Optimal Convective Heat-Transport

Josef Dalík; Oto Přibyl

Displaying similar documents to “Optimal Convective Heat-Transport”

Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths

Joel M. Cohen, Mauro Pagliacci, Massimo A. Picardello (2008)

Bollettino dell'Unione Matematica Italiana

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We compute recursively the heat semigroup in a rooted homogeneous tree for the diffusion with radial (with respect to the root) but non-isotropic transition probabilities. This is the discrete analogue of the heat operator on the disc given by $\Delta+c\frac{\partial}{\partial r}$ for some constant $c$ that represents a drift towards (or away from) the origin.

Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

Todor Gramchev, Grzegorz Łysik (2008)

Banach Center Publications

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We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $\partial_{t} u - Δ u = u^{M}$ . The approach is based on suitable iterative fixed point methods in $L^{p}$ based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.

Model of pulverized coal combustion in a furnace

Robert Straka, Jindřich Makovička (2007)

Kybernetika

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We describe behavior of the air-coal mixture using the Navier–Stokes equations for gas and particle phases, accompanied by a turbulence model. The undergoing chemical reactions are described by the Arrhenian kinetics (reaction rate proportional to $\exp (- \frac{E}{R T}),$ where $T$ is temperature). We also consider the heat transfer via conduction and radiation. Moreover we use improved turbulence-chemistry interactions for reaction terms. The system of PDEs is discretized using the finite volume method (FVM)...

Heat kernel estimates for the Dirichlet fractional Laplacian

Zhen-Qing Chen, Panki Kim, Renming Song (2010)

Journal of the European Mathematical Society

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We consider the fractional Laplacian $- {(- Δ)}^{α / 2}$ on an open subset in $ℝ^{d}$ with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in $C^{1, 1}$ open sets. This heat kernel is also the transition density of a rotationally symmetric $α$ -stable process killed upon leaving a $C^{1, 1}$ open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček (2001)

Mathematica Bohemica

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Steady-state system of equations for incompressible, possibly non-Newtonean of the $p$ -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain $Ω \subset ℝ^{n}$ , $n = 2$ or 3, with heat sources allowed to have a natural $L^{1}$ -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if $p > 3 / 2$ (for $n = 2$ ) or if $p > 9 / 5$ (for $n = 3$ ).

Weighted norm estimates for the maximal operator of the Laguerre functions heat diffusion semigroup

R. Macías, C. Segovia, J. L. Torrea (2006)

Studia Mathematica

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We obtain weighted $L^{p}$ boundedness, with weights of the type $y^{δ}$ , δ > -1, for the maximal operator of the heat semigroup associated to the Laguerre functions, ${ℒ_{k}^{α}}_{k}$ , when the parameter α is greater than -1. It is proved that when -1 < α < 0, the maximal operator is of strong type (p,p) if p > 1 and 2(1+δ)/(2+α) < p < 2(1+δ)/(-α), and if α ≥ 0 it is of strong type for 1 < p ≤ ∞ and 2(1+δ)/(2+α) < p. The behavior at the end points of the intervals where there is strong...

Optimization of plunger cavity

Salač, Petr

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In the contribution we present a problem of shape optimization of the cooling cavity of a plunger that is used in the forming process in the glass in dustry. A rotationally symmetric system of the mould, the glass piece, the plunger and the plunger cavity is considered. The state problem is given as a stationary heat conduction process. The system includes a heat source representing the glass piece that is cooled from inside by water flowing through the plunger cavity and from outside...

Inequalities involving heat potentials and Green functions

Neil A. Watson (2015)

Mathematica Bohemica

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We take some well-known inequalities for Green functions relative to Laplace’s equation, and prove not only analogues of them relative to the heat equation, but generalizations of those analogues to the heat potentials of nonnegative measures on an arbitrary open set $E$ whose supports are compact polar subsets of $E$ . We then use the special case where the measure associated to the potential has point support, in the following situation. Given a nonnegative supertemperature on an open set...

The Cauchy problem for a strongly degenerate quasilinear equation

F. Andreu, Vicent Caselles, J. M. Mazón (2005)

Journal of the European Mathematical Society

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We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation $u_{t} = div 𝐚 (u, D u)$ , where $𝐚 (z, ξ) = \nabla_{ξ} f (z, ξ)$ , and $f$ is a convex function of $ξ$ with linear growth as $∥ ξ ∥ \to \infty$ , satisfying other additional assumptions. In particular, this class includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.

Long time existence of solutions to 2d Navier-Stokes equations with heat convection

Jolanta Socała, Wojciech M. Zajączkowski (2009)

Applicationes Mathematicae

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Global existence of regular solutions to the Navier-Stokes equations for (v,p) coupled with the heat convection equation for θ is proved in the two-dimensional case in a bounded domain. We assume the slip boundary conditions for velocity and the Neumann condition for temperature. First an appropriate estimate is shown and next the existence is proved by the Leray-Schauder fixed point theorem. We prove the existence of solutions such that $v, θ \in W_{s}^{2, 1} (Ω^{T})$ , $\nabla p \in L_{s} (Ω^{T})$ , s>2.