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    Far-field boundary conditions in channeled lava flow with viscous dissipation

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    Cooling and dynamics of lava flowing in a rectangular channel driven by the gravity force is numerically modeled. The purpose is to evaluate the thermal process as a function of time involving the liquid lava in contact with the solid boundary that flanks lava. Lava rheology is dependent on temperature and strain rate according to a power law function. The model couples dynamics and thermodynamics inside the lava channel and describes the thermal evolution of the solid boundary enclosing the channel. Numerical tests indicate that the solution of the thermo-dynamical problem is independent of the mesh. The boundary condition at the ground and at the levees is treated assuming a solid boundary around the lava flow across which lava can exchange heat by conduction. A far field thermal boundary condition allows to overcome the assumption of constant temperature or constant heat flow as boundary conditions, providing more realistic results. The effect of viscous heating is evaluated and discussed

    Viscous dissipation in a flow with power-law, temperature dependent rheology: application to channeled lava flows

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    The cooling and the dynamics of a lava flowing down an inclined channel under the effect of the gravity force is studied through the finite volume method, taking into account the effect of viscous dissipation in the heat equation. The considered rheology is shear thinning and temperature dependent. The numerical solution is tested in order to verify the independence from the mesh. The dynamic and heat problems are addressed obtaining both the stationary and the transient solution. Results indicate that, considering viscous dissipation in the heat equation, a fluid with temperature-dependent nonlinear viscosity is faster and hotter with respect to the case in which viscous dissipation is neglected. The most important effect of viscous dissipation is on the solid boundaries where the fluid warms up, and the use of a variable Reynolds number allowed us to conclude that areas in which the flow is in the laminar regime and areas in which the flow is in the turbulent regime can coexist inside the fluid. This behavior seems independent of the channel shape and can explain the observed warming back after the initial cooling in the lava flow lobes emplacement on Kilauea Volcano

    Role of heat advection in a channeled lava flow with power law, temperature-dependent rheology

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    The cooling of a lava flow, both in the transient and the steady state, is investigated considering that lava rheology is pseudoplastic and dependent on temperature. Lava exits from the vent with constant velocity and flows down a slope under the effect of gravity force inside a channel of rectangular cross section. We consider that cooling of lava is caused by thermal radiation into the atmosphere and thermal conduction at the channel walls and at the ground. The heat equation is solved numerically in a 3D computational domain and the solution is tested to evaluate the numerical errors. We study the steady state and the initial transient period of lava cooling. Results indicate that the advective heat transport significantly modifies the cooling rate of lava slowing down the cooling process. Since the lava velocity depends on temperature, the cooling rate depends on the effusion temperature. Velocity profiles are modified during cooling showing two marginal static zones where the crust can form and remain stable. The fraction of crust coverage is calculated under the assumption that the solid lava is a plastic body with temperature dependent yield strength. We numerically confirm that heat advection can not be neglected in the mechanism of formation of lava tubes
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