MECE4450U - Final Report (Final)

FACULTY OF ENGINEERING AND APPLIED SCIENCE

MECE4450U

Energy and Economic Analysis of Ceiling Fans

for an Office Building in Turkey

GROUP PROJECT REPORT

Course Instructor: Dr. Marc Rosen

Teaching Assistant: Satyam Panchal

Project Report Submitted On: April 4, 2016

# Last Name First Name ID Signature

1 Bower Lowell 100500898

2 Karanwal Tushar 100481186

3 Owais Syed 100506689

Remarks:

If one in group cheats, the entire group will be responsible for it. Plagiarism and dishonesty will not be tolerated. The group member(s), who don’t sign the report, will be considered “not contributed” and given “zero” for

the report. This cover sheet should be fully completed.

MECE4450U - Energy and Economic Analysis of Ceiling Fans for an Office Building in Turkey

1

Table of Contents List of Figures ................................................................................................................................. 2

1.0 Introduction ............................................................................................................................... 3

1.1 Problem Statement ................................................................................................................ 3

1.2 Project Objectives ................................................................................................................. 3

2.0 Case Study ................................................................................................................................ 4

3.0 Proposed System ....................................................................................................................... 5

4.0 System Analysis ........................................................................................................................ 6

4.1 Sensible Cooling ................................................................................................................... 6

4.2 Latent Cooling ...................................................................................................................... 7

4.3 Building Energy Calculations ............................................................................................... 7

4.4 Economic Analysis ............................................................................................................... 8

5.0 Conclusion ................................................................................................................................ 9

6.0 Nomenclature .......................................................................................................................... 10

7.0 Appendix ................................................................................................................................. 11

7.1 Project Assumptions ........................................................................................................... 11

7.2 Sample Calculations............................................................................................................ 12

7.3 EES Code ............................................................................................................................ 16

References ..................................................................................................................................... 17


2

List of Figures

Figure 1: Initial total hourly cooling load for building ................................................................... 4

Figure 2: Proposed fan positions..................................................................................................... 5

Figure 3: Emerson CF705 fan [10] ................................................................................................. 5

Figure 4: Cylinder in cross flow [4] ................................................................................................ 6

Figure 5: Evaporation of water from a body of water [8] ............................................................... 7

Figure 6: Reduction in total cooling load for three rooms .............................................................. 8

Figure 7: C and m constants for cylinder in cross flow [10] ........................................................ 13


3

1.0 Introduction

This report will investigate whether the cooling load for a building can be mitigated through the

addition of ceiling fans. By reducing the cooling load for a building there will be corresponding

economic benefits and potentially a reduction in environmental harm depending on the source of

energy for the cooling system. In order to determine if there is an economic benefit, the initial cost,

operating costs, and payback period must be considered.

Fans can be used to reduce cooling load because the increased air movement reduces the effective

temperature the occupants would experience which allows for a lower set point for the room

thermostat [1]. This is due to the convection coefficient (ℎ̅) increasing as the wind velocity inside

the room increases which results in a larger sensible heat transfer rate (�̇�𝑠). There is also an increase

in latent heat transfer rate (�̇�𝑙) as the increased air movement results in greater evaporative cooling.

This report proposes to reduce the overall cooling load for a three story office building located in

Adana, Turkey by installing three ceiling fans. This report will begin by describing the problem

statement and project objectives defined by the team. Section 2.0 will describe the relevant

parameters of the sample building for the report. In Section 3.0 the proposed system will be

detailed including fan type and placement. Section 4.0 will analyze the proposed system by

estimated the reduction in sensible and latent cooling and the effect on building energy use. An

economic analysis will also be carried out to quantify the benefit of the proposed system. The final

section will conclude on the proposed design, looking at the advantages and disadvantages as well

as suggesting possible improvements.

1.1 Problem Statement

Design and analyze a system that incorporates three ceiling fans into an actual building. Reduction

in cooling loads and costs are to be considered.

1.2 Project Objectives

The following project objectives highlight the important parameters that must be met by the

proposed system and the final report:

Energy characterization of existing building

Proposed fan type and layout

Reduction in cooling load

Reduction in economic costs (consider initial and operating costs)


4

2.0 Case Study

The sample building that will be considered in this report is a three story office building located in

Adana, Turkey (36° 59’ latitude, 35° 18’ longitude, 20 m altitude) which is in the Mediterranean

portion of the country. This building was analyzed by Aktacir, Büyükalaca, and Yilmaz for a case

study on the effects of thermal insulation on cooling loads [2]. The building has 27 offices, with

two workers per office, and is occupied between the hours of 9:00 to 20:00.

This report will use the insulation and cooling load parameters for the Building A-type insulation

with 3 m high walls, and an overall thermal resistance (𝑈𝑜) for the wall, roof, and floor of 0.403

W/m2·K, 0.349 W/m2·K, and 0.07 W/m2·K respectively. The outdoor air conditions were for a dry

bulb temperature (𝑇𝑜𝑑𝑏) of 38 C and wet bulb temperature (𝑇𝑜𝑤𝑏) of 26 C. The indoor air conditions

were set to an indoor dry bulb temperature (𝑇𝑖𝑑𝑏) of 26 C with a relative humidity (𝜙) of 50%.

The total hourly cooling load for the building (�̇�𝑐𝑜𝑜𝑙,𝑡𝑜𝑡) has been characterized in Figure 1 which

is assumed to apply to the entire cooling season of 184 days between May and October. The

sensible heat factor (𝑆𝐻𝐹) for the building was 0.97 with an outdoor air requirement (�̇�𝑜) of 1596

m3/h. The peak cooling load of 94 kW occurs at 13:00 with the minimum cooling load of 10 kW

occurring at 5:00.

0

20000

40000

60000

80000

100000

120000

0 4 8 12 16 20 24

Tota

l Co

olin

g Lo

ad (

W)

Time of Day (hours)

Figure 1: Initial total hourly cooling load for building


5

3.0 Proposed System

Three of the offices on the first floor of the office building will each have a fan installed centrally;

one each for zone 1 (ZO1), zone 2 (ZO2), and zone 3 (ZO3) as can be seen in Figure 2. The fans

will be operated at full capacity during the hours that the office is occupied (9:00 to 20:00). It is

imagined that these fans are installed as a pilot project before installing fans for the entire building.

The fan chosen in this report is the Emerson CF705 (see Figure 3). This fan has a total diameter

of 52” with an input power of 52.2 W and an air flow rate of 3110 cfm [1]. This fan was chosen

due to its low input energy since some of this energy will be transferred to the room as heat

counteracting the desired cooling effect.

Figure 2: Proposed fan positions

Figure 3: Emerson CF705 fan [10]


6

4.0 System Analysis

This section will begin by analyzing the sensible/latent cooling from the fan and the effect on the

building energy use and conclude with an economic analysis. Sample calculations, project

assumptions, and the EES code use for calculations are included in Section 7.0 Appendix.

4.1 Sensible Cooling

To approximate the sensible cooling that an occupant would feel in a room with a fan, an external

flow heat transfer model was used. Wind flowing over a human being was modeled as cross

flowing air over an upright cylinder. An example of this is shown in the figure below.

The person was assumed to have a surface area of 1.8 m2 [3] with 30% of the skin exposed to the

wind to approximate clothes covering the skin. All of the ambient conditions of the conditioned

space are used in this model and the internal temperature of the human was assumed constant at a

temperature of 37.5 C.

Using the model described above, a Nusselt number was found which enabled a convection

coefficient to also be calculated. In this way the sensible heat loss (�̇�𝑠) the human would experience

in this wind was found to be approximately 312 W. This heat loss was assumed to be strictly

sensible, as the percentage of this heat which would promote latent cooling is difficult to

approximate.

An additional assumption was that this 312 W of additional cooling would reduce the cooling load

for the room by the same amount. Due to two occupants being present in each room, the total

cooling load reduction would then be 624 W per room.

Figure 4: Cylinder in cross flow [4]


7

4.2 Latent Cooling

Obtaining a model that would provide an accurate estimation of the latent cooling effects due to

the evaporation of sweat off of the human skin was a challenging task. From research, the simplest

procedure found was to calculate the rate of evaporation by using an empirical method determining

rate of evaporation from a body of water due to air flow across its surface. It was assumed that the

human has a coating of sweat across the exposed skin, and when the sweat evaporates it is

replenished immediately.

The assumptions of exposed skin and surface area of the human model from the sensible cooling

section are maintained for this portion. Modifications to the aforementioned empirical method

were made accordingly. After setting these parameters and constraints, it was determined that the

latent cooling experienced by 2 people in a room due to the installation of a fan is 382.2 W.

4.3 Building Energy Calculations

The additional sensible and latent cooling effects of the fan have been calculated in the previous

sections and they can now be removed from the total cooling load for the three proposed rooms.

The total cooling load for the three rooms (�̇�𝑐𝑜𝑜𝑙) was estimated by dividing the building cooling

load by the total number of offices (27 offices in the building). This is not entirely accurate since

it does not account for any variation in cooling load for offices on different floors or that are facing

different directions. For instance offices that are on a south-facing wall will receive more solar

radiation over the course of the day and require a larger cooling load [3].

The total reduction in cooling load due to the fan was calculated by subtracting the additional

sensible and latent cooling of 1006.2 W and adding the additional electrical consumption of 50.2

W from the fan. The net result was therefore 956 W per room for a total of 2868 W for all three

rooms. This reduction was only applied during the occupied hours of 9:00 to 20:00 since no benefit

would be seen if the office workers were not present.

Figure 5: Evaporation of water from a body of water [8]


8

As can be seen in Figure 6, the cooling load is displaced during the times of fan operation and

most importantly during the times of peak energy rates. By adding the three fans, the daily

reduction in cooling load is estimated to be 31.55 kW per day.

4.4 Economic Analysis

The fundamental reasoning behind implementing fans in this building was to decrease the cooling

load on the existing HVAC system and reduce costs. This section will consider the daily and annual

cost benefit of installing the fans as well as the payback period. All calculations were performed

in US dollars.

From the previous sections the reduction in cooling load for the three rooms was estimated at 2.868

kW over the 11 hour work day. Using an estimated cost of electricity in Turkey of 0.142 USD/kWh

[4], the total savings per day is $4.48. For 258 working days in Turkey in 2016 [5], the cost

saved per annum from the implementation of the three fans is $1157. The initial cost to install

the fans was estimated at $1797, given a fan cost of $199 [6] and an installation cost of $400 per

fan [7]. Using the estimated annual savings and cost to install the fan, the payback period for the

project is approximately 1.55 years.

0

2000

4000

6000

8000

10000

12000

0 4 8 12 16 20 24

Tota

l Co

olin

g Lo

ad (

W)

Time of Day (hours)

Without Fan

With Fan

Figure 6: Reduction in total cooling load for three rooms


9

5.0 Conclusion

This report has examined the energy and economic benefits of ceiling fans from a heat transfer

perspective. Additional sensible and latent cooling has resulted from the resulting increased air

movement which should reduce the cooling load on the HVAC system for the building. Ceiling

fans achieve this result by increasing the air flow around occupants resulting in greater sensible

heat transfer rates through convection and greater latent heat transfer rates through evaporative

cooling [8]. In this way the set point temperature for the cooling system can be increased without

sacrificing the comfort of the occupants. In the proposed system the fans are only run when the

office is occupied from 9:00 to 20:00 since the benefit results from occupants feeling comfortable

at higher indoor air temperatures.

It was initially assumed that the latent cooling effect would dominate, however latent cooling (�̇�𝑙)

was estimated at 382 W per room while sensible cooling (�̇�𝑠) was estimated at 624 W. It is unclear

why �̇�𝑠 is approximately double �̇�𝑙 since existing literature estimate that latent cooling should be

larger. In a study on livestock, Gebremedhin and Wu estimate latent and sensible heat loss at 182

W and 159 W respectively for an air velocity of 0.5 m/s under conditions of 30 C dry bulb

temperature and 20% relative humidity [9]. However when velocity is increased to 2.0 m/s the

latent heat loss increases to 368 W whereas the convective heat loss remains approximately

constant 149 W. The discrepancy in the proposed heat transfer models is likely due to simplifying

assumptions.

The decrease in cooling load for three rooms was estimated at 2.868 kW for a daily reduction of

31.55 kW which considered the additional electricity consumption of the fans. The savings from

installing the system was estimated at $4.48 per day and $1157 per year for a payback period of

1.55 years.

It was assumed that the fans would be operated at full operating speed during operating hours,

however a greater reduction in energy could result from more intelligent control. For instance a

motion sensor could be used to turn off the fans when the rooms were unoccupied for a certain

period. Depending on the usage of the room the additional cost of installing this system may be

justified. A major assumption that may not be justified was that the additional cooling afforded by

the fans would directly translate to a reduction in cooling load on the HVAC system in the office.

A more accurate model would consider the effective temperature seen by the occupants and relate

it to the change in set point of the cooling system. Additionally since only three of the rooms in

the building will have fans installed, there would only be a reduction in cooling load if each of the

rooms had their own thermostat. Although the proposed heat transfer models certainly have

inaccuracies, it has been demonstrated that there is likely some beneficial reduction in cooling load

through installation of ceiling fans.


10

6.0 Nomenclature

General

𝐴 - Exposed surface area [m2]

𝐶 - Factor of human body exposed

𝑑 - Diameter [m]

𝑔 - Evaporation rate [kgmoisture/s]

ℎ - Height [m]

ℎ̅ - Average convection coefficient [W/m2·K]

𝑘 - Thermal conductivity [W/m·K]

𝐿 - Depth of skin

𝑁𝑢𝐷 - Nusselt number [dimensionless]

𝑃𝑟 - Prandtl number [dimensionless]

𝑞" - Heat transfer rate per unit area [W/m2]

�̇� - Heat transfer rate [W]

�̇� - Volumetric flow rate [m3/s]

𝑅 - Thermal resistance [m2·K/W]

𝑅𝑒𝐷 - Reynolds number [dimensionless]

𝑆𝐻𝐹 - Sensible heat factor

𝑇 - Temperature [C or K]

𝑈𝑜 - Overall heat transfer coefficient [W/m2·K]

𝑉 - Velocity [m/s]

𝑊 - Absolute humidity ratio [kgmoisture/kgair]

Subscripts

𝑑𝑏 - Dry bulb

𝑖𝑑𝑏 - Indoor dry bulb

𝑙 - Latent

𝑜 - Outdoor

𝑠 - Sensible

𝑤𝑏 - Wet bulb

Greek Letters

𝜃 - Evaporation coefficient [kgmoisture/m2·h]

𝜈 - Kinematic viscosity [m2/s]

𝜙 - Relative humidity [kgmoisture/kgmoisture at saturation]


11

7.0 Appendix

7.1 Project Assumptions

Air

Ideal gas at 1 atm (101 kPa)

Outdoor Conditions

Dry Bulb Temperature

o 𝑇𝑑𝑏𝑜 = 38 𝐶

Wet Bulb Temperature

o 𝑇𝑤𝑏𝑜 = 26 𝐶

Building Conditions

Indoor Design Dry Bulb Temperature

o 𝑇𝑎𝑚𝑏 = 26 𝐶

Indoor Relative Humidity

o 𝜙 = 50%

Occupants (Men) per Room

o 𝑃𝑒𝑟𝑠𝑜𝑛𝑠 = 2

Total Number of Rooms

o 𝑅𝑜𝑜𝑚𝑠 = 27

Total Outdoor Air Flow

o �̇� = 1596𝑚3

ℎ= 0.443

𝑚3

𝑠

Base Room Air Flow Rate

o 𝑉 = 0.15𝑚

𝑠

Person

Surface Area

o 𝐴𝑡𝑜𝑡 = 1.82 𝑚2

Skin Temperature (Wind Project)

o 𝑇𝑠𝑘𝑖𝑛 = 37.5 °𝐶

Heat Transfer

30 % of total human skin is exposed and affected by the sensible and latent cooling

Human is modeled as a cylinder in cross flow

Constant internal temperature

Evaporation modeled as a person completely covered in perspiration


12

7.2 Sample Calculations

Convection Calculations

This section covers the calculations performed to produce the sensible cooling load reduction due

to the convectional heat loss.

First, the properties of air at the ambient design conditions of 26 C and 101.325 kPa were obtained

from Engineering Equation Solver (EES),

Kinematic Viscosity: 𝑣𝑎𝑖𝑟 = 1.571 ∗ 10−5 𝑚2

𝑠

Prandlt Number: Pr𝑎𝑖𝑟 = 0.7278

Number of People in Room: 𝑁𝑝𝑒𝑜𝑝𝑙𝑒 = 2

Then the fan velocity was to be calculated,

�̇�𝑓𝑎𝑛 = 3110𝑓𝑡3

𝑚𝑖𝑛≈ 1.56

𝑚3

𝑠

�̇�𝑓𝑎𝑛 = 𝐴𝑓𝑎𝑛𝑉𝑎𝑖𝑟

∴ 𝑉𝑎𝑖𝑟 =�̇�𝑓𝑎𝑛

𝐴𝑓𝑎𝑛=

�̇�𝑓𝑎𝑛𝜋

4∗𝐷𝑓𝑎𝑛

2

𝑉𝑎𝑖𝑟 =1.56

𝑚3

𝑠

𝜋

4[(52 𝑖𝑛𝑐ℎ)(

1𝑚

0.0254 𝑖𝑛𝑐ℎ)]

2 ≈ 1.1385𝑚

𝑠

To find the Reynolds number, the diameter of the cylinder would have to approximate. This

diameter would be found by constraining the height and surface area of the cylinder. It was

assumed that the average height of the workers in the building would be,

ℎ𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 6𝑓𝑡 ≈ 1.8288𝑚

The average area of human skin was obtained [3].

𝐴𝑠𝑘𝑖𝑛 = 1.82 𝑚2

The diameter of the cylinder is then,

𝑑𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =𝐴𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝜋ℎ𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟


13

𝑑𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 =1.82 𝑚2

𝜋∗1.8288 𝑚= 0.31678𝑚

The Reynolds number can then be found [10],

𝑅𝑒𝐷 =𝑉𝑎𝑖𝑟𝑑𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝑣𝑎𝑖𝑟=

(1.138𝑚

𝑠)(0.31678 𝑚)

(1.571·10−5 𝑚2

𝑠)

≈ 22958.3

To calculate the Nusselt number the following equation is used [10],

𝑁𝑢𝐷 =ℎ̅𝑑𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟

𝑘= 𝐶𝑅𝑒𝐷

𝑚Pr1

3

Where the C and m coefficients are shown in the table below, sorted by Reynolds Number,

With 𝐶 = 0.193 and 𝑚 = 0.618, the equation is then,


𝑘𝑠𝑘𝑖𝑛= (0.193)(22958.30.618)(0.7278

1

3) = 86.02

Where 𝑘𝑠𝑘𝑖𝑛 is the thermal conductivity of skin [11] and is taken as 𝑘𝑠𝑘𝑖𝑛 = 0.3075𝑊

𝑚·𝑘, the

average of the given range.

The above equation then gives the convection coefficient,


𝑘𝑠𝑘𝑖𝑛

∴ ℎ̅ =𝑁𝑢𝐷𝑘𝑠𝑘𝑖𝑛

𝑑𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟≈ 83.505

𝑊

𝑚2·𝑘

Using a thermal resistance circuit of the inside of the human skin, assuming that the thickness of

the skin is 𝐿𝑠𝑘𝑖𝑛 = 0.0025𝑚 [12].

𝑅𝑡𝑜𝑡𝑎𝑙 = 𝐿𝑠𝑘𝑖𝑛

𝑘𝑠𝑘𝑖𝑛+

1

ℎ=

0.0025𝑚

0.3075𝑊

𝑚2·𝑘

+1

83.505𝑊

𝑚2·𝑘

≈ 0.0201 𝑚2𝑘

𝑤

Figure 7: C and m constants for cylinder in cross flow [10]


14

The heat loss per square meter of human skin is then,

𝑞′′ =𝑇𝑠𝑘𝑖𝑛−𝑇𝑎𝑚𝑏

𝑅𝑡𝑜𝑡𝑎𝑙=

37.5℃−26℃

0.0201𝑚2𝑘

𝑤

≈ 571.99𝑤

𝑚2

Then the total heat loss per person is then found with the following. Notice the reduction of human

skin area, as assumed that only 30% is exposed, due to clothing.

�̇�𝑠 = 𝐶𝑁𝑝𝑒𝑜𝑝𝑙𝑒𝑞′′𝐴 = (0.2)(2 𝑝𝑒𝑜𝑝𝑙𝑒) (571.99𝑤

𝑚2) (1.82 𝑚2) ≈ 624.6 𝑊

Latent Cooling Calculations

The following parameters are required for determining the latent cooling effects due to

evaporation:

Surface Area of Body: 𝐴 = 1.82 𝑚2

Factor of Body Exposed to Air: 𝐶 = 0.3

Indoor Humidity Ratio: 𝑊𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡 = 0.0105𝑘𝑔𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒

𝑘𝑔𝑎𝑖𝑟

Saturated Humidity Ratio: 𝑊𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = 0.02164𝑘𝑔𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒


Number of People in Room: 𝑁𝑝𝑒𝑜𝑝𝑙𝑒 = 2

Diameter of Fan: 𝑑 = 1.3208 𝑚

Volumetric Flow Rate of Fan: �̇�𝑓𝑎𝑛 = 1.56𝑚3

𝑠

Temperature of Skin: 𝑇𝑠𝑘𝑖𝑛 = 37.5 𝐶

Ambient Temperature: 𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡 = 26 𝐶

To approximate the temperature of sweat on the skin an average of skin temperature and ambient

room temperature was taken.

𝑇𝑠𝑤𝑒𝑎𝑡 =𝑇𝑠𝑘𝑖𝑛+𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡

2=

37.5+26

2= 31.75 𝐶

Using 𝑉𝑎𝑖𝑟 = 1.1385𝑚

𝑠 from the previous section and introducing an exposure factor C we

obtain the evaporation rate.

𝑔ℎ = 𝜃𝐴𝑁𝑝𝑒𝑜𝑝𝑙𝑒𝐶(𝑊𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 − 𝑊𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡) [7]

Where the evaporation coefficient (𝜃) includes the air velocity,

𝜃 = 25 + 19𝑣 = 25 + 19 (1.1385𝑚

𝑠) ≈ 46.63

𝑘𝑔

𝑚2·ℎ


15

The amount of evaporated water per hour (𝑔ℎ) and per second (𝑔𝑠) can then be found:

𝑔ℎ = (46.63 𝑘𝑔

𝑚2·ℎ) (1.82 𝑚2)(2 𝑝𝑒𝑜𝑝𝑙𝑒)(0.3)(0.02164 − 0.0105)

𝑘𝑔𝑚𝑜𝑖𝑠𝑡𝑢𝑟𝑒


∴ 𝑔ℎ = 0.5673𝑘𝑔

ℎ𝑟

∴ 𝑔𝑠 = 1.575 · 10−4 𝑘𝑔

𝑠

By using EES, the value of the enthalpy of vaporization at 𝑇𝑠𝑤𝑒𝑎𝑡 is obtained. Multiplying by

the evaporation rate we obtain the latent cooling experienced by two people:

�̇�𝑙 = 𝑔𝑠ℎ𝑣𝑎𝑝 = (1.575 · 10−4 𝑘𝑔

𝑠) (2426

𝑘𝐽

𝑘𝑔) = 382.2 𝑊

Economic Analysis

A short economic analysis was conducted to financially quantify the benefits of implanting fans

throughout this building. The following are general calculations on the currency savings generated

by the fans and their payback period. All numbers are in US dollars.

Sensible cooling rate: �̇�𝑠 = 0.6246 𝑘𝑊

Latent cooling rate: �̇�𝑙 = 0.3822 𝑘𝑊

Fan energy consumption: �̇�𝑓𝑎𝑛 = 0.0502 𝑘𝑊

Cost of One Fan: 𝐶𝑜𝑠𝑡𝑓𝑎𝑛 = $199

Cost of Installing One Fan: 𝐶𝑜𝑠𝑡𝑖𝑛𝑠𝑡𝑎𝑙𝑙 = $400

Sensible cooling is equivalent to the value determined in the convection sample calculations. The

energy consumption and cost of the fan were provided by manufacturing specifications, and

installation cost was from published values.

�̇�𝑐𝑜𝑜𝑙,𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 3(�̇�𝑠 + �̇�𝑙 − �̇�𝑓𝑎𝑛) = 3(0.6246 + 0.3822 − 0.0502) 𝑘𝑊 ≈ 2.868 𝑘𝑊

𝐶𝑜𝑠𝑡𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 = (�̇�𝑐𝑜𝑜𝑙,𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛)(𝑟𝑎𝑡𝑒)(𝑢𝑠𝑒)

∴ 𝐶𝑜𝑠𝑡𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 = (2.868 𝑘𝑊) ($ 0.142

𝑘𝑊ℎ) (11

ℎ𝑜𝑢𝑟𝑠

𝑑𝑎𝑦) ≈ $4.48 𝑝𝑒𝑟 𝑑𝑎𝑦

𝐶𝑜𝑠𝑡𝑠𝑎𝑣𝑒,𝑎𝑛𝑛𝑢𝑚 = 𝐶𝑜𝑠𝑡𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 (258 𝑑𝑎𝑦𝑠

𝑦𝑒𝑎𝑟) = (

$4.48

𝑑𝑎𝑦) (

258 𝑑𝑎𝑦𝑠

𝑦𝑒𝑎𝑟) ≈ $1157 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

𝐶𝑜𝑠𝑡𝑓𝑎𝑛,𝑡𝑜𝑡𝑎𝑙 = 3(𝐶𝑜𝑠𝑡𝑓𝑎𝑛 + 𝐶𝑜𝑠𝑡𝑖𝑛𝑠𝑡𝑎𝑙𝑙) = 3($199 + $400) ≈ $1797

𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 =𝐶𝑜𝑠𝑡𝑓𝑎𝑛,𝑡𝑜𝑡𝑎𝑙

𝐶𝑜𝑠𝑡𝑠𝑎𝑣𝑒,𝑎𝑛𝑛𝑢𝑚=

($1797)

($1157

𝑦𝑒𝑎𝑟)

≈ 1.55 𝑦𝑒𝑎𝑟𝑠


16

7.3 EES Code "Enter Parameters" A= 1.82 "Surface area of body" C= 0.3 "Percentage of body exposed to air, aka no clothes" x_env= 0.0105 "Relative humidity of room" Num_people= 2 "Number of people in room" x_sat= 0.02164 "Saturated at indoor temp" d = 1.3208 "Diameter of fan" Q = 1.56 "flowrate of fan" T_skin = 37.5 "Skin temp" T_ambient = 26 "Ambient temp" T_sweat = (T_skin + T_ambient)/2 A_fan = pi*(d^2)/4 Q = A_fan * v g_h = theta*A*Num_people*C*(x_sat - x_env) theta = 25 + 19*v h_vap=Enthalpy_vaporization(Water,T=T_sweat) q_dot_l = (g_h/3600)*h_vap "ECONOMIC ANALYSIS" Fan_gain = .0502 "Fan operational cost" q_dot_s = .6246 Total_reduction_fan = (3*q_dot_s) + (3*q_dot_l) - (3*Fan_gain) Cost_elec_Turkey = (Total_reduction_fan *(.142)*(11)) "Electrical energy saved from total cooling" Cost_Fan = 199 Fan_installation_cost = 400 Total_fan_cost = (Cost_Fan*3) + (Fan_installation_cost*3) "Total fan installation and purchase cost" Cost_save_annum = Cost_elec_Turkey * 258 "Annual money saved from adding fans per fan" Payback_Period = Total_fan_cost/Cost_save_annum "Payback period"


17

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[12] H. J. Bennett, "Ever wondered about your skin?," 25 May 2014. [Online]. Available:

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[14] "Evaporation from water surfaces," engineeringtoolbox.com, 2016. [Online]. Available:

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March 2016].

Documents

MECE4450U - Final Report (Final)