Buoyancy-driven convection in cylindrical geometries

1969 ◽  
Vol 36 (2) ◽  
pp. 239-258 ◽  
Author(s):  
S. F. Liang ◽  
A. Vidal ◽  
Andreas Acrivos
Keyword(s):  
Numerical Solutions ◽  
Perturbation Expansion ◽  
Boussinesq Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cylindrical Cell ◽  
Prandtl Numbers ◽  
Buoyancy Driven Convection ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.

Effects of Temperature-Dependent Viscosity Variations and Boundary Conditions on Fully Developed Laminar Forced Convection in a Semicircular Duct

1998 ◽  
Vol 120 (3) ◽  
pp. 600-605 ◽  
Author(s):  
T. M. Harms ◽  
M. A. Jog ◽  
R. M. Manglik
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Numerical Solutions ◽  
Strong Dependence ◽  
Laminar Flows ◽  
Temperature Fields ◽  
Traditional Values ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Fully developed laminar flows in a semicircular duct with temperature-dependent viscosity variations in the flow cross section are analyzed, where the viscosity-temperature behavior is described by the Arrhenius model. Both the T and H1 boundary conditions are considered, as they represent the most fundamental heating/cooling conditions encountered in practical compact heat exchanger applications. Numerical solutions for the flow velocity and the temperature fields have been obtained by finite difference technique. The friction factor and Nusselt number results display a strong dependence on the viscosity ratio (μw/μb), and this is correlated using the classical power-law relationship. However, results indicate that the power-law exponents are significantly different from traditional values for circular tube. They are found to be functions of the flow geometry, boundary condition, and direction of heat transfer (heating or cooling).

scholarly journals Numerical Study of Free Convection inside the Differentially Heated Cavity incorporating Variable Property Al2O3-H2O Nanofluid

2021 ◽  
Author(s):  
Bishwajit Sharma ◽  
◽  
Md. Feroz Alam ◽  
Mayur Krishna Bora ◽  
Rabindra Nath Barman ◽  
...  
Keyword(s):  
Free Convection ◽  
Volume Fraction ◽  
Numerical Study ◽  
Particle Diameter ◽  
Nano Particle ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Percentage Concentration ◽  
Prandtl Numbers ◽  
Dependent Viscosity

This paper investigates free convection in a partially heated square cavity filled with alumina-water nanofluid. The investigation is carried out at the three-volume fraction of nanoparticles (0, 0.03, 0.05), two Prandtl numbers (2.66, 6), and constant Grashof number (105) with three shapes of insulating obstacles (Square, Circular, and Rectangular). The results show that the nanofluid volume fraction and Prandtl number significantly enhance the heat transfer. The user-defined function (UDF) is developed and computed to investigate the effect of nanoparticle diameter and its temperature-dependent viscosity on convection. The average Nusselt number (Nu) increased with the temperature-dependent viscosity model and by increasing the percentage concentration of the nanoparticles. For all obstacle shapes, the thermal performance improved with increase in the nano-particle diameter.

scholarly journals Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 956-966 ◽  
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Murad Ullah ◽  
Ilyas Khan ◽  
Tawfeeq Abdullah Alkanhal ◽  
...  
Keyword(s):  
Shooting Method ◽  
Numerical Solutions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Wire Coating ◽  
Gradient Parameter ◽  
Dependent Viscosity ◽  
Method Analysis

Abstract The most important plastic resins used in wire coating are high/low density polyethylene (LDPE/HDPE), plasticized polyvinyl chloride (PVC), nylon and polysulfone. To provide insulation and mechanical strength, coating is necessary for wires. Simulation of polymer flow during wire coating dragged froma bath of Oldroyd 8-constant fluid incompresible and laminar fluid inside pressure type die is carried out numerically. In wire coating the flow depends on the velocity of the wire, geometry of the die and viscosity of the fluid.The non-dimensional resulting flow and heat transfer differential equations are solved numerically by Ruge-Kutta 4th-order method with shooting technique. Reynolds model and Vogel’s models are encountered for temperature dependent viscosity. The numerical solutions are obtained for velocity field and temperature distribution. The solutions are computed for different physical parameters.It is observed that the non-Newtonian propertis of fluid were favourable, enhancing the velocity in combination with temperature dependent variable. The Brinkman number contributes to increase the temperature for both Reynolds and Vogel’smodels. With the increasing of pressure gradient parameter of both Reynolds and Vogel’s models, the velocity and temperature profile increases significantly in the presence of non-Newtonian parameter. Furthermore, the present result is also compared with published results as a particular case.

Square-pattern convection in fluids with strongly temperature-dependent viscosity

1985 ◽  
Vol 150 ◽  
pp. 451-465 ◽  
Author(s):  
F. H. Busse ◽  
H. Frick
Keyword(s):  
Numerical Solutions ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Square Lattice ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
The Stability ◽  
Dependent Viscosity ◽  
Theoretical Results

Three-dimensional numerical solutions are obtained describing convection with a square lattice in a layer heated from below with no-slip top and bottom boundaries. The limit of infinite Prandtl number and a linear dependence of the viscosity on temperature are assumed. The stability of the three-dimensional solutions with respect to disturbances fitting the square lattice is analysed. It is shown that convection in the form of two-dimensional rolls is stable for low variations of viscosity, while square-pattern convection becomes stable when the viscosity contrast between upper and lower parts of the fluid layer is sufficiently strong. The theoretical results are in qualitative agreement with experimental observations.

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