Question
Download Solution PDF\(\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} = 0\) किस समीकरण के लिए है? [जहाँ T = तापमान]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
सामान्यीकृत 3D चालन समीकरण फूरियर समीकरण द्वारा दिया गया है जो है:
\(\frac{{{\partial ^2}T}}{{\partial {x^2}}} + \frac{{{\partial ^2}T}}{{\partial {y^2}}} + \frac{{{\partial ^2}T}}{{\partial {z^2}}} + \frac{{\dot q}}{k} = \frac{1}{\alpha }\left( {\frac{{\partial T}}{{\partial \tau }}} \right)\)
बिना ऊष्मा उत्पादन के 3D, स्थिर, अवस्था ऊष्मा समीकरण और स्थिर ऊष्मीय चालकता के साथ
\(\frac{{{\partial ^2}T}}{{\partial {x^2}}} + \frac{{{\partial ^2}T}}{{\partial {y^2}}} + \frac{{{\partial ^2}T}}{{\partial {z^2}}} = 0\)
\({\nabla ^2}T = 0\) ⇒ लाप्लास समीकरण
याद रखने योग्य बातें
\({\nabla ^2}T + \frac{q}{k} = 0 \Rightarrow\) पॉइसन समीकरण
\({{\rm{\Delta }}^2}T = \frac{1}{\alpha }\frac{{\partial T}}{{\partial t}}\) ⇒ फूरियर समीकरण
Last updated on Jul 15, 2025
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