The insulating layer (lower ( k )) dominates the total resistance, even though it’s thinner. Problem 2: Convection – Determining the Heat Transfer Coefficient Scenario: Air at ( T_\infty = 20^\circ\text{C} ) flows over a flat plate maintained at ( T_s = 80^\circ\text{C} ). The plate area is ( 0.5 , \text{m}^2 ). The measured heat transfer rate from the plate to the air is ( 600 , \text{W} ). Find the average convection coefficient ( h ).
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} ] heat transfer example problems
First, compute the thermal resistances per unit area: [ R_A = \frac{0.2}{1.2} = 0.1667 , \text{m²·K/W} ] [ R_B = \frac{0.1}{0.15} = 0.6667 , \text{m²·K/W} ] [ R_{total} = 0.1667 + 0.6667 = 0.8334 , \text{m²·K/W} ] The insulating layer (lower ( k )) dominates
Try modifying the numbers: add a contact resistance, change the emissivity, or switch to a different fluid. That’s where the real learning happens. The measured heat transfer rate from the plate
For a cylindrical system: [ \frac{Q}{L} = \frac{T_{hot} - T_{cold}}{\frac{1}{h_i (2\pi r_1)} + \frac{\ln(r_2/r_1)}{2\pi k} + \frac{1}{h_o (2\pi r_2)}} ]