# Derivation of heat transfer equation for spherical coordinates

 P: 39 1. The problem statement, all variables and given/known data where λ= thermal conductivity $\dot{q}$= dissipation rate per volume 2. Relevant equations qx=-kA$\frac{dT}{dx}$ 3. The attempt at a solution I don't know where to start from to be honest, so any help would be greatly appreciated Attached Thumbnails
 P: 39 OK so this is what I got: -λ4r2$\frac{dT}{dr}$ + $\dot{q}$4∏r2dr = ρc4∏r2$\frac{dT}{dτ}$dr -4∏r2(λ$\frac{dT}{dr}$ + $\frac{d}{dr}$(λ$\frac{dT}{dr}$)dr) Is this correct? Since the flow is steady the time derivative $\frac{dT}{dτ}$=0 But then when I rearrange everything I get: r2$\frac{d}{dr}$(λ$\frac{dT}{dr}$) + $\dot{q}$r2 = 0 can I just take the r2 inside the differential bracket? EDIT: missed out a dr in the rearranged equation: r2$\frac{d}{dr}$(λ$\frac{dT}{dr}$)dr + $\dot{q}$r2 = 0