Thermal convection in the Earth's mantle: Mode coupling induced by temperature-dependent viscosity in a three-dimensional spherical shell

1992 ◽  
Vol 19 (4) ◽  
pp. 337-340 ◽  
Author(s):  
Cheryl A. Stewart
Keyword(s):  
Spherical Shell ◽  
Thermal Convection ◽  
Mode Coupling ◽  
Three Dimensional ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Earth’S Mantle ◽  
Dependent Viscosity

Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity

1991 ◽  
Vol 233 ◽  
pp. 299-328 ◽  
Author(s):  
Masaki Ogawa ◽  
Gerald Schubert ◽  
Abdelfattah Zebib
Keyword(s):  
Thermal Convection ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Rectangular Pattern ◽  
Four Corners ◽  
Layer Mode ◽  
Constant Viscosity ◽  
Dependent Viscosity

Numerical calculations are presented for the steady three-dimensional structure of thermal convection of a fluid with strongly temperature-dependent viscosity in a bottom-heated rectangular box. Viscosity is assumed to depend on temperature T as exp (− ET), where E is a constant; viscosity variations across the box r (= exp (E)) as large as 105 are considered. A stagnant layer or lid of highly viscous fluid develops in the uppermost coldest part of the top cold thermal boundary layer when r > rc1, where r = rc1 ≡ 1.18 × 103Rt0.309 and Rt is the Rayleigh number based on the viscosity at the top boundary. Three-dimensional convection occurs in a rectangular pattern beneath this stagnant lid. The planform consists of hot upwelling plumes at or near the centre of a rectangle, sheets of cold sinking fluid on the four sides, and cold sinking plume concentrations immersed in the sheets. A stagnant lid does not develop, i.e. convection involves all of the fluid in the box when r < rc1. The whole-layer mode of convection occurs in a three-dimensional bimodal pattern when r > rc2 = 3.84 × 106Rt−1.35. The planform of the convection is rectangular with the coldest parts of the sinking fluid and the hottest part of the upwelling fluid occurring as plumes at the four corners and at the centre of the rectangle, respectively. Both hot uprising plumes and cold sinking plumes have sheet-like extensions, which become more well-developed as r increases. The whole-layer mode of convection occurs as two-dimensional rolls when r < min (rc1, rc2). The Nusselt number Nu depends on the viscosity at the top surface more strongly in the regime of whole-layer convection than in the regime of stagnant-lid convection. In the whole-layer convective regime, Nu depends more strongly on the viscosity at the top surface than on the viscosity at the bottom boundary.

scholarly journals Energy and Temperature-Dependent Viscosity Analysis on Magnetized Eyring-Powell Fluid Oscillatory Flow in a Porous Channel

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7829
Author(s):  
Meng Yang ◽  
Munawwar Ali Abbas ◽  
Wissam Sadiq Khudair
Keyword(s):  
Thermal Radiation ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Engineering Sciences ◽  
Dependent Viscosity ◽  
The Impact

In this research, we studied the impact of temperature dependent viscosity and thermal radiation on Eyring Powell fluid with porous channels. The dimensionless equations were solved using the perturbation technique using the Weissenberg number (ε ≪ 1) to obtain clear formulas for the velocity field. All of the solutions for the physical parameters of the Reynolds number (Re), magnetic parameter (M), Darcy parameter (Da) and Prandtl number (Pr) were discussed through their different values. As shown in the plots the two-dimensional and three-dimensional graphical results of the velocity profile against various pertinent parameters have been illustrated with physical reasons. The results revealed that the temperature distribution increases for higher Prandtl and thermal radiation values. Such findings are beneficial in the field of engineering sciences.

scholarly journals Plume generation in natural thermal convection at high Rayleigh and Prandtl numbers

2001 ◽  
Vol 434 ◽  
pp. 1-21 ◽  
Author(s):  
C. LITHGOW-BERTELLONI ◽  
M. A. RICHARDS ◽  
C. P. CONRAD ◽  
R. W. GRIFFITHS
Keyword(s):  
Boundary Layer ◽  
Thermal Convection ◽  
Large Scale ◽  
Lower Boundary ◽  
Secular Change ◽  
Scaling Analysis ◽  
Temperature Dependent Viscosity ◽  
Earth’S Mantle ◽  
Dependent Viscosity ◽  
Rayleigh Numbers

We study natural thermal convection of a fluid (corn syrup) with a large Prandtl number (103–107) and temperature-dependent viscosity. The experimental tank (1 × 1 × 0.3m) is heated from below with insulating top and side boundaries, so that the fluid experiences secular heating as experiments proceed. This setup allows a focused study of thermal plumes from the bottom boundary layer over a range of Rayleigh numbers relevant to convective plumes in the deep interior of the Earth's mantle. The effective value of Ra, based on the viscosity of the fluid at the interior temperature, varies from 105 at the beginning to almost 108 toward the end of the experiments. Thermals (plumes) from the lower boundary layer are trailed by continuous conduits with long residence times. Plumes dominate flow in the tank, although there is a weaker large-scale circulation induced by material cooling at the imperfectly insulating top and sidewalls. At large Ra convection is extremely time-dependent and exhibits episodic bursts of plumes, separated by periods of quiescence. This bursting behaviour probably results from the inability of the structure of the thermal boundary layer and its instabilities to keep pace with the rate of secular change in the value of Ra. The frequency of plumes increases and their size decreases with increasing Ra, and we characterize these changes via in situ thermocouple measurements, shadowgraph videos, and videos of liquid crystal films recorded during several experiments. A scaling analysis predicts observed changes in plume head and tail radii with increasing Ra. Since inertial effects are largely absent no transition to ‘hard’ thermal turbulence is observed, in contrast to a previous conclusion from numerical calculations at similar Rayleigh numbers. We suggest that bursting behaviour similar to that observed may occur in the Earth's mantle as it undergoes secular cooling on the billion-year time scale.

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