engineering recuitment GATE ME 2023-24 Test Series Heat Transfer Conduction General Heat Conduction Equation
Heat conduction equation in spherical coordinate system will be when temperature varies in r direction only
1
\(\frac{{\partial^2T}}{{\partial r^2}}\;+\;\frac{{1}}{{2r}}\frac{{\partial T}}{{\partial r}}\;+\;\frac{{q_g}}{{k}}=\frac{{1}}{{2\alpha}}\frac{{\partial T}}{{\partial\tau }}\)
2
\(\frac{{\partial^2T}}{{\partial r^2}}\;+\;\frac{{1}}{{r}}\frac{{\partial T}}{{\partial r}}\;+\;\frac{{q_g}}{{k}}=\frac{{1}}{{\alpha}}\frac{{\partial T}}{{\partial\tau }}\)
3
\(\frac{{\partial^2T}}{{\partial r^2}}\;+\;\frac{{2}}{{r}}\frac{{\partial T}}{{\partial r}}\;+\;\frac{{q_g}}{{k}}=\frac{{1}}{{\alpha}}\frac{{\partial T}}{{\partial\tau }}\)
4
\(\frac{{\partial^2T}}{{\partial r^2}}\;+\;\frac{{2}}{{r}}\frac{{\partial T}}{{\partial r}}\;+\;\frac{{q}}{{2k}}=\frac{{1}}{{\alpha}}\frac{{\partial T}}{{\partial\tau }}\)