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The one-dimensional unsteady state heat conduction equation in a hollow cylinder with a constant heat source q is

$$ \frac{\partial T}{\partial t}=\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial T}{\partial r})+q$$

If A and B are arbitrary constants, then the steady solution to the above equation is

  1. T(r) = -$\frac{{qr^2}}{2}$ + $\frac{A}{r}$ + B
  2. T(r) = -$\frac{{qr^2}}{4}$ + AInr + B
  3. T(r) = AInr + B
  4. T(r) = $\frac{{qr^2}}{4}$ + AInr + B
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