scholarly journals Temporal Evolution of Cooling by Natural Convection in an Enclosed Magma Chamber

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 108
Author(s):  
Carlos Enrique Zambra ◽  
Luciano Gonzalez-Olivares ◽  
Johan González ◽  
Benjamin Clausen
Keyword(s):  
Natural Convection ◽  
Magma Chamber ◽  
Temporal Evolution ◽  
Basaltic Magma ◽  
Boussinesq Equations ◽  
Rhyolitic Magma ◽  
The Times ◽  
Volume Method ◽  
The Mathematical Model ◽  
Liquid Magma

This research numerically studies the transient cooling of partially liquid magma by natural convection in an enclosed magma chamber. The mathematical model is based on the conservation laws for momentum, energy and mass for a non-Newtonian and incompressible fluid that may be modeled by the power law and the Oberbeck–Boussinesq equations (for basaltic magma) and solved with the finite volume method (FVM). The results of the programmed algorithm are compared with those in the literature for a non-Newtonian fluid with high apparent viscosity (10–200 Pa s) and Prandtl (Pr = 4 × 104) and Rayleigh (Ra = 1 × 106) numbers yielding a low relative error of 0.11. The times for cooling the center of the chamber from 1498 to 1448 K are 40 ky (kilo years), 37 and 28 ky for rectangular, hybrid and quasi-elliptical shapes, respectively. Results show that for the cases studied, natural convection moved the magma but had no influence on the isotherms; therefore the main mechanism of cooling is conduction. When a basaltic magma intrudes a chamber with rhyolitic magma in our model, natural convection is not sufficient to effectively mix the two magmas to produce an intermediate SiO2 composition.

Effect of Inner Wall Rotation on Multicellular Natural Convection Flow in a Vertical Annulus

2003 ◽  
Author(s):  
A. Sergent ◽  
P. Le Que´re´ ◽  
S. P. Vanka
Keyword(s):  
Reynolds Number ◽  
Natural Convection ◽  
Boussinesq Equations ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Time Stepping ◽  
Concentric Cylinders ◽  
Vertical Annulus ◽  
Volume Method ◽  
Weak Influence

Numerical simulations have been performed to study the effects of the inner wall rotation on the unsteady multicellular flow of natural convection in the conductive regime (Ra = 8000). We consider a tall air-filled vertical annulus between differentially heated concentric cylinders with the inner cylinder allowed to rotate. The unsteady Boussinesq equations are discretized using a finite volume method with a second order time stepping scheme. The natural convection flow is axisymmetric in this regime, whereas it is known that the mixed convection flow becomes 3D over a range of Reynolds number. We observe the transition in a range of Reynolds number close to the critical Reynolds number of the Taylor-Couette flow. The rotation has a weak influence on the axisymmetric time-periodic natural convection flow before the transition, whereas the flow becomes 3D and chaotic after.

Entropy generation optimization for MHD natural convection of a nanofluid in porous media-filled enclosure with active parts and viscous dissipation

2017 ◽  
Vol 27 (2) ◽  
pp. 379-399 ◽  
Author(s):  
M.A. Mansour ◽  
Sameh Elsayed Ahmed ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Convection Flow ◽  
Negative Effects ◽  
Content Type ◽  
Volume Method

Purpose This paper aims to investigate the entropy generation due to magnetohydrodynamic natural convection flow and heat transfer in a porous enclosure filled with Cu-water nanofluid in the presence of viscous dissipation effect. The left and right walls of the cavity are thermally insulated. There are heated and cold parts, and these are placed on the bottom and top wall, respectively, whereas the remaining parts are thermally insulated. Design/methodology/approach The finite volume method is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published woks is presented and is found to be in an excellent agreement. Findings The minimization of entropy generation and local heat transfer according to different values of the governing parameters are presented in details. It is found that the presence of magnetic field has negative effects on the local entropy generation because of heat transfer and the local total entropy generation. Also, the increase in the heated part length leads to a decrease in the local Nusselt number. Originality/value This problem is original, as it has not been considered previously.

Natural Convection in a Porous, Horizontal Cylindrical Annulus

1994 ◽  
Vol 116 (3) ◽  
pp. 621-626 ◽  
Author(s):  
J. P. Barbosa Mota ◽  
E. Saatdjian
Keyword(s):  
Natural Convection ◽  
Initial Conditions ◽  
Hysteresis Loops ◽  
Boussinesq Equations ◽  
Radius Ratio ◽  
Fine Grid ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Fluid Layers ◽  
Horizontal Cylinders

Natural convection in a porous medium bounded by two horizontal cylinders is studied by solving the two-dimensional Boussinesq equations numerically. An accurate second-order finite difference scheme using an alternating direction method and successive underrelaxation is applied to a very fine grid. For a radius ratio above 1.7 and for Rayleigh numbers above a critical value, a closed hysteresis loop (indicating two possible solutions depending on initial conditions) is observed. For a radius ratio below 1.7 and as the Rayleigh number is increased, the number of cells in the annulus increases without bifurcation, and no hysteresis behavior is observed. Multicellular regimes and hysteresis loops have also been reported for fluid layers of same geometry but several differences between these two cases exist.

Effect of Periodic Imposed Heat Flux on Three-Dimensional Natural Convection in a Partially Heated Cubical Enclosure

2016 ◽  
Vol 831 ◽  
pp. 83-91
Author(s):  
Lahoucine Belarche ◽  
Btissam Abourida
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Control Volume ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Maximum Temperature ◽  
Cubical Enclosure ◽  
Simplec Algorithm ◽  
Volume Method

The three-dimensional numerical study of natural convection in a cubical enclosure, discretely heated, was carried out in this study. Two heating square sections, similar to the integrated electronic components, are placed on the vertical wall of the enclosure. The imposed heating fluxes vary sinusoidally with time, in phase and in opposition of phase. The temperature of the opposite vertical wall is maintained at a cold uniform temperature and the other walls are adiabatic. The governing equations are solved using Control volume method by SIMPLEC algorithm. The sections dimension ε = D / H and the Rayleigh number Ra were fixed respectively at 0,35 and 106. The average heat transfer and the maximum temperature on the active portions will be examined for a given set of the governing parameters, namely the amplitude of the variable temperatures a and their period τp. The obtained results show significant changes in terms of heat transfer, by proper choice of the heating mode and the governing parameters.

scholarly journals Numerical Simulation of Wave Propagation, Breaking, and Setup on Steep Fringing Reefs

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1147 ◽  
Author(s):  
Shanju Zhang ◽  
Liangsheng Zhu ◽  
Jianhua Li
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Boussinesq Equations ◽  
Transformation Process ◽  
Wave Transformation ◽  
Computational Accuracy ◽  
Irregular Wave ◽  
Eddy Viscosity Model ◽  
Fringing Reefs ◽  
Volume Method

The prediction of wave transformation and associated hydrodynamics is essential in the design and construction of reef top structures on fringing reefs. To simulate the transformation process with better accuracy and time efficiency, a shock-capturing numerical model based on the extended Boussinesq equations suitable for rapidly varying topography with respect to wave transformation, breaking and runup, is established. A hybrid finite volume–finite difference scheme is used to discretize conservation form of the extended Boussinesq equations. The finite-volume method with a HLL Riemann solver is applied to the flux terms, while finite-difference discretization is applied to the remaining terms. The fourth-order MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) scheme is employed to create interface variables, with in which the van-Leer limiter is adopted to improve computational accuracy on complex topography. Taking advantage of van-Leer limiter, a nested model is used to take account of both computational run time and accuracy. A modified eddy viscosity model is applied to better accommodate wave breaking on steep reef slopes. The established model is validated with laboratory measurements of regular and irregular wave transformation and breaking on steep fringing reefs. Results show the model can provide satisfactory predictions of wave height, mean water level and the generation of higher harmonics.

Numerical Study of Natural Convection in Vertical Cylindrical Annular Enclosure Filled with Cu-Water Nanofluid under Magnetic Fields

2019 ◽  
Vol 392 ◽  
pp. 123-137 ◽  
Author(s):  
Mohamed A. Medebber ◽  
Abderrahmane Aissa ◽  
Mohamed El Amine Slimani ◽  
Noureddine Retiel
Keyword(s):  
Natural Convection ◽  
Magnetic Fields ◽  
Volume Fraction ◽  
Numerical Study ◽  
Physical Parameters ◽  
Cold Temperatures ◽  
Simpler Algorithm ◽  
Wide Range ◽  
Nanoparticles Volume Fraction ◽  
Volume Method

The two dimensional study of natural convection in vertical cylindrical annular enclosure filled with Cu-water nanofluid under magnetic fields is numerically analyzed. The vertical walls are maintained at different uniform hot and cold temperatures, THand TC, respectively. The top and bottom walls of the enclosure are thermally insulated. The governing equations are solved numerically by using a finite volume method. The coupling between the continuity and momentum equations is effected using the SIMPLER algorithm. Numerical analysis has been carried out for a wide range of Rayleigh number (103≤Ra≤106), Hartmann number (1 ≤Ha≤100) and nanoparticles volume fraction (0 ≤φ≤0.08). The influence of theses physical parameters on the streamlines, isotherms and average Nusselt has been numerically investigated.

scholarly journals Natural Convection of Dusty Hybrid Nanofluids in an Enclosure Including Two Oriented Heated Fins

2019 ◽  
Vol 9 (13) ◽  
pp. 2673 ◽  
Author(s):  
Raizah
Keyword(s):  
Natural Convection ◽  
Volume Fraction ◽  
Simple Algorithm ◽  
Systems Of Equations ◽  
Nusselt Numbers ◽  
Pressure Distributions ◽  
Nanoparticles Volume Fraction ◽  
Hybrid Nanofluids ◽  
Volume Method ◽  
Present Simulation

In the current work, the natural convection of dusty hybrid nanofluids in an enclosure including two inclined heated fins has been studied via mathematical simulation. The inclined heated fins are arranged near to the enclosure center with variations on their orientations and lengths. The present simulation is represented by two systems of equations for the hybrid nanofluids that are dusty. The pressure distributions for the dusty phase and hybrid nanofluids phase are evaluated using a SIMPLE algorithm based on the finite volume method. The numerical results are examined using contours of the streamlines, isotherms for the hybrid nanofluids and velocity components for the dusty phase. In addition, the graphical illustrations for profiles of the local and average Nusselt numbers are presented. The main results reveal that an increase in the mixture densities ratio and dusty parameter reduces the rate of the heat transfer. Both the local and average Nusselt numbers are supported as the fins lengths increase regardless of the fins’ rotation. In addition, the nanoparticles volume fraction enhances the thermal boundary layer near the top wall.

Numerical Survey of the Melting Driven Natural Convection Using Generation Heat Source: Application to the Passive Cooling of Electronics Using Nano-Enhanced Phase Change Material

2019 ◽  
Vol 12 (2) ◽  
Author(s):  
Hamza Faraji ◽  
Mustapha Faraji ◽  
Mustapha El Alami
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Source ◽  
Phase Change ◽  
Phase Change Material ◽  
Metallic Nanoparticles ◽  
Simple Algorithm ◽  
Bottom Side ◽  
Volume Method ◽  
Change Material

Abstract The present paper reports numerical results of the melting driven natural convection in an inclined rectangular enclosure filled with nano-enhanced phase change material (NePCM). The enclosure is heated from the bottom side by a flush-mounted heat source (microprocessor) that generates heat at a constant and uniform volumetric rate and mounted on a substrate (motherboard). All the walls are considered adiabatic. The purpose of the investigation is analyzing the effect of nanoparticles insertion by quantifying their contribution to the overall heat transfer. Combined effects of the PCM type, the inclination angle and the nanoparticles fraction on the structure of the fluid flow and heat transfer are investigated. A 2D mathematical model based on the conservation equations of mass, momentum, and energy was developed. The governing equations were integrated and discretized using the finite volume method. The SIMPLE algorithm was adopted for velocity–pressure coupling. The obtained results show that the nanoparticles insertion has an important quantitative effect on the overall heat transfer. The insertion of metallic nanoparticles with different concentrations affects the thermal behavior of the heat sink. They contribute to an efficient cooling of the heat source. The effect of nanoparticles insertion is also shown at the temperature distribution along the substrate.

Effect of the Soil Inclination on Natural Convection in Half-Elliptical Greenhouses

2020 ◽  
Vol 50 ◽  
pp. 70-78
Author(s):  
Djedid Taloub ◽  
Abdelkarim Bouras ◽  
Zied Driss
Keyword(s):  
Natural Convection ◽  
Cfd Simulation ◽  
Numerical Study ◽  
Boussinesq Approximation ◽  
Elliptic Cavity ◽  
Horizontal Cavity ◽  
Inclined Cavity ◽  
Volume Method ◽  
Heat Transfers ◽  
Work Done

A numerical study of the natural convection of laminar heat transfers in the stationary state in a half-elliptic inclined cavity, which represents a continuation of the work done, we studied the influence of the tilt of the cavity by varying the angle — entered 0 degrees, which corresponds to the horizontal cavity, up to 15 degrees. For each value of δ we varied the Rayleigh number from 2.13 103 to 106. The system of equations governing the problem solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. Both bottom and upper walls maintained at a constant temperature. The interest of this study is to see the influence of the tilt of the half-elliptic cavity on the structure of the flow and the distribution of temperature. These results can exploited in semi-elliptic agricultural greenhouses that rest on sloping soils. We chose a Prandtl number 0.71 that corresponds to the air. Keywords: Heat transfer; half-elliptical; Natural convection; Laminar flow; Multicellular; CFD simulation

Sign in / Sign up

Export Citation Format

Share Document