scholarly journals Numerical study of magneto-hydrodynamic (MHD) mixed convection flow in a lid-driven triangular cavity

2015 ◽  
Vol 12 (1) ◽  
pp. 21-32
Author(s):  
Mohammed Nasir Uddin ◽  
Aki Farhana ◽  
Md. Abdul Alim
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Numerical Study ◽  
Bulk Temperature ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Coupled Equations ◽  
Wide Range

In the present paper, the effect of magneto-hydrodynamic (MHD) on mixed convection flow within a lid-driven triangular cavity has been numerically investigated. The bottom wall of the cavity is considered as heated. Besides, the left and the inclined wall of the triangular cavity are assumed to be cool and adiabatic. The cooled wall of the cavity is moving up in the vertical direction. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Rayleigh number, Hartmann number and the cavity aspect ratio. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters Rayleigh number Ra (103-104), Prandtl number Pr (0.7 - 3) and Hartmann number Ha (5 - 50). The numerical results are presented in terms of stream functions, temperature profile and Nussult numbers. It is found that the streamlines, isotherms, average Nusselt number, average fluid bulk temperature and dimensionless temperature in the cavity strongly depend on the Rayleigh number, Hartmann number and Prandtl number.

Linear stability analysis of mixed-convection flow in a vertical pipe

2000 ◽  
Vol 422 ◽  
pp. 141-166 ◽  
Author(s):  
YI-CHUNG SU ◽  
JACOB N. CHUNG
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Shear Instability ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Vertical Pipe ◽  
Prandtl Numbers ◽  
The Stability ◽  
Rayleigh Numbers

A comprehensive numerical study on the linear stability of mixed-convection flow in a vertical pipe with constant heat flux is presented with particular emphasis on the instability mechanism and the Prandtl number effect. Three Prandtl numbers representative of different regimes in the Prandtl number spectrum are employed to simulate the stability characteristics of liquid mercury, water and oil. The results suggest that mixed-convection flow in a vertical pipe can become unstable at low Reynolds number and Rayleigh numbers irrespective of the Prandtl number, in contrast to the isothermal case. For water, the calculation predicts critical Rayleigh numbers of 80 and −120 for assisted and opposed flows, which agree very well with experimental values of Rac = 76 and −118 (Scheele & Hanratty 1962). It is found that the first azimuthal mode is always the most unstable, which also agrees with the experimental observation that the unstable pattern is a double spiral flow. Scheele & Hanratty's speculation that the instability in assisted and opposed flows can be attributed to the appearance of inflection points and separation is true only for fluids with O(1) Prandtl number. Our study on the effect of the Prandtl number discloses that it plays an active role in buoyancy-assisted flow and is an indication of the viability of kinematic or thermal disturbances. It profoundly affects the stability of assisted flow and changes the instability mechanism as well. For assisted flow with Prandtl numbers less than 0.3, the thermal–shear instability is dominant. With Prandtl numbers higher than 0.3, the assisted-thermal–buoyant instability becomes responsible. In buoyancy-opposed flow, the effect of the Prandtl number is less significant since the flow is unstably stratified. There are three distinct instability mechanisms at work independent of the Prandtl number. The Rayleigh–Taylor instability is operative when the Reynolds number is extremely low. The opposed-thermal–buoyant instability takes over when the Reynolds number becomes higher. A still higher Reynolds number eventually leads the thermal–shear instability to dominate. While the thermal–buoyant instability is present in both assisted and opposed flows, the mechanism by which it destabilizes the flow is completely different.

Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 2. Mean flow characteristics

1999 ◽  
Vol 398 ◽  
pp. 87-108 ◽  
Author(s):  
S. A. SUSLOV ◽  
S. PAOLUCCI
Keyword(s):  
Mixed Convection ◽  
Mass Flux ◽  
Flow Characteristics ◽  
Vertical Channel ◽  
Physical Nature ◽  
Reynolds Numbers ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Mean Flow ◽  
Wide Range

Based on amplitude expansions developed in Part 1 (Suslov & Paolucci 1999), we examine the mean flow characteristics of non-Boussinesq mixed convection flow of air in a vertical channel in the vicinity of bifurcation points for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. The constant mass flux and constant pressure gradient formulations are shown to lead to qualitatively similar, but quantitatively different, results. The physical nature of the distinct shear and buoyancy disturbances is investigated, and detailed mean flow and energy analyses are presented. The variation of the total mass of fluid in a flow domain as disturbances develop is discussed. The average Nusselt number and mass flux are estimated for supercritical regimes for a wide range of governing parameters.

Mixed convection flow due to a moving vertical plate parallel to free stream under the influence of Newtonian heating and thermal radiation

2014 ◽  
Vol 5 (3) ◽  
pp. 859-870
Author(s):  
Prabhugouda Patil ◽  
S. Roy
Keyword(s):  
Prandtl Number ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Free Stream ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Newtonian Heating ◽  
Mixed Convection Parameter ◽  
Convection Parameter

The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show that the streamwise co-ordinate  significantly influences the flow and thermal fields which indicate the importance of non-similar solutions. Also, it is observed that the increase of mixed convection parameter causes the increase in the magnitude of velocity profile about 65% for lower Prandtl number fluids (Pr=0.7), while it decreases in the temperature profile about 30%. Present results are compared with previously published work and are found to be in excellent agreement.

Numerical Study of Combined Radiation and Turbulent Mixed Convection Heat Transfer in a Compartment Containing Participating Media

2015 ◽  
Vol 31 (4) ◽  
pp. 467-480 ◽  
Author(s):  
A. Asghari ◽  
S. A. Gandjalikhan Nassab ◽  
A. B. Ansari
Keyword(s):  
Mixed Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Convection Heat Transfer ◽  
Simple Algorithm ◽  
Convection Flow ◽  
Algebraic Equations ◽  
Mixed Convection Flow ◽  
Participating Media

AbstractThe effect of radiation on turbulent mixed convection flow, generated by two plane wall jets with different temperatures inside a cavity was studied numerically. The medium is treated as a gray, absorbing, emitting and scattering. The two-dimensional Reynolds-average Navier-Stokes equations, coupled with the energy equation are solved by using the computational fluid dynamic (CFD) techniques, while the AKN low-Reynolds-number model is employed for computation of turbulence fluctuations. The Boussinesq approximation is used to calculate the buoyancy term, and the radiation part of the problem is solved by numerical solution of the radiative transfer equation (RTE) with the well known discrete ordinate method (DOM). The governing equations are discretized by the finite volume technique into algebraic equations and solved with the SIMPLE algorithm. The effects of radiation conduction parameter, scattering albedo, optical thickness and Richardson number on the thermal behavior of the system are carried out. Results show that the gas radiation has a significant effect on the temperature distribution inside the turbulent mixed convection flow.

Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall(s)

2007 ◽  
Author(s):  
E. Natarajan ◽  
Tanmay Basak ◽  
S. Roy
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Vertical Wall ◽  
Side Wall ◽  
Convection Flow ◽  
Left Wall ◽  
Wide Range ◽  
Stream Functions ◽  
Side Walls

The present numerical study deals with natural convection flow in a trapezoidal cavity when the bottom wall is uniformly heated and the vertical wall(s) are linearly heated and cooled whereas the top wall is well insulated. Nonlinear coupled partial differential equations governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Parametric study for the wide range of Rayleigh number (Ra), 103 ≤ Ra ≤ 105 and Prandtl number (Pr), 0.07 ≤ Pr ≤ 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For linearly heated side walls symmetry is observed while representing the flow patterns in terms of stream functions whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. Local Nusselt number becomes negative at the side wall for linearly heated side walls and at the left wall for linearly heated left wall and cooled right wall indicating the reversal of heat flow. The effect of Prandtl number in the variation of average Nusselt numbers is more significant for Prandtl numbers in the range 0.07 to 0.7 than 10 to 100.

Sign in / Sign up

Export Citation Format

Share Document