Required information Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of R value, which has the unit of ft2-hr-F/Btu. A certain manufacturer offers a double-pane window with R=2.5 and also a triple-pane window with R=3.4. Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F. Assume that a homeowner buys 20 such triple-pane windows for the house. A typical winter equals about 120 heating days at AT= 45°F. Each triple-pane window costs $85 more than a double-pane window. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings? 9.5 years

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
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### Heat Loss Through Windows: An Example Problem

**Required Information**

Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of \( R \) value, which has the unit of \( \text{ft}^2 \cdot \text{hr} \cdot ^\circ\text{F} / \text{Btu} \). A certain manufacturer offers a double-pane window with \( R = 2.5 \) and also a triple-pane window with \( R = 3.4 \). Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F.

**Scenario**

Assume that a homeowner buys 20 such triple-pane windows for their house. A typical winter equals about 120 heating days at \( \Delta T = 45^\circ \text{F} \). Each triple-pane window costs $85 more than a double-pane window. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings?

**Solution**

To solve this problem, the first step is to calculate the heat loss through both types of windows and determine the savings from the more efficient triple-pane option. Given that the need is to cover the additional costs through savings, the number of years required to recover these costs will be computed.

**Result**

The calculated time to cover the additional cost of installing the triple-pane windows is shown to be:
- **9.5 years**

**Navigation**
- **Previous:** Problem 4
- **Next:** Problem 6 

(Note: The solution to the problem necessitates mathematical computations which are to be done separately for educational purposes.)
Transcribed Image Text:### Heat Loss Through Windows: An Example Problem **Required Information** Sometimes equations can be developed and practical problems solved by knowing nothing more than the dimensions of the key parameters. For example, consider the heat loss through a window in a building. Window efficiency is rated in terms of \( R \) value, which has the unit of \( \text{ft}^2 \cdot \text{hr} \cdot ^\circ\text{F} / \text{Btu} \). A certain manufacturer offers a double-pane window with \( R = 2.5 \) and also a triple-pane window with \( R = 3.4 \). Both windows are 3.5 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside is 45°F. **Scenario** Assume that a homeowner buys 20 such triple-pane windows for their house. A typical winter equals about 120 heating days at \( \Delta T = 45^\circ \text{F} \). Each triple-pane window costs $85 more than a double-pane window. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings? **Solution** To solve this problem, the first step is to calculate the heat loss through both types of windows and determine the savings from the more efficient triple-pane option. Given that the need is to cover the additional costs through savings, the number of years required to recover these costs will be computed. **Result** The calculated time to cover the additional cost of installing the triple-pane windows is shown to be: - **9.5 years** **Navigation** - **Previous:** Problem 4 - **Next:** Problem 6 (Note: The solution to the problem necessitates mathematical computations which are to be done separately for educational purposes.)
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