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A NEW ORIGINAL UNCODITIONALY STABLE MIXED FINITE ELEMENT
APPROACH IN TRANSIENT HEAT ANALYSIS WITHOUT DIMENSIONAL
REDUCTIONDubravka Mijuca, Bojan MedjoFaculty of Mathematics,
Department of MechanicsUniversity of [email protected]
Seminar for Rheology, 15 Mart, 2005
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ReferenceThe Finite Element Method - Volume 1: The Basis; O.C.
Zienkiewicz, R.L. TaylorFinite Element Procedures; K. J. BatheOn
hexahedral finite element HC8/27 in elasticity, Mijuca D.Mijuca D,
iberna A, Medjo B (2005) A new multifield finite element method in
steady state heat analysis, Thermal Science, in pressCannarozzi AA,
Ubertini F (2001) A mixed variational method for linear coupled
thermoelastic analysis. International Journal of Solids and
Structures. 38: 717-739 LUSAS Theory Manual 1, Version 13STRAUS 7
Verification ManualANSYS Verification Manual
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1st Law of ThermodynamicsInitial condition:Boundary
conditions:
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Heat Transfer ModesConductionConvectionRadiation
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ConductionFourriers Law (1822.)k - Thermal Conductivity
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Thermal Conductivities
Wood 0.05Water 0.7Glass 0.8Steel10-20Iron 80Copper 400Silver
450k [W/mK] (Room Temperature)
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ConvectionConvection involves the exchange of Heat between a
Fluid and a SurfaceNatural Convection Forced Convection1701 Newtons
Cooling Law T,T0 Temperatures of the surface and the FluidhC
Convective (Film) Coefficient
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Convective Coefficient depends on:Temperature
Difference;Fluid;Fluid Speed;Geometry of the Surface;Roughness of
the Surface.
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RadiationConsequence of the Stefan-Boltzmanns Law:T -
Temperature at the Surface of the BodyT0 - Temperature of the
Environment or the other BodyF1-2 - Shape Factors -
Stefan-Boltzmann Constante - Emissivity of the Surface of the
Body
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Galerkin Approximation Of The Energy Balance Equation
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Galerkin Approximation Of The Energy Balance Equation
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Galerkin Approximation of the Fourriers Law:
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Symmetric Weak Mixed Formulation
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Finite Element Approximation Function Spaces that Enables
Continuity
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Finite difference time discretization
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Finite element matrix equations
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Numerical Examples
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A Ceramic Strip Model Problem
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EA Ceramic Strip Model Problem
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A Ceramic Strip Model Problemanimacija_straus_vth2.htm
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A Ceramic Strip Model Problem
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A Ceramic Strip Model Problem
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Transient Temperature Distribution in an Orthotropic Metal
Bar
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1234Transient Temperature Distribution in an Orthotropic Metal
Bar
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animacija_ansys_vm113.htmTransient Temperature Distribution in
an Orthotropic Metal Bar
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Transient Temperature Distribution in an Orthotropic Metal
Bar
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Steel Ball Numerical Example
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Steel Ball Numerical Example
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Steel Ball Numerical Example
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Steel Ball Numerical Example
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Steel Ball Numerical Example
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A Cylindrical Concrete Vessel for Storing the Core of a Nuclear
ReactorThe walls of the cylinder have tubular cooling vents, which
carry a cooling fluid.Heat flow rate through the walls over a
period of 5 hours.
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Nuclear Reactor Straus7 Non averaged Results, t=62000s
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Nuclear Reactor Straus7 Results
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Nuclear Reactor Present Results
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ConclusionA new robust and reliable finite element procedure for
calculations of heat transient problem of a solid bodies is
presentedApproach is fully 3d thus enabling possible bridging with
nano and micro analysis of regions of interest in the solid body
Reliable semi-coupling with mechanical analysis is enabled also,
which is matter of future report
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ADENDUM Time Integration Schemes
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Explicit and implicit schemesExplicit scheme: Fully implicit
scheme:Crank-Nicholson scheme:Galerkin scheme:
