Combined Free and Forced Convection in Inclined Circular Tubes

1976 ◽  
Vol 98 (2) ◽  
pp. 322-324 ◽  
Author(s):  
J. A. Sabbagh ◽  
A. Aziz ◽  
A. S. El-Ariny ◽  
G. Hamad
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Circular Tube ◽  
Circular Tubes ◽  
Theoretical Predictions ◽  
Free And Forced Convection ◽  
Axial Heat ◽  
Peripheral Temperature

The problem of combined free and forced convection in an inclined circular tube with uniform peripheral temperature and axial heat flux has been studied experimentally. For fixed Pr and Ra, experimental data showing the effect of tube inclination and Reynolds number on temperature and axial velocity profiles are reported and found to agree qualitatively with the theoretical predictions [7]. Also shown is the variation of Nusselt number with inclination angle for Ra Re = 30,000. No optimum angle for maximum Nusselt number was found.

Oscillatory Heat Transfer in a Pipe Subjected to a Laminar Reciprocating Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 592-597 ◽  
Author(s):  
T. S. Zhao ◽  
P. Cheng
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Nusselt Number ◽  
Numerical Study ◽  
Temperature Cycle ◽  
Uniform Heat Flux ◽  
Fluid Temperature ◽  
Cycle Space ◽  
Reciprocating Flow

An experimental and numerical study has been carried out for laminar forced convection in a long pipe heated by uniform heat flux and subjected to a reciprocating flow of air. Transient fluid temperature variations in the two mixing chambers connected to both ends of the heated section were measured. These measurements were used as the thermal boundary conditions for the numerical simulation of the hydrodynamically and thermally developing reciprocating flow in the heated pipe. The coupled governing equations for time-dependent convective heat transfer in the fluid flow and conduction in the wall of the heated tube were solved numerically. The numerical results for time-resolved centerline fuid temperature, cycle-averaged wall temperature, and the space-cycle averaged Nusselt number are shown to be in good agreement with the experimental data. Based on the experimental data, a correlation equation is obtained for the cycle-space averaged Nusselt number in terms of appropriate dimensionless parameters for a laminar reciprocating flow of air in a long pipe with constant heat flux.

In-Plane Bending of Curved Circular Tubes

1968 ◽  
Vol 90 (4) ◽  
pp. 666-670 ◽  
Author(s):  
D. H. Cheng ◽  
H. J. Thailer
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Compatibility Condition ◽  
Circular Tube ◽  
Series Expansions ◽  
Center Line ◽  
Complementary Energy ◽  
Circular Tubes ◽  
Binomial Expansion ◽  
Plane Bending

A general solution is presented for a thin, curved circular tube under in-plane bending. It includes the solution given by Clark and Reissner as a particular case in which the ratio of the radius of the tube to the radius of its center line is very small. The series expansions satisfy the equilibrium equation for any radius ratio while the compatibility condition is guaranteed by minimizing the complementary energy. The minimization is achieved in the manner of Raileigh-Ritz whereas the evaluation of integrals are facilitated by the use of binomial expansion. Numerical results correlate well with the experimental data. The solution is more rapidly convergent as compared to the existing analytical methods.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Empirical Correlation of Factors Influencing Departure From Nucleate Boiling in Steam-Water Mixtures Flowing in Vertical Round Tubes

1966 ◽  
Vol 88 (4) ◽  
pp. 367-373 ◽  
Author(s):  
D. Pasint ◽  
R. H. Pai
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Forced Convection ◽  
Mass Flow ◽  
Nucleate Boiling ◽  
Vertical Tube ◽  
Empirical Correlation ◽  
Factors Influencing ◽  
Vertical Tubes ◽  
Heated Length

An empirical correlation of forced convection DNB for steam-water mixtures between 500 and 3000 psia in uniformly heated vertical tubes is proposed. DNB quality is expressed in terms of pressure, mass flow, inlet enthalpy, heated length from inlet to DNB point, and tube dia. The experimental data of the authors at 2000–3000 psia, 250,000–1,000,000 lb/hr sq ft2 mass flow, and 40,000–180,000 Btu/hr sq ft heat flux, obtained from a 6 ft long, 3/4-in-ID electrically heated vertical tube, are correlated with other published results ranging from 500 to 2000 psia.

An Interferometric Study of Combined Free and Forced Convection in a Horizontal Isothermal Tube

1981 ◽  
Vol 103 (2) ◽  
pp. 249-256 ◽  
Author(s):  
W. W. Yousef ◽  
J. D. Tarasuk
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Forced Convection ◽  
Average Nusselt Number ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Reynolds Numbers ◽  
Nusselt Numbers ◽  
Free And Forced Convection

A Mach-Zehnder interferometer was employed to determine the three-dimensional temperature field, and the circumferential and average Nusselt numbers for laminar flow of air in the entrance region of an isothermal horizontal tube where the velocity and the temperature profiles were developing simultaneously. The influence of free convection due to buoyancy on forced convection heat transfer was investigated. The Reynolds numbers ranged from 120 to 1200, the Grashof numbers ranged from 0.8 × 104 to 8.7 × 104, and the ratio L/D was varied from 6 to 46. The free convection increases, substantially, the average Nusselt number, by up to a factor of 2.0 from the analytical predictions, which account for forced convection only, near the tube inlet. Far from the tube inlet the free convection tends to decrease the average Nusselt number below the analytical predictions.

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