Flow in heated curved pipes

1978 ◽  
Vol 88 (2) ◽  
pp. 339-354 ◽  
Author(s):  
Lun-Shin Yao ◽  
Stanley A. Berger
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Temperature Distribution ◽  
Dean Number ◽  
Representative Case ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Axial Temperature ◽  
Buoyancy Forces ◽  
Rayleigh Numbers

The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case.

Investigation Into Thermal Stress Characteristics of Pipe-in-Pipe Under High Temperature Condition

2018 ◽  
Author(s):  
Si-Hwa Jeong ◽  
Min-Gu Won ◽  
Nam-Su Huh ◽  
Yun-Jae Kim ◽  
Young-Jin Oh ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
High Temperature ◽  
Temperature Distribution ◽  
Heat Transfer Analysis ◽  
Piping System ◽  
Curved Pipe ◽  
High Temperature Condition ◽  
Single Pipe ◽  
Radiation Conditions

In this paper, the thermal stress characteristics of the pipe-in-pipe (PIP) system under high temperature condition are analyzed. The PIP is a type of pipe applied in sodium-cooled faster reactor (SFR) and has a different geometry from a single pipe. In particular, under the high temperature condition of the SFR, the high thermal stress is generated due to the temperature gradient occurring between the inner pipe and outer pipe. To investigate the thermal stress characteristics, three cases are considered according to geometry of the support. The fully constrained support and intermediate support are considered for case 1 and 2, respectively. For case 3, both supports are applied to the actual curved pipe. The finite element (FE) analyses are performed in two steps for each case. Firstly, the heat transfer analysis is carried out considering the thermal conduction, convection and radiation conditions. From the heat transfer analysis, the temperature distribution results in the piping system are obtained. Secondly, the structural analysis is performed considering the temperature distribution results and boundary conditions. Finally, the effects of the geometric characteristics on the thermal stress in the PIP system are analyzed.

Entropy hemodynamics particle-fluid suspension model through eccentric catheterization for time-variant stenotic arterial wall: Catheter injection

2019 ◽  
Vol 16 (11) ◽  
pp. 1950164 ◽  
Author(s):  
Kh. S. Mekheimer ◽  
A. Z. Zaher ◽  
A. I. Abdellateef
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Temperature Distribution ◽  
Wall Shear Stress ◽  
Outer Cylinder ◽  
Flow Characteristics ◽  
Two Phase ◽  
Eccentric Cylinder ◽  
Wall Shear ◽  
Suspension Model

Catheterization has an imperative rule in heat transfer investigations, which are frequently applied to analyze and deal with the heart transfer studies. Here, the entering of a catheter adjusts the flow of the blood and it affects the hemodynamic status in the artery region. In practical clinical cases, catheters cannot be precisely concentric with the artery. The impartial of this work is to investigate the behavior of a blood streaming characteristics, in the case of injecting the catheter eccentrically all the way through a stenotic overlapping artery. In this paper, we consider the heat transfer within the presence of blood corpuscle which has been characterized by a macroscopic two-phase model (i.e. a suspension of erythrocytes in plasma). The model here considers the blood fluid as a liquid fluid with adjourned particles in the gap bounded by the eccentric cylinder. The inside cylinder is identically rigid demonstrating the movable thin catheter and kept at constant temperature, where the outer cylinder is a taper cylinder demonstrating the artery that has overlapping stenosis and it is cooled and maintained at zero temperature. The coupled differential equations for both fluid (plasma) and particle (erythrocyte) phases have been solved. The expressions for the flow characteristics, namely, the flow rate, the impedance (resistance to flow), the wall shear stress and the temperature distribution, have been derived. The model is very useful in medicine, where the hemodynamic speed is higher for eccentric case than that of concentric one. Also, the temperature distribution and the entropy generation in the state of eccentric position are higher than in the case of the concentric position. A significant increase in the magnitude of the impedance and the wall shear stress occurs for an increase in the hematocrit, C for diseased blood.

A Numerical Study of Laminar and Turbulent Natural Convective Heat Transfer From an Isothermal Vertical Plate With a Wavy Surface

2010 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Convective Heat Transfer ◽  
Transfer Rate ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
Buoyancy Forces ◽  
Rayleigh Numbers

Natural convective heat transfer from a wide isothermal plate which has a wavy surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The main purpose of the study was to examine the effect of the surface waviness on the conditions under which transition from laminar to turbulent flow occurred and to study the effect of the surface waviness on the heat transfer rate. The surface waves, which have a saw-tooth cross-sectional shape, are normal to the direction of flow over the surface and have a relatively small amplitude. The range of Rayleigh numbers considered in the present study extends from values that for a non-wavy plate would be associated with laminar flow to values that would be associated with fully turbulent flow. The flow has been assumed to be steady and fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. A standard k-epsilon turbulence model with full account being taken of the effects of the buoyancy forces has been used in obtaining the solution. The solution has been obtained using the commercial CFD solver FLUENT. The solution has the following parameters: the Rayleigh number based on the plate height, the Prandtl number, the dimensionless amplitude of the surface waviness, and the dimensionless pitch of the surface waviness. Results have been obtained for a Prandtl number of 0.7 and for a single dimensionless pitch value for Rayleigh numbers between approximately 106 and 1012. The effects of Rayleigh number and dimensionless amplitude on the mean heat transfer rate have been studied. It is convenient in presenting the results to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface.

Turbulent convection in a horizontal layer of water

1973 ◽  
Vol 60 (1) ◽  
pp. 141-159 ◽  
Author(s):  
T. Y. Chu ◽  
R. J. Goldstein
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Rayleigh Number ◽  
Power Law ◽  
Bounding Surface ◽  
Interferometric Method ◽  
Number Range ◽  
Mean Temperature ◽  
The Mean ◽  
Rayleigh Numbers

Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra0·278 in the range 2·76 × 105 < Ra < 1·05 × 108. Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107. Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 105) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z−2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z−1 power law is also found.

Mechanism of Convective Heat Transfer of Airflow in Deep Airway

2011 ◽  
Vol 243-249 ◽  
pp. 4998-5002
Author(s):  
Yi Jiang Wang ◽  
Guo Qing Zhou ◽  
Lei Wu ◽  
Yong Lu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Mining Depth ◽  
Axial Temperature ◽  
Criterion Equation

With the increase of mining depth, an investigation of the convective heat transfer of airflow in deep airway is urgently required. The velocity and temperature distribution were derived by using the turbulence model for smooth tube. In order to simplify calculation and avoid the complicated calculation of integration, with the help of velocity-temperature distribution analogy, the criterion equation of convective heat transfer was obtained by using the model of constant heat flux. The coefficient of convective heat transfer between airflow and airway was calculated, and criterion correlation of convective heat transfer was regressed according to test data. Test results show that the axial temperature distribution of airflow is linear, which is encouraging agreement with theoretical calculating results. Hence model of constant heat flux is a viable method for studying the convective heat transfer of airflow in deep airway.

Flow Visualization Experiments on Secondary Flow Patterns in an Isothermally Heated Curved Pipe

1987 ◽  
Vol 109 (1) ◽  
pp. 55-61 ◽  
Author(s):  
K. C. Cheng ◽  
F. P. Yuen
Keyword(s):  
Flow Visualization ◽  
Secondary Flow ◽  
Theoretical Models ◽  
Flow Patterns ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Number Range ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Numerical Predictions

Secondary flow patterns at the exit of a 180 deg bend (tube inside diameter d = 1.99 cm, radius of curvature Rc = 10.85 cm) are presented to illustrate the combined effects of centrifugal and buoyancy forces in hydrodynamically and thermally developing entrance region of an isothermally heated curved pipe with both parabolic and turbulent entrance velocity profiles. Three cases of upward, horizontal, and downward-curved pipe flows are studied for constant wall temperatures Tw=55–91°C, Dean number range K=22–1209 and ReRa=1.00×106–8.86×107. The flow visualization was realized by the smoke injection method. The secondary flow patterns shown are useful for future comparison with numerical predictions and confirming theoretical models. The results can be used to assess qualitatively the limit of the applicability of the existing correlation equations for laminar forced convection in isothermally heated curved pipes without buoyancy effects.

scholarly journals Experimental and Numerical Study of Free Convection in a Vertical Channel with Opposing Buoyancy Forces

2021 ◽  
Author(s):  
Derek Roeleveld
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Vertical Channel ◽  
Ansys Fluent ◽  
Fully Developed Flow ◽  
Wall Functions ◽  
Buoyancy Forces ◽  
Rayleigh Numbers ◽  
Steady Laminar

Free convective heat transfer inside a vertical channel was studied both experimentally and numerically. An experimental model of an isothermally, asymmetrically heated vertical channel was constructed to study various cases of opposing buoyancy forces. Many studies in the literature have investigated buoyancy forces in a single direction. The study presented here investigated opposing buoyancy forces, where one wall is warmer than the ambient and the other wall is cooler than the ambient. Five different temperature ratios were studied using four different channel spacings between the two channel walls. A Mach-Zehnder interferometer provided temperature field visualization. In addition, local and average heat transfer measurements were made with the interferometer. Flow visualization was conducted to determine the flow pattern inside the channel. The measured local and average Nusselt number data were compared to numerical solutions obtained using ANSYS FLUENT. A steady laminar model and a steady k-ε turbulence model with two different wall functions were used. Numerical solutions were obtained for a Prandtl number of 0.71 and Rayleigh numbers ranging from the laminar fully developed flow regime to the turbulent isolated boundary layer regime.

scholarly journals Experimental Study and Conjugate Heat Transfer Simulation of Pulsating Flow in Straight and 90° Curved Square Pipes

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3953
Author(s):  
Guanming Guo ◽  
Masaya Kamigaki ◽  
Yuuya Inoue ◽  
Keiya Nishida ◽  
Hitoshi Hongou ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Steady Flow ◽  
Conjugate Heat Transfer ◽  
Reverse Flow ◽  
Pulsating Flow ◽  
Temperature Fields ◽  
Dean Number ◽  
Curved Pipe

The turbulent pulsating flow and heat transfer in straight and 90° curved square pipes are investigated in this study. Both experimental temperature field measurements at the cross-sections of the pipes and conjugate heat transfer (CHT) simulation were performed. The steady turbulent flow was investigated and compared to the pulsating flow under the same time-averaged Reynolds number. The time-averaged Reynolds number of the pulsating flow, as well as the steady flow, was approximately 60,000. The Womersley number of the pulsating flow was 43.1, corresponding to a 30 Hz pulsating frequency. Meanwhile, the Dean number in the curved pipe was approximately 31,000. The results showed that the local heat flux of the pulsating flow was greater than that of the steady flow when the location was closer to the upstream pulsation generator. However, the total heat flux of the pulsating flow was less than that of the steady flow. Moreover, the instantaneous velocity and temperature fields of the simulation were used to demonstrate the heat transfer mechanism of the pulsating flow. The behaviors, such as the obvious separation between the air and pipe wall, the low-temperature core impingement, and the reverse flow, suppress the heat transfer.

Heat Convection in a Horizontal Curved Pipe

1984 ◽  
Vol 106 (1) ◽  
pp. 71-77 ◽  
Author(s):  
L. S. Yao
Keyword(s):  
Centrifugal Force ◽  
Small Region ◽  
Relative Importance ◽  
Dean Number ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Developing Flow ◽  
Physical Importance ◽  
Hydrodynamically Developing Flow ◽  
Pipe Inlet

Thermally and hydrodynamically developing flow in heated horizontal curved pipes is analyzed. The perturbation solution is quantitatively valid only in a small region near the pipe inlet. The solution, however, provides information about the physical importance of centrifugal force and buoyancy on the developing flow. It also reveals the length and the velocity scales for the downstream regions where the secondary flow can not be treated as a small perturbation. The relative importance of centrifugal force and buoyancy is determined by the ratio of the Dean number and the Grashof number.

Sign in / Sign up

Export Citation Format

Share Document