Environmental Physics Chapter 5: Home Energy Conservation and Heat- Transfer Control Copyright © 2008 by DBS

Environmental Physics

Chapter 5:Home Energy Conservation and Heat-

Transfer Control

Copyright © 2008 by DBS

Introduction

Figure 4.1: U.S. household energy consumption by end use. 1 Quad = 1015 Btu.

Residential sector uses 50% for space heating

~20% of all the energy in US is used for heating and cooling buildings

Energy (conservation) efficiency should be first step in dealing with environmental impacts…

Introduction

• Amount of our total energy that is used for heating and cooling of buildings is massive (20%)

• Heat is transferred from hot objects to cold objects by conduction, convection and radiation

• Important to learn how to control the exchange of heat with our surroundings

– New home designs

– Retrofitting

Building Materials

• Conductors and insulators

• Good conductors of electricity are usually good conductors of heat energy

e.g. copper in electrical wires and water pipes

• Poor conductors of electricity are usually poor conductors of heat energy

e.g. Styrofoam, fiberglass (or any other material containing trapped air)

• Insulating materials are said to have a high ‘resistance’ to heat transfer

Aerogel is composed of 99.8% air and is chemically similar to ordinary glass. Being the world's lightest known solid, it weighs only three times that of air.

Building Materials

• Amount of heat radiated by an object depends on its temperature (SB law)

• Color of material also influences heat transfer via radiation

– Black objects are excellent emitters as well as excellent absorbers

– White objects reflect and does not absorb/emit as much

• Kirchoff’s law: Objects that are good emitters of radiation are also good absorbers

• Starting at the same temperature, a hot black object will radiate energy faster than a similar hot light-colored object

Demo

Question

How is heat lost from a cup of coffee?

I have just poured myself a cup of coffee but not yet added the milk, when there is a knock at the door and I have to go and see someone. I’ll be gone a few minutes – should I add the cream before I go or after I get back in order to have the coffee at the maximum temperature when I drink it?

Building Materials

• Before you go!

– Cream makes the coffee lighter in color = poorer radiator

– Temperature will drop when cream is added so the rate of heat transfer by conduction and radiation will decrease as a result of the smaller ΔT

Figure 5.1: For coffee to be the hottest when you are ready to drink it at a later time, you should add the cream initially, not just before drinking, as these data for the two cases illustrate.

Building Materials

• Thermos – reduces heat transfer

• A bottle within a bottle separated by a vacuum

• Vacuum prevents conduction and convection

• Radiation is controlled by silvered surfaces

Figure 5.2: Thermos bottle (cutaway view).

House Insulation and Heating Calculations

• Insulation of houses is one of the easiest and most cost-effective means of reducing energy consumption


• Rate of heat flow via conduction is given by:

Where Q = heat (J) transferred in time t (s), k = thermal conductivity (W m-1 K-1), A = surface area, δ = thickness, T1 and T2 are temperatures on each side


• “R-value” is a measure of the resistance of a material to heat flow, it is a function of the type of material and its thickness:

R = δ / k

• High R-value equals better insulating properties

• Substituting this equation into the conductivity equation:

Qc = 1 x A x ΔT

t R


R-values of some common materials

e.g. 1” expanded polystyrene is rated R-4

1” Brick is rated R-0.20

polystyrene is 20x as insulating

would need a 2 ft wide brick wall


Show why the units are ft2.h.°F/Btu

Qc = 1 x A x ΔT

t R


Figure 5.3: To obtain an R-value of 22 ft2-h-°F/Btu, you would have to use the indicated thicknesses of various materials.

Question

Calculate the total heat transfer for 12 hours through an insulated window that measures 4ft x 7 ft, when the outside temperature is 5 °F and the inside temperature is 65 °F

Calculate the total heat transfer for 3” of expanded polystyrene foam

R-value = 1.54 ft2.h.°F/Btu

A = 28 ft2

ΔT = 60 °F

Qc = 13,100 Btu

Qc(foam) = 1680 Btu


• Homes are made up of many different materials

• To find the total thermal resistance of a composite structure add the R-values

Rtotal = R1 + R2 + R3 + …

Figure 5.4: Example of the calculation of thermal resistance value for a composite wall.


• R-values change depending on wind speed

• Tabulated values calculated based on 10 mph

End

• Review


• Heat loss by convection on the inside of a window

– Increases if air is allowed to move

– Can be decreased using curtains/drapes that touch the floor

Figure 5.5: (a) Thermal drapes mounted in this arrangement will contribute to heat losses rather than stop them. (b) This arrangement is better for reducing convective losses.

Layer of still air next to window


• Heat loss through insulated glass windows

• Wider gaps in double glazed windows not much higher R-values

• Smaller gaps have greater heat loss via conduction, larger gaps allow more convection leading to higher convective heat loss

Variations: (i) evacuated or filled with inert gas (e.g. Ar) which has a lower thermal conductivity than air, (ii) low-e coating, thin metal coating reflects heat


• Windows: can be a large source of heat loss or gain

• ~35% of the energy requirements or a typical home are a result of heat loss through windows

• Double pane windows required in most parts

• Storm windows (inside or outside) cut down heat losses considerably (colder climates)

In most areas energy savings not significant enough to warrant installation


• Air infiltration: major source of heat losses

• Cold air from outside leaks into the house from cracks, doors, windows, basement

• Can be reduced by sealing the gaps

Figure 5.6: Cold air infiltration can account for 50% of the energy needs of a house. Wherever there is a way for the air to get in, it will. Winds can significantly increase infiltration rates.


Figure 5.7: Types of weather stripping. Caulking all cracks and weather stripping all windows will reduce air infiltration. Such work is easy to do and very cost-effective (with payback times of one heating season or less).


• Infiltration heat losses can be calculated using the “air-exchange” method

Qinfil = 0.018 x V x K x ΔT

t

• Where V = volume (ft3), ΔT = inside/outside temperature difference, 0.018 = volume heat capacity of air (Btu/ft3-°F), K = no. of air changes per hour

• K is measured using a ‘blower door’ and measuring the rate of decrease of a tracer gas usually 0.5 – 1.5 h-1


5 °C is the ‘design temp.’ or the lowest expected for the locality


• When calculating the heating load for a house efficiency must also be taken into account

e.g. natural gas furnace at 70 % efficiency, we would need:

36,000/0.70 = 51,000 Btu/h


• To calculate heat losses for an entire year you could sum A x ΔT/Rtotal for each day x 24 h/d

Easier to use “degree-day”

Degree Day (DD) = 65 °F – Tavg (-ve DD are taken as zero)

• Total no. of DD for a year is the sum of the individual DD

• Annual total heating needs for conductive loses:

Q total = Σ (A/R) x (24 h/day) x (no. annual DD)

Figure 5.8: Annual heating degree-days (DD).


• If the insulated house was located in Buffalo, NY, with 7000 DD per yr,


Q total = 1/14 Btu/ft2-h-°F x 4600 ft2 x 24 h/d x 7000 DD

= 55.3 x 106 Btu

• Add to infiltration losses:

Qinfil = 0.018 Btu/ft3- ° F x 15,000 ft3 x 1/h x 24 h/d x 7000 DD = 45.4 x 106 Btu

Total load = Q total + Qinfil = 101 x 106 Btu = 101 MBtu

• Assume cost elecricity Is 0.07 cents per kWh

$0.07/kWh x 1 kWh / 3413 Btu x 106 Btu/Mbtu = $20.51 / Mbtu

Cost = $20.51 /Mbtu x 101 Mbtu = $2071 (does not take into account efficiency

Site Selection

Figure 5.9: Planting trees on the leeward side of a hill can substantially reduce the wind velocity over the site. Vegetation or walls can block or deflect natural air flow patterns and so reduce convective heat loss.

• Wind increases convective heat loss Increase from 10 – 20 mph increases infiltration by 100-200 %

Impact of Energy Conservation Measures

Impact of Energy Conservation Measures

Figure 5.10: Summary of the effects of energy conservation measures on space heating requirements for a typical 1500-ft2 house in three climates.

Question

Problem 4

a.) 0.5 + 1.0 + 0.8 = 2.3

b.) 19 + 2.3 = 21.3,

21.3-2.3 / 21.3 = 89%

c.) Qtotal = (1/2.3) x 6500 x 1 ft2 x 24 h/d = 67,826 Btu / ft2.yr

0.067826 MBtu/ft2.yr x $10 / MBtu = $0.68 / ft2.yr

d.) Qnew total = (1 ft2)(24)(6500) / 21.3 = 7324 Btu savings of 67,826 – 7324 = 60,502 Btu / ft2.yr

Electricity cost = $10 / MBtu

savings of 0.060502 MBtu / ft2.yr x $10/MBtu = $0.60 / ft2.yr

Since fiberglass is 40 cents a ft2, payback is less than a season

End

• Review

Cooling

• Use same equations with cooling degree days (average of days high and low temp. minus 75 °F)

Cooling Degree-day (CDD) = Tavg - 75 °F

• Factors affecting cooling

– Outdoor temperature and intensity of solar radiation are important

– Heat gains from solar heating of walls, roofs and windows must be taken into account

– Heat gains from lights, appliances and people

– thermal storage causes a time delay in indoor temperatures

• Demand for air conditioning:

– 66 % of US households

– 83 % commercial space

– 6 % of household energy use

Cooling

Passive cooling (far less expensive)

• Site selection – location, orientation, vegetation

– Natural ventilation - evaporative cooling of human body (perspiration)

– Evaporative coolers (swamp coolers in SE USA)

– Desiccants

• Architectural features – surface-to-volume ratio, overhangs, window sizes, shades

– Shading can reduce indoor temps. 10-20 °F

– Coolth tubes

• Building skin features – insulation, thermal mass, glazing

– Opposing windows, skylights and high windows – act as thermal chimneys

Cooling

• Insulation using ‘radiant barrier’ materials

• Restrict passage of low wavelength IR radiation, e.g. aluminum foil backed fiberglass insulation

• May be painted on, chips or film

Figure 5.12: Radiant barriers can reduce heat gain in the attic of a house.

Air Conditioners and Heat Pumps

• Heat from cooler indoors is transferred to the warmer outdoors

• Not a violation of 2nd law! Why?


• Requires and energy source (electricity)

Figure 5.13: Air conditioner operation.

EVAPORATORworking fluid evaporates → gas

CONDENSERworking fluid temperature > outside air so condenses → liquid

COMPRESORRaises temp. and pressure of gas

Question

A room air conditioner has a capacity of 6000 Btu/h. Would this be sufficient to maintain the temperature of a small hut at 70 °F when the outside temperature is 95 °F? Assume the hut is 10 ft x 10 ft x 6 ft and the exterior surfaces are made of 1 in softwood

From the table of R-values - R = 1.25

Qc = 1 x A x ΔTt R

Qc = (4 x 60 ft2 + 2 x 100 ft2) x 25 °F = 8800 Btu/h1.25

Answer is NO! (no infiltration included)


• Heat pumps

A residential heat pump.

(1) Refrigerant liquid absorbs heat from outside air and evaporates

(2) Resulting gas is compressed(3) Hot gas transfers heat to

room and is condensed

(1) Cold refrigerant liquid absorbs heat from warmer room

(2) Resulting gas is compressed(3) Transfers heat to outside air


• Coefficient of Performance (COP):

COP = heat transferred / electricity input

e.g. a heat pump with COP = 30,000 Bu/h and a compressor rating of 3.2 kW has

COP = 30,000 Btu/h = 2.75

3.2 kW x (3413 Btu/h/kW)

• Heat pump is 2.75 x cheaper to operate than a electrical resistance system

• COP reduces as outside temperature decreases

• The lower the outdoor temperature, the less heat there is

e.g. if heat has to be extracted from 10 ° F air, working fluid must be below 10 °F, compressor must work harder

Fig. 5-16, p. 153

Figure 5.16: Relative costs of different types of heating fuels. To determine the cost of using a heat pump, find the unit cost of electricity on the x-axis and move vertically to the appropriate heat pump C.O.P. curve. Then move horizontally to the y-axis to find the operating cost per million Btu. Find the intersection of this value with the line for gas or oil, and read off its cost on the x-axis. For example (as shown with dashed lines), using a heat pump with C.O.P. = 2.0 at an electricity cost of $0.05/kWh is equivalent to using gas at $0.52/therm or fuel oil at $0.67/gallon (with the furnace efficiencies shown).

Summary

• Household energy conservation has a substantial impact on your energy bill

• Heat gains or losses can be reduced by using insulation and infiltration control

• Heating load may be calculated using the equation for the rate of heat transfer via conduction

Qc = 1 x A x ΔT

t R

•To find total heat losses for a season, Qtotal, we use the Degree-Day concept


• Infiltration losses must be added to this to find the total heating load for the house

Documents

Environmental Physics Chapter 5: Home Energy Conservation and Heat- Transfer Control Copyright © 2008 by DBS