scholarly journals On the onset of instabilities in a Bénard-Marangoni problem in an annular domain with temperature gradient

2017 ◽  
Vol 21 (suppl. 3) ◽  
pp. 585-596 ◽  
Author(s):  
Sergio Hoyas ◽  
Andrea Ianiro ◽  
María Perez-Quiles ◽  
Pablo Fajardo
Keyword(s):  
Boundary Condition ◽  
Prandtl Number ◽  
Marangoni Number ◽  
Outer Wall ◽  
Bond Number ◽  
Thermal Boundary Condition ◽  
Annular Domain ◽  
Aspect Ratios ◽  
High Prandtl Number ◽  
Lateral Walls

This manuscript addresses the linear stability analysis of a thermoconvective problem in an annular domain. The flow is heated from below, with a linear decreasing horizontal temperature profile from the inner to the outer wall. The top surface of the domain is open to the atmosphere and the two lateral walls are adiabatic. The effects of several parameters in the flow are evaluated. Three different values for the ratio of the momentum diffusivity and thermal diffusivity are considered: relatively low Prandtl number (Pr = 1), intermediate Prandtl number (Pr = 5) and high Prandtl number (ideally Pr ? ? , namely Pr = 50). The thermal boundary condition on the top surface is changed by imposing different values of the Biot number, Bi. The influence of the aspect ratio (?) is assessed for through by studying several aspect ratios, ?. The study has been performed for two values of the Bond number (namely Bo = 5 and 50), estimating the perturbation given by thermocapillarity effects on buoyancy effects. Different kinds of competing solutions appear on localized zones of the ?-Bi plane. The boundaries of these zones are made up of co-dimension two points. Co-dimension two points are found to be function of Bond number, Marangoni number and boundary conditions but to be independent on the Prandtl number.

scholarly journals Viscous Dissipation Effects in A Microchannel Caused by Oscillation of One Surface

2019 ◽  
Vol 1 (1) ◽  
pp. 13-17
Author(s):  
Chee Hao Hor ◽  
Chih Ping Tso ◽  
Gooi Mee Chen
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Prandtl Number ◽  
Viscous Dissipation ◽  
Diffusion Rate ◽  
Lower Surface ◽  
Angular Frequency ◽  
Thermal Boundary Condition ◽  
Effect Of Temperature ◽  
Brinkman Number

The viscous dissipation effects in a microchannels caused by an oscillatory lower surface is investigated numerically. An asymmetric thermal boundary condition, particularly at upper plate insulated and lower plate with constant surface temperature is solved and analyzed in details graphically. Results reveal that effect of temperature field is strongly dependent on Brinkman number, while the thermal diffusion rate on the heat induced relies on the Prandtl number. The angular frequency has influence on the temperature field gradient.

scholarly journals Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

2021 ◽  
Vol 63 (1) ◽  
Author(s):  
Thomas Schaub ◽  
Frederik Arbeiter ◽  
Wolfgang Hering ◽  
Robert Stieglitz
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Permanent Magnet ◽  
Local Nusselt Number ◽  
Velocity Profiles ◽  
Thermal Boundary Condition ◽  
Backward Facing Step ◽  
Heating Plate

Abstract In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments. Graphical Abstract

An experimental investigation of natural convection in a horizontal cylinder

1970 ◽  
Vol 44 (3) ◽  
pp. 545-561 ◽  
Author(s):  
Irving H. Brooks ◽  
Simon Ostrach
Keyword(s):  
Boundary Condition ◽  
Experimental Investigation ◽  
Steady State ◽  
Natural Convection ◽  
Initial Conditions ◽  
Horizontal Cylinder ◽  
Thermal Boundary Condition ◽  
Cylinder Wall ◽  
Horizontal Diameter ◽  
High Prandtl Number

This work deals with an experimental investigation of natural convection inside a horizontal cylinder. The fluid, geometry, and thermal boundary condition were chosen so as to have a high Prandtl number and unit-order Grashof number.The thermal boundary condition was established by imposing temperatures at two points, 180° apart, on the circumference of the cylinder. The resulting boundary condition for the full 360° was found experimentally and is presented. The apparatus was constructed so that the entire cylinder could be rotated in order to introduce an arbitrary heating angle into the boundary condition.Temperature profiles and streamline patterns were observed at steady state for various values of this heating angle and for various initial conditions. For some cases, velocity profiles were also plotted. It was found that the interior ‘core’ of fluid was thermally stratified when the diameter containing the two imposed temperatures was horizontal. The flow occurred primarily in the region close to the cylinder wall. The cylinder was rotated so that the diameter containing the two imposed temperatures made an angle with the horizontal. The hotter of the imposed temperatures was always below the horizontal diameter of the cylinder. As this angle of rotation increased, it was found that the velocities encountered in the fluid increased and the degree of thermal stratification in the core region decreased. It was also found that the steady-state results were identical for the different initial conditions imposed. The results of this study are compared with previous work, both analytic and experimental.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

2004 ◽  
Vol 16 (5) ◽  
pp. 1746-1757 ◽  
Author(s):  
D. E. Melnikov ◽  
V. M. Shevtsova ◽  
J. C. Legros
Keyword(s):  
Prandtl Number ◽  
Liquid Bridge ◽  
High Prandtl Number

Transition in high Prandtl number buoyant-thermocapillary convection

2008 ◽  
Author(s):  
Bin Zhou ◽  
Li Duan ◽  
Liang Hu ◽  
Qi Kang
Keyword(s):  
Prandtl Number ◽  
Thermocapillary Convection ◽  
High Prandtl Number
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