FE Mechanical Heat Transfer Practice Problems

The current FE Mechanical specification assigns 7-11 of the 110 exam questions to Heat Transfer. Form A contains 8 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A composite panel consists of a 12 mm thick stainless steel plate ( $k = 15$ W/(m·K)) bonded to an 8 mm thick aluminum plate ( $k = 180$ W/(m·K)). The bond has a thermal contact resistance of $2.5 \times 1 0^{- 4} m^{2} \cdot K/W$ . Under steady one-dimensional conduction the exposed steel face is held at 210 °C and the exposed aluminum face at 90 °C. The heat flux through the panel is most nearly:

(A)76 kW/m²
(B)110 kW/m²
(C)142 kW/m²
(D)150 kW/m²

Show worked solution

Answer: (B)

The bonded joint contributes nearly one quarter of the series resistance, holding the flux to about 110 kW/m².

Series resistances per unit area govern the panel, and the bonded joint enters the chain exactly as a solid layer does.

R_{t o t}^{''} = \frac{L _{1}}{k _{1}} + R_{t, c}^{''} + \frac{L _{2}}{k _{2}}

R_{t o t}^{''} = \frac{0.012}{15} + 2.5 \times 1 0^{- 4} + \frac{0.008}{180} = 1.094 \times 1 0^{- 3} m^{2} \cdot K/W

One-dimensional steady flow drives the entire 120 K face-to-face difference through that single chain.

q^{''} = \frac{Δ T}{R _{t o t}^{''}} = \frac{120}{1.094 \times 1 0 ^{- 3}} = 1.10 \times 1 0^{5} W/m^{2}

The joint absorbs 27 K of the drop against only 4.9 K for the aluminum, so discarding contact resistance would overstate the flux by about 30 percent.

Δ T_{c} = q^{''} R_{t, c}^{''} = 1.096 \times 1 0^{5} (2.5 \times 1 0^{- 4}) = 27.4 K

FE Reference Handbook — Heat Transfer: Conduction Through a Plane Wall and Thermal Resistances in Series

Why the other choices appear

(A)Uses the steel conductivity for the aluminum layer as well, raising the total to 1.583e-3 m²·K/W and giving 75.8 kW/m².
(C)Omits the contact resistance, leaving 8.44e-4 m²·K/W and 142 kW/m².
(D)Counts only the steel layer, 120 divided by 8.0e-4, giving 150 kW/m².