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Channel flow with temperature-dependent viscosity and internal viscous dissipation
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In this paper, the authors used asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation.Abstract:
This paper uses asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation. When the Nahme–Griffith number is large we show how the flow evolves from Poiseuille flow with a uniform temperature distribution to a plug flow with hot boundary layers on the walls. An asymptotic solution is obtained for the flow in the region of transition from Poiseuille to plug flow and an explicit equation is derived for the pressure gradient in terms of the local downstream co-ordinate in this transition region.read more
Citations
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Viscous heating in fluids with temperature-dependent viscosity: implications for magma flows
Antonio Costa,Giovanni Macedonio +1 more
TL;DR: In this paper, the authors studied the thermal and mechanical effects caused by viscous heating in infinitely long tubes of finite lengths and found that viscous heat 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.
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Modelling ice sheet dynamics
TL;DR: In this article, a simplified model for two-dimensional plane ice sheets is derived, and both isothermal and non-isothermal cases are co-occurrence cases are considered.
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The form of blow-up for nonlinear parabolic equations
TL;DR: On considere des equations paraboliques semi lineaires de la forme u t =⊇ 2 u+Sf(u), ou f est positive and ∫ 0 ∞ ds/f(s) est finie as discussed by the authors.
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On the computation of blow-up
TL;DR: In this article, a class of time-stepping strategies that correspond to a time-continuous re-scaling of the underlying differential equation is proposed; this class is analyzed and criteria established to determine suitable choices for the rescaling.
References
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Journal ArticleDOI
On the nonlinear equations $\Delta u + e^u = 0$ and $\partial v/\partial t = \Delta v + e^v$
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Variable-viscosity flows in channels with high heat generation
TL;DR: In this paper, the authors present a similarity solution for plane channel flow of a very viscous fluid, whose viscosity is exponentially dependent upon temperature, when heat generation is very large.
Journal ArticleDOI
Variable-viscosity flows in heated and cooled channels
Hilary Ockendon,J. R. Ockendon +1 more
TL;DR: In this article, an asymptotic description of Newtonian fluid flow in a channel which is suddenly heated or cooled is given, where the viscosity is assumed to be purely a function of temperature.