Radiation dominates at high temperatures. Even with a 200 K difference, over 3 kW is transferred. Problem 4: Overall Heat Transfer Coefficient (Conduction + Convection) Scenario: A steam pipe (inner radius ( r_1 = 0.05 , \text{m} ), outer radius ( r_2 = 0.06 , \text{m} )) has ( k = 15 , \text{W/m·K} ). Inside: steam at ( T_{hot} = 200^\circ\text{C} ) with ( h_i = 100 , \text{W/m}^2\text{K} ). Outside: room air at ( T_{cold} = 25^\circ\text{C} ) with ( h_o = 10 , \text{W/m}^2\text{K} ). Find the heat loss per unit length ( Q/L ).
[ Q = 5.67 \times 10^{-8} \cdot 5.44 \times 10^{10} = 5.67 \times 544 = 3084 , \text{W} ] heat transfer example problems
[ R_{conv,i} = \frac{1}{100 \cdot 2\pi \cdot 0.05} = \frac{1}{31.416} = 0.03183 , \text{m·K/W} ] Radiation dominates at high temperatures
Using conduction through Layer A: [ q = k_A \frac{T_1 - T_2}{L_A} \quad \Rightarrow \quad 1260 = 1.2 \cdot \frac{1100 - T_2}{0.2} ] [ 1260 = 6 \cdot (1100 - T_2) \quad \Rightarrow \quad 210 = 1100 - T_2 ] [ T_2 = 890^\circ\text{C} ] Inside: steam at ( T_{hot} = 200^\circ\text{C} )
[ R_{total} = 0.03183 + 0.00193 + 0.2653 = 0.2991 , \text{m·K/W} ]
[ \frac{Q}{L} = \frac{200 - 25}{0.2991} = \frac{175}{0.2991} \approx 585 , \text{W/m} ]