Activity1.3b – Conduction and Convection

Purpose

The human race is poorly suited for exposure to the environment and physically weak when compared to other mammals, yet we dominate and alter the earth as no other species. This has happened because we discovered how to tap into the vast reservoirs of energy available. We have developed engines to harness that energy and apply it to our desires. In order to understand the concept of heat engines or those devices for converting heat to work, we must first start with an understanding of how heat is transferred from place to place. We will examine how heat moves by studying our homes and how to calculate the additional heating or cooling energy we need to supply.

With buildings, we refer to heat flow in a number of different ways. The most common reference is "R-value," or resistance to heat flow. The higher the R-value of a material, the better it is at resisting heat loss (or heat gain). U-factor (or "U-value," as it is often called) is a measure of the flow of heat--thermal transmittance--through a material, given a difference in temperature on either side. In the inch-pound (I-P) system, the U-factor is the number of BTUs (British Thermal Units) of energy passing through a square foot of the material in an hour for every degree Fahrenheit difference in temperature across the material (Btu/ft2hr°F). In metric, it's usually given in watts per square meter per degree Celsius (w/m2°C)

Equipment:

Tape measure

Calculator

Graph Paper (Optional)

Excel Spreadsheet (Optional)

Step-by-Step Procedure:

  1. Select a room with at least two walls and a ceiling on the exterior of your home.
  1. Create sketches for each of the external walls. The sketch should be to scale and include overall dimensions for the wall and openings (doors and windows) as well as their positions in the walls. The sketch should be attached to your report.
  1. Create a sketch of the floor plan of the room including overall dimensions.
  1. For the sake of this activity we will ignore inside walls and floor but will use the ceiling area as part of the calculations.
  1. From your dimensioned sketches calculate the following information. Show all your work.
  • Total Ceiling area
  • Area of windows
  • Area of external door
  • Total exterior wall area minus the area taken by the windows and doors
  1. Using the R Value Table calculate the total R value of your wall and Ceiling. If you can’t find out how it is constructed look for what is standard construction for your area. Do this by sketching the cross sectional view of your wall in the space below. Label the materials and fill in the chart below.

Material / R-Value
Air Film / .17
Air Film / .17
Total
  1. Repeat the process for your Ceiling.

Table 1

Material / R-Value
Air Film / .17
Air Film / .17
Total

NOTE: R-values, which are standard in the construction industry, stand for the thermal resistance of a material. A higher R-value means better insulation against heat transfer. This means that less heat energy passes through a barrier. The calculation of thermal energy through a barrier must result in higher heatflow with less insulation. Mathematically, the reciprocal of the R-value is U-value, sometimes called the thermal conductance.

This can be shown as: U =

The Conduction Heat Loss Equation:

  1. To figure out heat loss(or gain) through a barrier, such as the wall in your house you will use the formula ; where

is the heat loss in BTUs per hour

is the Reciprocal of the R-Value

is the area of the wall

is the difference in temperature on either side of the wall.

  1. Consider the various terms of the heat loss equation in Step 8. In Step 4 you were instructed to neglect inside walls. Explain whythis isa logical thing to do.
  1. Using an inside temperature of 75F and an outside temperature of -5F, calculate the heat loss or gain through:
  2. the exterior walls
  3. the ceiling
  4. the windows and doors (use R =2 for windows and doors)

Show your work!

Qwalls=

Qceiling=

Qwin+doors=

QTotal (add up all three) =

Think back to the last time someone complained about having a door left open. When this happens air from the outside is exchanged with the inside.

All buildings must have some portion of its air exchanged with outside air on a regular basis. Too small of an exchange rate, and the air inside becomes depleted of oxygen, laden with odor, and otherwise “stale.” Too much of an exchange rate, and the building’s heating or air conditioning system can not keep up with heating or cooling the outside air coming in. The engineer’s job is to properly size the heating/cooling system, insulation, and air exchange rate to create a comfortable yet energy efficient environment.

The Convection Heat Loss Equation:

The equation which describes the heat loss due to convection is:

where:

is the heat energy rate,

is the mass flow rate of the air entering ( and also leaving ) the building,

C is the heat capacity of the air, and

is the difference in temperature between the inside and outside.

The equation explained: Basically, for every cubic foot of heated air leaving a building through an opening, another cubic foot of unheated air must enter somewhere else. If this were not true, the air pressure in the building would be different from the outside, which obviously is not true unless you are in a pressurized building. This equation calculates the amount of energy needed to heat the quantity of incoming air from outside temperature to inside temperature per unit of time.

The volume flow rate of air is:= Area x velocity of the air mass

The mass flow rate of air is: = density x

From reference tables, the density of air is 0.079 lbm/ft3

For example:to find the heat energy rate wasted when a 7 foot by 3 foot door is left open for 10 minutes. A 10 Mile an hour wind is blowing in the 40oF outside air. The inside temperature is 65oF

The volume flow rate,

= Area x velocity = 3 ft x 7 ft x 880 ft/min = 18480 ft3/min

From reference tables, the density of air is 0.079 lb/ft3

= density x = 0.079 lb/ft3 x 18480 ft3/min = 1459.92 lb/min

From reference tables the heat capacity C for air is .015 BTU/(lb.oF)

So, =

And

  1. Now calculate the heat loss for a 10 ft2 door or window going to the exterior.Calculate what the heat loss will be if you leave it open for 10 minutes today.Use an average wind speed of 10.0 mph. Use 75F for inside temperature and -5F for outside temperature. Find the air density in the table.Use the problem on the previous page as an example. Show your work.

Conclusion

  1. Find the cost per BTU of natural gas energy for your home. Look on the PoE webpage, under Unit 1.3 Attachments. There is a document there from the Department of Energy called “E7-5141.pdf” The cost per 100,000 BTU’s is listed.
  1. If you left the window in Problem 11 open for 10 minutes today approximately how much would it have added to your energy bill, assuming a cost of $0.000015/BTU?
  1. Examine the heat loss equation in Step 8. Explain why setting the thermostat to a lower setting can dramatically decrease the cost of heating your home.
  1. Would adding insulation to your home as it is now be a wise investment?
  1. Are there drafts in your home?How do drafts affect energy usage?
  1. Explain how your home might lose energy through conduction, convection, and radiation.