An engineer who is working on the heat transfer analysis of a house in English units needs the convection heat transfer coefficient on the outer surface of the house. But the only value he can find from his handbooks is \(22 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), which is in SI units. The engineer does not have a direct conversion factor between the two unit systems for the convection heat transfer coefficient. Using the conversion factors between \(\mathrm{W}\) and \(\mathrm{Btu} / \mathrm{h}, \mathrm{m}\) and \(\mathrm{ft}\), and \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\), express the given convection heat transfer coefficient in Btu/ \(\mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\). Answer: \(3.87 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\)

Step by step solution

01

Identify conversion factors

We need the following conversion factors: 1. Power: 1 W = 0.000947819 Btu/h 2. Length: 1 m = 3.28084 ft 3. Temperature: 1 K = 1.8 °F Note that the temperature conversion factor for Kelvin (K) to Celsius (°C) is the same as for Fahrenheit (°F) and the factor is 1.8 °F/K. Now, let's convert the given convection heat transfer coefficient using these conversion factors.

02

Convert power

First, we will convert the power from W to Btu/h by multiplying the given coefficient by the conversion factor: \(22 \frac{\text{W}}{\text{m}^2 \cdot \text{K}} \times 0.000947819 \frac{\text{Btu}}{\text{h} \cdot \text{W}} = 0.020852 \frac{\text{Btu}}{\text{h} \cdot \text{m}^2 \cdot \text{K}}\)

03

Convert length

Next, we will convert the length from meters to feet using the conversion factor: \(0.020852 \frac{\text{Btu}}{\text{h} \cdot \text{m}^2 \cdot \text{K}} \times \left(\frac{3.28084 \text{ft}}{\text{m}}\right)^2 = 0.022418 \frac{\text{Btu}}{\text{h} \cdot \text{ft}^2 \cdot \text{K}}\)

04

Convert temperature

Finally, we will convert the temperature from Kelvin to Fahrenheit using the conversion factor: \(0.022418 \frac{\text{Btu}}{\text{h} \cdot \text{ft}^2 \cdot \text{K}} \times 1 \frac{1.8^\circ \text{F}}{1\text{K}} = 3.87 \frac{\text{Btu}}{\text{h} \cdot \text{ft}^2 \cdot {}^\circ\text{F}}\)

05

Write the answer

Our final result for the convection heat transfer coefficient in English units is: \(3.87 \frac{\text{Btu}}{\text{h} \cdot \text{ft}^2 \cdot {}^\circ\text{F}}\)

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