# PDE:Mathematical Modeling

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solution Let the temperature ${\displaystyle u\,}$ inside a solid sphere be a function only of radial distance ${\displaystyle r\,}$ from the center and time ${\displaystyle t\,}$. Show that the equation for heat diffusion is now $\displaystyle u_t = \ u(u_{rr}+2u_r/r)\,$ .