(Solved): using the matlab For cylindrical coordinate system, the transient heat conduction equation can be wr ...

For cylindrical coordinate system, the transient heat conduction equation can be written as, \( \frac{\partial^{2} T}{\partial r^{2}}+\frac{1}{r} \frac{\partial T}{\partial r}=\alpha \frac{\partial T}{\partial t} \) Develop an explicit numerical scheme using finite difference method for this PDE. Initial condition: \( \mathrm{T}(0, \mathrm{r})=\mathrm{T}_{0} \), Boundary conditions: \( \frac{\partial T(0, t)}{\partial r}=0 \mathrm{~T}(\mathrm{t}, 0), \mathrm{T}(\mathrm{R}, \mathrm{t})=\mathrm{T}_{\mathrm{s}} \). \( R \) is the radius of a given rod, \( T_{0} \) and \( T_{s} \) are given constant temperatures.