Chapter 3, Problem 3.147P

A homeowner's wood stove is equipped with a top burner for cooking. The $D=200\text{-mm}$ -diameter burner is fabricated of east iron $\left(k=65\text{W/m}\cdot \text{K}\right).$ The bottom (combustion) side of the burner has 8 straight fins of uniform cross section, arranged as shown in the sketch. A very thin ceramic coating $\left(\epsilon =0.95\right)$ is applied to all surfaces of the burner. The top of the burner is exposed to room conditions $\left(T_{\text{sur,t}}=T_{\infty ,t}=20°\text{C,}{h}_t=40{\text{W/m}}^{\text{2}}\cdot \text{K}\right),$ while the bottom of the burner is exposed to combustion conditions $\left(T_{\text{sur}}{}_{,b}=T_{\infty ,b}=450°\text{C},h_b=50{\text{W/m}}^{\text{2}}\cdot \text{K}\right).$ Compare the top surface temperature of the finned burner to that which would exist for a burner without fins. Hint: Use the same expression for radiation heat transfer to the bottom of the tinned burner as for the burner with no fins.