To find the temperature of the right-hand side surface of the wall ( T 2 T 2 ), we use the principle of energy conservation under steady-state conditions.
1. Identify the Heat Transfer Mechanism
Under steady state with no internal heat generation, the heat flux entering the right side of the wall via convection from the hot air must equal the heat flux conducted through the wall to the left side.
- Convection Heat Flux: $q'' = h (T_\infty - T_2)$
- Conduction Heat Flux: $q'' = \frac{k}{L} (T_2 - T_1)$
2. Set Up the Energy Balance Equation
Equating the two expressions for heat flux:
$h (T_\infty - T_2) = \frac{k}{L} (T_2 - T_1)$
Where:
- $T_\infty$ (Hot air temperature) = $50 \text{ }^\circ C$
- $T_1$ (Left surface temperature) = $25 \text{ }^\circ C$
- $k$ (Thermal conductivity) = $100 \text{ W/m}\cdot\text{K}$
- $L$ (Wall thickness) = $0.2 \text{ m}$
- $h$ (Convective coefficient) = $50 \text{ W/m}^2\text{K}$
3. Calculate the Surface Temperature ($T_2$)
Substitute the values into the equation:
$50 (50 - T_2) = \frac{100}{0.2} (T_2 - 25)$
$50 (50 - T_2) = 500 (T_2 - 25)$
Divide both sides by 50:
$(50 - T_2) = 10 (T_2 - 25)$
$50 - T_2 = 10T_2 - 250$
Rearrange to solve for $T_2$:
$50 + 250 = 10T_2 + T_2$
$300 = 11T_2$
$T_2 = \frac{300}{11} \approx 27.2727 \text{ }^\circ C$
Final Answer:
Rounding to one decimal place, the temperature of the right-hand side surface is 27.3 $^\circ C$.
Important Questions from Conduction
In M - L - t - T system, the dimension of thermal diffusivity is -
The transfer of heat through the molecules of matter in any body is called ________.
Unit of thermal diffusivity is
When heat is transferred from one particle of hot body to another by actual motion of the heated particles, it is referred to as heat transfer by:
Which of the following is a case of steady state heat transfer?
