Abstract
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.
Highlights
To understand the processes that occur in magma chambers it is necessary to use multidisciplinary knowledge from geology, fluid dynamics and engineering [1]
Transient natural convection cooling (RaT = 1 × 106 ) of a highly non-Newtonian fluid with a high Prandtl number (4 × 104 ) inside a square cavity surrounded by a solid was studied numerically
Temperatures decrease from the center to the edges of the chamber except at the bottom edge
Summary
To understand the processes that occur in magma chambers it is necessary to use multidisciplinary knowledge from geology, fluid dynamics and engineering [1]. Rheology governs processes such as the rise of magma, the mixing of various batches, the settling of crystals and the transport of xenoliths [2]. Basaltic magma is usually treated as a quasi-Newtonian fluid, but several laboratory experiments have shown that, even for low viscosity, quasi-Newtonian behavior cannot be applied [4]. A. Fluid Dynamics: Finite Volume]Method, 2nd ed.; Limited, P.E., \ding{66} K \ding{75} T The \ding{84} \ding{93} f \ding{102}.
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