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Article

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

1
Department of Mechanical Engineering, Faculty of Engineering, University of Talca, Curicó 3460000, Chile
2
Geoscience Research Institute, University of Montemorelos, Montemorelos 67510, Mexico
3
Department of Earth and Biological Sciences, Geoscience Research Institute, Loma Linda University, Loma Linda, CA 92350, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Chenn Q. Zhou and Tyamo Okosun
Processes 2022, 10(1), 108; https://doi.org/10.3390/pr10010108
Received: 6 December 2021 / Revised: 23 December 2021 / Accepted: 29 December 2021 / Published: 5 January 2022
(This article belongs to the Special Issue Multiphase Reacting Flows: Modeling and Simulation)
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. View Full-Text
Keywords: magma chamber processes; numerical approximations and analysis; mechanics; modeling; fluid mechanics; heat flow; multiphase flows magma chamber processes; numerical approximations and analysis; mechanics; modeling; fluid mechanics; heat flow; multiphase flows
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  • Externally hosted supplementary file 1
    Link: https://bclausen.net/Zambra/Program_Validation.txt
    Description: The source codes are available for downloading at the link: Code used to obtain validation results in Section 3.1 can be obtained from (https://bclausen.net/Zambra/Program_Validation.txt. Last access 03/01/2022). Code used to obtain results for case 3 (Section 3.2) can be obtained from (https://bclausen.net/Zambra/Program_Chamber_case3.txt. Last access 03/01/2022).
MDPI and ACS Style

Zambra, C.E.; Gonzalez-Olivares, L.; González, J.; Clausen, B. Temporal Evolution of Cooling by Natural Convection in an Enclosed Magma Chamber. Processes 2022, 10, 108. https://doi.org/10.3390/pr10010108

AMA Style

Zambra CE, Gonzalez-Olivares L, González J, Clausen B. Temporal Evolution of Cooling by Natural Convection in an Enclosed Magma Chamber. Processes. 2022; 10(1):108. https://doi.org/10.3390/pr10010108

Chicago/Turabian Style

Zambra, Carlos E., Luciano Gonzalez-Olivares, Johan González, and Benjamin Clausen. 2022. "Temporal Evolution of Cooling by Natural Convection in an Enclosed Magma Chamber" Processes 10, no. 1: 108. https://doi.org/10.3390/pr10010108

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