A metal sphere is subjected to a heat flux, 5000 W/m2. It is originally at 20 C. How long does it take to heat to 90 C?
D = 5 cm
density = 8522 kg/m3
cp = 0.385 kJ/kg-K
k = 104 W/m-k
rate of heat input = rate of heat accumulation
-k*A*dT/dr = m*cp*dT/dt
The Attempt at a Solution
I've never done one of these where I'm given a heat flux. If this said that the sphere was exposed to a constant external temperature, I would have no problem solving it, because I have those solutions to the differential equations in the book. I'm stuck on trying to solve that differential equation above though. I know that rate of heat input also equals the 5000 W/m2 that the problem statement gives. But if I say that 5000 = m*cp*dT/dt, integrate and solve that for time, it gives me an unreasonably short answer.