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%.

Analytical Prediction of Heat Transfer in Tape Generated Swirl Flow

2017 ◽  
Author(s):  
R. J. Yadav ◽  
Sandeep Kore ◽  
V. N. Riabhole
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Swirl Flow ◽  
Twisted Tape ◽  
Analytical Prediction ◽  
Transfer Coefficients ◽  
Numerical Predictions ◽  
Twisted Tapes ◽  
Wide Range ◽  
Prandtl Numbers

Heat transfer and pressure drop characteristics in a circular tube with twisted tapes have been investigated experimentally and numerically using different working fluids by many researchers for wide range of Reynolds number. The swirl was generated by tape inserts of various twist ratios. The various twist ratios are considered Many researchers formed generalized correlations to predict friction factors and convective heat transfer coefficients with twisted tapes in a tube for a wide range of Reynolds numbers and Prandtl numbers. Satisfactory agreement was obtained between the present correlations and the data of others validate the proposed correlations. The experimental or numerical predictions were compared with earlier correlations revealing good agreement between them. From the literature review it is observed that most studies are mainly focused on the heat transfer enhancement using twisted tape by experimental or numerical solution. An investigation with analytical approach is rarely reported. Therefore, the main aim of the present work is to form a correlation from theoretical approach for Nusselt number for circular tube with twisted tape. Application of dimensional analysis to heat transfer in tape generated swirl flow is carried out.

Heat Transfer in Turbulent Pipe Flow With Optically Thin Radiation

1969 ◽  
Vol 91 (3) ◽  
pp. 330-335 ◽  
Author(s):  
C. S. Landram ◽  
R. Greif ◽  
I. S. Habib
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Constant Heat Flux ◽  
Turbulent Pipe Flow ◽  
Radiation Problem ◽  
Constant Heat ◽  
Nusselt Numbers ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

The problem considered is the determination of the heat transfer in fully developed turbulent flow of a radiating optically thin gas in a circular tube. The radiation problem is formulated in terms of the Planck mean and the modified Planck mean coefficients and the temperature profiles and Nusselt numbers have been determined. It is shown that the simple constant shear, constant heat flux formulation yields results that are in very good agreement with more complex calculations.

Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

Viscous Dissipation Effects on Developing Laminar Flow in Adiabatic and Heated Tubes

1975 ◽  
Vol 189 (1) ◽  
pp. 129-137 ◽  
Author(s):  
M. W. Collins
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Circular Tube ◽  
Recent Experimental Data ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Constant Wall Heat Flux ◽  
Finite Difference Solution ◽  
Viscosity Variation ◽  
Temperature And Pressure

A finite-difference solution is presented for the problem of laminar developing flow in a circular tube, allowing for viscous dissipation and viscosity variation with temperature. Predictions of temperature and pressure under adiabatic conditions compare reasonably with published experimental and analytical results. Polak's postulation of a hot slip zone is considered. Heat transfer, with constant wall heat flux, is also studied and it is concluded, with reference to some recent experimental data, that it is not necessary to postulate viscous dissipation as being a substantial aiding effect. Predicted Nusselt numbers are, in fact, reduced by allowing for the effect.

Correlations for Laminar Mixed Convection Flows on Vertical, Inclined, and Horizontal Flat Plates

1986 ◽  
Vol 108 (4) ◽  
pp. 835-840 ◽  
Author(s):  
T. S. Chen ◽  
B. F. Armaly ◽  
N. Ramachandran
Keyword(s):  
Free Convection ◽  
Mixed Convection ◽  
Forced Flow ◽  
Flat Plates ◽  
Maximum Increase ◽  
Nusselt Numbers ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Flow Configurations ◽  
Prandtl Numbers

Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature

1988 ◽  
Vol 110 (1) ◽  
pp. 103-108 ◽  
Author(s):  
H. R. Lee ◽  
T. S. Chen ◽  
B. F. Armaly
Keyword(s):  
Natural Convection ◽  
Wall Temperature ◽  
Spline Interpolation ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Variable Surface ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Spline Interpolation Technique ◽  
Vertical Cylinders

Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature Tw(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of Tw(x) = T∞ + axn, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.

Heat Transfer From a Rotating Disk to Fluids for a Wide Range of Prandtl Numbers Using the Asymptotic Model

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Correlation Method ◽  
Rotating Disk ◽  
Compact Model ◽  
Asymptotic Model ◽  
Simple Method ◽  
Nusselt Numbers ◽  
Proposed Model ◽  
Wide Range ◽  
Prandtl Numbers

A simple method for calculating heat transfer from a rotating disk to fluids for a wide range of Prandtl numbers using asymptotic analysis is presented. Nusselt numbers for a heated rotating disk for different Prandtl numbers is expressed in terms of the asymptotic Nusselt numbers corresponding to a very small value of Prandtl numbers and Nusselt numbers corresponding to a very large value of Prandtl numbers. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model can be determined at Prandtl numbers corresponding to the intersection of the two asymptotes.

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.

scholarly journals A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 148
Author(s):  
Seyed Amin Nabavizadeh ◽  
Himel Barua ◽  
Mohsen Eshraghi ◽  
Sergio D. Felicelli
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Bgk Model ◽  
Flow Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

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