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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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