scholarly journals Regularization models for natural convection of a pseudoplastic liquid in a closed differentially heated cavity

2021 ◽  
pp. 13-22
Author(s):  
D. S. Loenko ◽  
◽  
M. A. Sheremet ◽  
Keyword(s):  
Natural Convection ◽  
Effective Viscosity ◽  
Additional Term ◽  
Mathematical Physics ◽  
Algebraic Model ◽  
Pseudoplastic Fluid ◽  
The Finite Difference Method ◽  
Papanastasiou Model ◽  
Pseudoplastic Liquid ◽  
Pseudoplastic Fluids

Simulation of convective heat and mass transfer in systems filled with pseudoplastic fluids deals with computational difficulties due to the appearance of an infinite level of effective viscosity as the intensity of deformation rates tends to zero. To solve this problem, various regularization models are used by introducing a small additional term into the expression for the effective viscosity. The present research is devoted to analysis of widespread regularization models for studying the natural convection of a pseudoplastic fluid in a closed differentially heated cavity. The pseudoplastic nature of the fluid flow was described by the Ostwald-de Waele power law. Three regularization models were investigated, namely, the simplest algebraic model, the Bercovier and Engleman model, and the Papanastasiou model. The boundary value problem of mathematical physics formulated using the conservation laws of mass, momentum and energy, was solved by the finite difference method. The obtained results were compared with data of other authors.

Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
B. M. Shankar ◽  
Jai Kumar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Prandtl Number ◽  
Traveling Wave ◽  
Effective Viscosity ◽  
Darcy Number ◽  
Wave Mode ◽  
Dielectric Fluid ◽  
Fluid Viscosity ◽  
The Stability

The stability of natural convection in a dielectric fluid-saturated vertical porous layer in the presence of a uniform horizontal AC electric field is investigated. The flow in the porous medium is governed by Brinkman–Wooding-extended-Darcy equation with fluid viscosity different from effective viscosity. The resulting generalized eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Grashof number Gc, the critical wave number ac, and the critical wave speed cc are computed for a wide range of Prandtl number Pr, Darcy number Da, the ratio of effective viscosity to the fluid viscosity Λ, and AC electric Rayleigh number Rea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to be independent of Rea. The interconnectedness of the Darcy number and the Prandtl number on the nature of modes of instability is clearly delineated and found that increasing in Da and Rea is to destabilize the system. The ratio of viscosities Λ shows stabilizing effect on the system at the stationary mode, but to the contrary, it exhibits a dual behavior once the instability is via traveling-wave mode. Besides, the value of Pr at which transition occurs from stationary to traveling-wave mode instability increases with decreasing Λ. The behavior of secondary flows is discussed in detail for values of physical parameters at which transition from stationary to traveling-wave mode takes place.

scholarly journals Contaminant spreading by natural convection in a box

2016 ◽  
Vol 38 (2) ◽  
pp. 141-152
Author(s):  
Tran Van Tran ◽  
Nguyen Ngoc Thang ◽  
Nguyen Thi Thuy
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Convective Motion ◽  
Simultaneous Action ◽  
Contaminant Concentration ◽  
Spreading Process ◽  
Contaminant Source ◽  
The Finite Difference Method ◽  
Ventilation Scheme ◽  
Contaminant Spreading

In this paper the spreading of a contaminant accompanied  with natural convection in a box is numerically simulated. The box may be  considered as a cooking room or a working place where some sources of heat  and contaminant are in the simultaneous action. The box floor is supposed to  be divided into several domains with different boundary conditions for  temperature or heat flux. Here the purpose of the simulation is to  understand the contaminant spreading process in the box under the influence  of a convective motion. The model can be also applied for an enclosure with  separated parts differentially heated by the sunlight on its boundaries. A  good knowledge of this process is very useful for setting an efficient  ventilation scheme. In this paper the finite difference method based on the  Samarski scheme with ADI technique is applied for numerical simulation. Here  the box floor is divided into two domains of equal sizes but with different  temperature or heat flux. The contaminant source locates in the middle of  the box bottom. The simulation shows that over the part of the floor where  temperature or heat flux is greater the contaminant concentration is lager.  That result is in the accordance with the experiment done in the framework  of this~investigation.

CFD Study of the Mixing of Pseudoplastic Fluids with Yield Stress in a Two-Staged Stirred Tank

2011 ◽  
Vol 354-355 ◽  
pp. 604-608
Author(s):  
Fan Jin Hu ◽  
Shen Jie Zhou ◽  
Feng Ling Yang ◽  
Lei Shi
Keyword(s):  
Yield Stress ◽  
Xanthan Gum ◽  
High Viscosity ◽  
Impeller Speed ◽  
3D Flow ◽  
Pseudoplastic Fluid ◽  
Power Number ◽  
Mixing Performance ◽  
Multi Stage ◽  
Pseudoplastic Fluids

The 3D flow field generated by two-stage impellers in the agitation of xanthan gum, a pseudoplastic fluid with yield stress, was simulated using the commerical CFD package. The effect of impeller speed and impeller spacing on power number, cavern size and viscosity distribution was investigated in this work. The results showed that the power number was slightly influenced by impeller spacing. Higher impeller speed and larger impeller spacing contributed to creation of a bigger cavern. The range of high viscosity zone between the impellers increased with an increase in impeller spacing. Impeller speed and impeller spacing could be used as important parameters to improve the mixing performance of multi-stage impellers in the mixing of pseudoplastic fluids with yield stress.

scholarly journals Transient Heat Transfer Between Two Horizontal Pipelines in a Heat Tracing Enclosure

Energies ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1440
Author(s):  
C.J. Ho ◽  
G.N. Sou ◽  
Chi-Ming Lai
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Heat Transfer Coefficient ◽  
Average Heat ◽  
Current Test ◽  
Test Conditions ◽  
The Finite Difference Method

In this study, a numerical simulation of natural convection between two horizontal differentially heated pipelines inside a circular air-filled enclosure is performed using the finite difference method. The relevant parameters of the problem are the inclinations of the two cylinders (positioned vertically in this study, with the cold cylinder above the hot cylinder), the distance between cylinders and the Rayleigh number. The results show that transient irregular fluctuations in the flow field and heat transfer occur when the Rayleigh number increases or the distance between cylinders decreases. Under the current test conditions, increasing the Rayleigh number significantly increases the average heat transfer coefficient between the cold and hot cylinders.

Long-wave evolution model of thermocapillary convection in an evaporating thin film of pseudoplastic fluids

2019 ◽  
Vol 29 (12) ◽  
pp. 4764-4787 ◽  
Author(s):  
Elaine Lim ◽  
Yew Mun Hung
Keyword(s):  
Liquid Film ◽  
Thermocapillary Convection ◽  
Thin Liquid Film ◽  
Thermocapillary Flow ◽  
Evolution Model ◽  
Pseudoplastic Fluid ◽  
Content Type ◽  
Wave Evolution ◽  
Long Wave ◽  
Pseudoplastic Fluids

Purpose By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid. Design/methodology/approach The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots. Findings The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter. Originality/value This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.

Study of Melting of a Pure Gallium in a Rectangular Enclosure

2016 ◽  
Vol 683 ◽  
pp. 548-554
Author(s):  
Nadezhda S. Bondareva ◽  
Mikhail A. Sheremet
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Natural Convection ◽  
Liquid Phase ◽  
Finite Difference Method ◽  
Grid Size ◽  
Phase Front ◽  
Left Wall ◽  
Dimensionless Variables ◽  
The Finite Difference Method

Phase change problems with natural convection in the liquid phase are of prime importance in accurate technological applications. In this work a melting of pure gallium in a rectangular cavity heated from the left wall is simulated using the finite difference method. Numerical algorithm based on dimensionless variables stream function and vorticity has been checked by experimental data of previously published papers. The effect of the grid size on results of calculations was identified. Motion of phase front and changing parameters of heat and mass-transfer were studied

Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

scholarly journals Thermal Behavior of the Natural Convection of Air Confined in a Trapezoidal Cavity

2021 ◽  
pp. 69-80
Author(s):  
Windé Nongué Daniel Koumbem ◽  
Issaka Ouédraogo ◽  
Noufou Bagaya ◽  
Pelega Florent Kieno
Keyword(s):  
Natural Convection ◽  
Heat Flow ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Thermal Behavior ◽  
Systems Of Equations ◽  
Constant Heat ◽  
The Finite Difference Method ◽  
Mass Transfers

The thermal behavior of air by natural convection in a confined trapezoidal cavity, one of the walls of which is subjected to a constant heat flow in hot climates, has been analyzed numerically. The heat and mass transfers are carried out by the classical equations of natural convection. These equations are discretized using the Finite Difference Method and the algebraic systems of equations thus obtained are solved with the Thomas and Gauss algorithms. We analyze the influence of the number on the current and isothermal lines as well as the effects of the aspect ratio A = l / H and the angle of inclination φ. In particular, we have shown that convective exchanges in the cavity are preponderant for high Ra numbers. Also we have watches the increase in the values ​​of the isothermal lines and the decrease in the intensity of the streamlines for the low values ​​of A and of the angle φ.

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