Question #280827

A solid cylinder, 0 ≤ r ≤ b, is initially at zero temperature. For times t > 0, internal energy is generated in the solid at a rate of g(t) per unit volume (W/m3), whereas the boundary surface at r = b dissipates heat by convection into a medium at zero temperature. Obtain an expression for the temperature distribution T(r,t) in the cylinder for times t > 0.



1
Expert's answer
2021-12-20T13:58:02-0500

At t>0t>0 r=0,T(r,t)=g(t)vr=0,T(r,t)=\frac{g(t)}{v}

At t>0t>0 r=b,T(r,t)=g(t)r=b,T(r,t)=-g(t)


 T(r,t)=g(t,)vg(t)\therefore\ T(r,t)=\frac{g(t,)}{v}-g(t)



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