Answer:
The fin temperature in °C at a distance of 10 cm from the base = 33.78°C
Explanation:
The following assumptions will be made to solve this problem
- The heat transfer coefficient does not change with the time or distance.
- The temperature of the fins varies just in only one direction.
The temperature of the fin at x = 10 cm = 0.10 m from the base can be calculated from the temperature variation with distance formula for a very long fin.
(T - T∞) = (T₀ - T∞)e⁻ᵐˣ
T = T(x) = temperature at any point along the fin
T∞ = temperature at the tip of the fin = ambient temperature = 25°C
T₀ = temperature at the base of thw fin = 50°C
x = any distance along the length of the fin from the base of the fin = 0.1 m
m = √(hP/KA)
h = Heat transfer coefficient = 123 W/m².K
P = perimeter in contact with the base = πD = π × 0.03 = 0.0943 m
K = thermal conductivity = 150 W/m.K
A = surface area in contact with the base = πD²/4 = π(0.03)²/4 = 0.0007071 m²
m = √(123 × 0.0943)/(150 × 0.0007071)
m = 10.46
mx = 10.46 × 0.1 = 1.046
(T - 25) = (50 - 25) e⁻¹•⁰⁴⁶
T = 25 + 25 e⁻¹•⁰⁴⁶ = 25 + 8.78 = 33.78°C
