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[{ALLOW view All}] |
[{ALLOW edit,upload Trusted}] |
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[{MathInline fontsize='14' |
[{LTMath fontsize='14' |
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[{MathInline fontsize='14' latex='q_x=-\\lambda\\frac{\\partial T}{\\partial x}' }], |
[{MathInline fontsize='14' latex='q_y=-\\lambda\\frac{\\partial T}{\\partial y}' }], |
[{MathInline fontsize='14' latex='q_z=-\\lambda\\frac{\\partial T}{\\partial z}' }] |
[{LTMath fontsize='14' latex='q_x=-\\lambda\\frac{\\partial T}{\\partial x}' }], |
[{LTMath fontsize='14' latex='q_y=-\\lambda\\frac{\\partial T}{\\partial y}' }], |
[{LTMath fontsize='14' latex='q_z=-\\lambda\\frac{\\partial T}{\\partial z}' }] |
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!!Okrajové podmínky |
!Ustálené vedení tepla |
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* okrajová podmínka I. druhu - Dirichletova |
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Je zadána teplota povrchu tělesa T%%sub s%% jako funkce času. |
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[{Math fontsize='12' latex='T(t,\\forall x\\in\\Gamma)=T_s(t)' }] |
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* okrajová podmínka II. druhu - Neumannova |
!Neustálené vedení tepla |
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Je zadána hustota tepelného toku [{Math fontsize='12' latex='\\vec{q}'}] na povrchu tělesa jako funkce času. |
[{LTMath |
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[{Math fontsize='12' |
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\vec{q}(t,\forall x\in\Gamma)=\vec{q}_S(t)=-\lambda . \left. \frac{\partial T}{\partial x} \right|_{x\in\Gamma} |
\frac{\partial T}{\partial t} = \frac{\lambda}{c_p\rho}\left(\frac{\partial^2 T}{\partial x^2} |
+\frac{\partial^2 T}{\partial y^2}+\frac{\partial^2 T}{\partial z^2}\right) |
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* okrajová podmínka III. druhu - Fourierova |
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Tepelný tok vedením na povrchu tělesa je roven tepelnému toku konvekcí, neboli |
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[{Math fontsize='12' |
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\left. \lambda . \frac{\partial T}{\partial x} \right|_{x=0}=\alpha (T_a-T_s) |
}] |
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Doplnte |
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