dorsal/arxiv
View SchemaViscous heating in fluids with temperature-dependent viscosity: implications for magma flows
| Authors | A. Costa, G. Macedonio |
|---|---|
| Categories | |
| ArXiv ID | physics/0302100 |
| URL | https://arxiv.org/abs/physics/0302100 |
| DOI | 10.5194/npg-10-545-2003 |
| Journal | Nonlinear Process in Geophysics 2003, 10 (6): 545-555 |
Abstract
Viscous heating plays an important role in the dynamics of fluids with strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local temperature increase near the tube walls with a consequent decrease of the viscosity which may dramatically change the temperature and velocity profiles. These processes are mainly controlled by the Pecl\'et number, the Nahme number, the flow rate and the thermal boundary conditions. The problem of viscous heating in fluids was investigated in the past for its practical interest in the polymer industry, and was invoked to explain some rheological behaviours of silicate melts, but was not completely applied to study magma flows. In this paper we focus on the thermal and mechanical effects caused by viscous heating in tubes of finite lengths. We find that in magma flows at high Nahme number and typical flow rates, viscous heating is responsible for the evolution from Poiseuille flow, with a uniform temperature distribution at the inlet, to a plug flow with a hotter layer near the walls. When the temperature gradients induced by viscous heating are very pronounced, local instabilities may occur and the triggering of secondary flows is possible. For completeness, this paper also describes magma flow in infinitely long tubes both at steady state and in transient phase.
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"abstract": "Viscous heating plays an important role in the dynamics of fluids with\nstrongly temperature-dependent viscosity because of the coupling between the\nenergy and momentum equations. The heat generated by viscous friction produces\na local temperature increase near the tube walls with a consequent decrease of\nthe viscosity which may dramatically change the temperature and velocity\nprofiles. These processes are mainly controlled by the Pecl\\\u0027et number, the\nNahme number, the flow rate and the thermal boundary conditions. The problem of\nviscous heating in fluids was investigated in the past for its practical\ninterest in the polymer industry, and was invoked to explain some rheological\nbehaviours of silicate melts, but was not completely applied to study magma\nflows. In this paper we focus on the thermal and mechanical effects caused by\nviscous heating in tubes of finite lengths. We find that in magma flows at high\nNahme number and typical flow rates, viscous heating is responsible for the\nevolution from Poiseuille flow, with a uniform temperature distribution at the\ninlet, to a plug flow with a hotter layer near the walls. When the temperature\ngradients induced by viscous heating are very pronounced, local instabilities\nmay occur and the triggering of secondary flows is possible. For completeness,\nthis paper also describes magma flow in infinitely long tubes both at steady\nstate and in transient phase.",
"arxiv_id": "physics/0302100",
"authors": [
"A. Costa",
"G. Macedonio"
],
"categories": [
"physics.geo-ph",
"physics.flu-dyn"
],
"doi": "10.5194/npg-10-545-2003",
"journal_ref": "Nonlinear Process in Geophysics 2003, 10 (6): 545-555",
"title": "Viscous heating in fluids with temperature-dependent viscosity: implications for magma flows",
"url": "https://arxiv.org/abs/physics/0302100"
},
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