Question

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: \(3.87 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\)

Short answer

Question: Convert the convection heat transfer coefficient, 22 W/m²·K, from SI units to English units. Answer: The convection heat transfer coefficient in English units is 3.87 Btu/h·ft²·°F.

Step-by-step solution

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.

Convert power

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

Convert length

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

Convert temperature

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

Write the answer

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

Key concepts

Unit Conversion

Unit conversion is a fundamental skill, particularly in fields like engineering and science. It allows you to translate measurements from one set of units to another, making it possible to communicate and apply data universally. Converting between units usually involves multiplication or division by a conversion factor. These conversion factors can be derived from standard equivalencies, like how 1 meter equals 3.28084 feet or 1 W is equivalent to 0.000947819 Btu/h.

When you encounter a problem requiring unit conversion, it’s important to ensure that you use the correct factors, as using the wrong ones can lead to inaccurate results. A systematic approach is necessary: identify the starting unit, apply the appropriate conversion factor, and ensure the units cancel out properly to leave you with the desired end unit.

In the context of this exercise, unit conversion is crucial for determining the convection heat transfer coefficient in the units of Btu/h·ft²·°F from the given SI units.

Conduction and Convection

Conduction and convection are two primary modes of heat transfer, essential to understand in thermal sciences. Conduction is the process by which heat is transferred through a material without the movement of the material itself. It primarily occurs in solids, where the heat is passed from molecule to molecule via direct contact.

Convection, on the other hand, involves the transfer of heat through a fluid (liquid or gas) in motion. It involves both the diffusion of heat due to temperature gradients and the bulk movement of the fluid. In the context of buildings, understanding convection is crucial because it affects how heat is transferred to or from the exterior surfaces.

Analyzing a house's heat loss or gain often involves assessing both conduction through the walls and convection at the surfaces. Together, these modes of heat transfer can significantly impact heating and cooling requirements.

Heat Transfer Coefficient

The heat transfer coefficient is a measure of how effectively heat is transferred by convection. It is used in calculating heat transfer rates and designing systems that regulate temperature, such as heating or cooling a building. This coefficient represents the amount of heat transferred per unit area per unit temperature difference between the surface and the fluid around it.

The unit of the heat transfer coefficient in the SI system is W/m²·K, whereas in the Imperial system, it is Btu/h·ft²·°F. The coefficient depends on several factors, such as the type of fluid, velocity, temperature, and surface characteristics. It can be determined experimentally or calculated from empirical correlations.

In the exercise, converting from SI units to English units was necessary due to differences in how the heat transfer processes might be assessed in different regions, owing to standard practices and preferred measurement systems.

Temperature Units Conversion

Temperature units conversion often involves moving between metric units (Celsius or Kelvin) and imperial units (Fahrenheit). A straightforward linear conversion equation exists between these units because they differ in scale and offset. For instance, converting from Kelvin to Fahrenheit involves scaling by a factor of 1.8 (since there are 1.8 Fahrenheit degrees for every Kelvin) and adjusting the offset from a Celsius zero point.

In this particular exercise, the conversion focused on changing temperature units in the context of heat transfer coefficients. Since the coefficient is provided per degree unit, being precise about temperature conversion is crucial to obtaining an accurate final value in the desired unit system.

Understanding temperature units conversion is essential not only for this exercise but also when dealing with thermal problems in science and engineering, where precise temperature measurements are critical to predicting system behaviors accurately.