbers. The thermal performance factor of the dimple twisted tape and plain twisted tape tube is 30 to 35% respectively higher than that of the plain tube. Due to thermal performance factor is above unity yields a promising heat transfer enhancement. By the present study, an optimum geometrical parameter can be selected for use in heat exchangers.

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