Question

A glass plate at 40°C is heated by passing hot air over it with a convection coefficient of 18 W/m²K. If the temperature change over 1mm thickness is not to exceed 5°C to avoid distortion damage, determine the maximum allowable temperature of the air. Thermal conductivity of the plate material is 1.4 W/mK.

A. 120°C
B. 150°C
C. 180°C
D. 200°C

Answer 1

The maximum allowable temperature of the air is 200°C.

Step-by-step explanation:

To determine the maximum allowable temperature of the air, we need to use the formula for conduction heat transfer:

Q = (k * A * ΔT) / d

Where Q is the heat transfer, k is the thermal conductivity, A is the surface area, ΔT is the temperature difference, and d is the thickness of the material.

In this case, the temperature change over the thickness of the glass plate should not exceed 5°C. We can rearrange the formula to solve for ΔT:

ΔT = (Q * d) / (k * A)

Substituting the given values, we have:

5°C = (18 W/m²K * 0.001m) / (1.4 W/mK * A)

Simplifying the equation, we find:

A = (18 W/m²K * 0.001m) / (1.4 W/mK * 5°C)

Calculating, we get:

A ≈ 0.00257 m²

Therefore, the maximum allowable temperature of the air is:

ΔT = 0.00257 m² * (18 W/m²K / 1.4 W/mK) = 0.0333 K = 33.3°C

So, the correct answer is D. 200°C.