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# System prepended metadata

title: Untitled

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# CL246 COURSE PROJECT 

* Group 15

![](https://lh6.googleusercontent.com/4flBPjD9SChB-Nyyh7af9srYdupER_fsgy_FbVUZj9qsmYi3i_fKSXhcxdlonhv2IbtY5LyebyjsC8mM1Rpfn1Hysoilcax7RbjCXOUYmoNFp7Wb1g5gOU7rV8K0MZEfsgQ0wpPC)

REDUCTION OF HEAT LOAD OF HOUSEHOLDS USING EVAPORATIVE COOLING

  
  

## GROUP MEMBERS:

### SOLVERS
-   Laxman Desai
-   Jos Katiyare
    

### GENERATORS
-   Akshata Jain
-   Abhay Kadapa

 PLANNERS
-   Krishi Mantri
-   Saurabh Mhaiskar
    

 IDEATORS

-   Diksha Chandna
-   Ritesh Meena


Table Of Contents

1.  Introduction
    
2.  User Story 
    
3.  Sources of Heat Gain
    
4.  Proposed Solution
    
5.  Tasks Performed as a part of the Project
    
6.  Final Problem Statement (Like textbook)
    
7.  Evaporative cooling and Status Quo
    
8.  Types of Evaporative Cooling
    -   Active Direct Evaporative Cooling Systems 
    -   Passive Direct Evaporative Cooling Systems
    -   Indirect Evaporative Cooling Systems   
    

9.   Qualitative Temperature Profile - Direct Evaporative roof cooling system
    
10.  Overall Assembly of roof and house 
    
11.  Control Volume Analysis 
      -   Case 1 - Roof without water 
      -   Case 2 - Roof with a layer of water
    

12.  Basic Mathematical Model and Common equations 
    
13.  Conclusion

14.  Numerical Computation
      -   Case 1 - without water layer
      -   Case 2 - with water layer

15.  Bibliography
 -->

## Introduction

As the world continues to urbanise, significant challenges arise in the environment, energy, and water sustainability in cities. Energy is an essential requirement for the existence and development of human life, primarily consisting of domestic sources such as fossil fuels (coal, oil, and natural gas) and electricity. Increasing energy efficiency is necessary to cut carbon emissions, secure energy, and save on energy bills.  

## User Story

In a tropical country like India, there are large regions that have high temperatures and low humidity, where the solar radiation incident on roofs of domestic and commercial buildings is very high in summer. Buildings in such regions face the problem of excessive heating as an effect of the hot climate. If not taken seriously, these conditions will waste energy for cooling the room. Energy consumption will increase when a building is designed without keeping environmental conditions and protection from direct sunlight in mind. The energy cost in such areas goes on increasing year-on-year and hence, there is a need to find sustainable solutions with low investments which can help in solving this problem by reducing the heat flux inside the house like evaporative cooling.

![](https://lh3.googleusercontent.com/IbT7e949gJfoevFUYz5OgrlPYozLhAihJWSJ1QmJkgwdT5j38cBXVyIEOn6dYI6WtlDbrDd7YLHhhphjZEjegw5-u1sM_S2t7SKp25so6Sw88QNUt_IYEQQ7GIGtEiP3EepfTzdo)

**Fig 1:**   Shows the highest expenditure of air conditioning in India. Hence, shoeing the need to develop sustainable methods to reduce heat load of houses

## Sources of Heat Gain

Sources of heat gain for the building include:

1. Heat inflow from roof (direct solar radiation).
Majority of heat gained by houses in hot and dry places is through solar heat flux through the roof . The reason being that the sun is overhead for a longer period and the intensity of solar radiation during that period is maximum. The major modes of heat transfer involved through the roof are convection through the air , radiation from the solar flux and conduction through the roof.

2. Heat inflow from walls (angled solar radiation) and windows (through hot air flowing in).
This source of heat gain is majorly due to the temperature gradient between the air outside and that inside. The major modes of heat transfer are convection through air and conduction through the wall envelope.

3. Casual heat gain due to devices operating inside as well as occupants of the space. This type of heat gain is unavoidable and is not that major source of heat gain.  

Integral Heat balance in the house:

<!-- ![](https://lh5.googleusercontent.com/6NECLDbF7ypgMetQ1dogavBockwEKCm1AEVzklO8BmOlGUIbr3EJPwMN57G5u8Ev9IG9GiCluk1qaSRqrd8OaqqxqUsR0e8YeOHjzpTYbJRpiR3bpYLeTmI-UooOuyROhdXx94MS)
 -->
$$
M_R  \frac{\mathrm{d} T_R}{\mathrm{d} t} = \dot{Q}_W(t) + \dot{Q}_R + \dot{Q}_D(t) - \dot{Q}_F(t) - \dot{Q}_{inf/ven}(t)
$$

where
\begin{align*}
 \dot Q_W(t)&: \text{heat flux through the walls} \\
 \dot Q_R&: \text{heat flux through the roof} \\
 \dot Q_D(t)&: \text{heat flux through the door} \\
 \dot Q_{inf/ven}(t)&: \text{heat flux due to air flow caused by infiltration/ventilation}  \\
\end{align*}


<img src= "https://lh6.googleusercontent.com/N1ogjF3-Y8iu5bg6DnY9qtpfkQg_jLAIg3KqrINbmFCPKKOZcwnfKgRxi06wRfdVGOrc28hyiq8jwZ2-e7fDM-NmayNpam2ERN1kd3XznDFyGf_Q5KForg-LOQg5uG0yoRfMJq8H">
**Fig 2:** Shows the all the three different ways in which heat is gained in the house through the various modes of heat transfer majorly solar radiation, convection through air and conduction through the building envelope  

## Proposed Solution

The cost of artificially cooling houses using high cost air-conditioning systems require both higher investment and energy costs. Therefore, sustainable solutions like Evaporative cooling, stratified ventilation and geothermal heat-pumps are suggested.

In this project we have tried to model evaporative roof cooling for a house in hot and dry places like New Delhi where some of the incident solar radiation and convection energy is lost in evaporation of water.  

## Tasks Performed as a part of the Project

- Modelling the evaporative roof cooling using simple modes of macroscopic heat transfer mainly conduction, convection and radiation by control volume analysis.
- Control Volume estimation and estimation of heat transfers of roof in both cases namely one with water and one without water layer
- Established a complex mathematical and differential equations model using literature survey
- Solving a simplified steady state mathematical model of evaporative roof cooling using text-book correlations and equations.

Note: Basic approaches in both the models remain the same but the simplification done in the second model renders the equations solvable .
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<img src = "https://lh3.googleusercontent.com/yRXD0EHMYT3hf01eFQffCr1vUkvFXHP6SXauO0Ydyb_sqsSah9YJcflUkd_01xrfxVVqnqsxKIa8OOoMbSMmG14kJEPP4rODbdAANl1_QIdC2nWKgu4V2oclgip218bPijQoN5VO" style="display: block; margin-left: auto; margin-right: auto; width: 50%;">

**Fig 3:** Shows the schematic of Evaporative roof cooling and reduced heat transfer due to use of a fraction of incident heat in evaporation of water

## Final Problem Statement

Estimate and compare  the heat flux through the roof of a house in a place with hot and dry conditions in two cases:

1.  Normal conditions with just a three layered roof exposed to the the solar radiation and wind convection during afternoon when the solar radiation can be assumed to constant (invariable with time)
2.  Now a thin water layer is added to the roof (thin enough to neglect temperature variation along the thickness of the water layer) which uses some of the heat incident into evaporation . This phenomena of reduction of inlet heat flux in the house is known as evaporative cooling.
    
Considerations: 

- Ambient room temperature i.e. inside room temperature: $27^\circ C$
- Temperature outside vary between $35^\circ C$ to $50^\circ C$ and is constant at any point of time
- Heat transfer majorly involves conduction through roof, convection through air and water and conduction through the roof layers

<img src = "https://lh4.googleusercontent.com/9sogABx9WcSAD248HpWjaJR8v_uPxmd2n3zXiSU989Jn3cFAvZX03E7AtGxUivMfgBIDA9Kbw1SND00LoZsKwJKcdLxfG4pHwUQHF261r6ijRl3cBvwKxqBFqjpHkqixFJrf6p9X" style="display: block; margin-left: auto; margin-right: auto; width: 50%;" >

**Fig 4:** This shows the overall schematic of evaporative cooling problem suggested above.

## Evaporative Cooling and Status Quo

Air conditioners or HVAC systems are used for cooling and ventilation purposes, and generally have high electricity costs associated with them. Design and structural changes such as adding insulation under the roof and walls aim to reduce the rate of incoming heat, but do so to a limited extent. Instead, using additional techniques such as evaporative cooling can help reduce the heat transfer rate as well as the overall incoming heat through the roof. Given that the roof of a building is directly exposed to solar radiation and thus forms the bulk of the heat absorption, using this method on the roof would considerably reduce the energy needed to maintain cooler temperatures in the building. Additionally, in places that face frequent power cuts (particularly during the summer months), high load inverters are required to support air conditioners, which would also need to be recharged frequently - this energy requirement is mitigated to some extent by using evaporative cooling, which is a relatively simple, low-cost method.

Further, the cooling effect observed increases with the rise in temperature and drop in humidity, conditions that prevail in large parts of states such as Rajasthan, Maharashtra, Gujarat and Madhya Pradesh. 

The main operating cost of an Evaporative Roof Cooling System is water. The evaporation of 1 litre of water will absorb 0.67 kilowatt-hour of heat energy per hour. One ton of air conditioning is the equivalent of 3.517 kilowatt-hour of energy. Therefore, evaporation of fewer than 5.5 litres of water per hour is required to provide the equivalent cooling effect of one ton of air conditioning. For every one ton of heat load removed by an evaporative roof cooling system means one less ton of cooling load placed on your facility’s HVAC system.

Other advantages of evaporative cooling systems include a low setup cost and low maintenance requirement - for a properly set up system, the day-to-day operation only requires replenishment of water and minimal cleaning and practically no operational constraints.  
  
## Types of Evaporative Cooling

### Active Direct Evaporative Cooling Systems

An active evaporative cooling system uses a system of fans or blowers to drive the ambient air through the wet pad into the system. This system can function against high static pressure and it can be combined with a heat exchanger (indirect evaporative cooling).

### Passive Direct Evaporative Cooling Systems

Passive cooling techniques use natural phenomena, energies, and heat sinks for cooling buildings without the use of mechanical apparatus or consumption of electrical energy. This is the oldest method of evaporative cooling and sometimes referred to as zero energy cooling as it does not consume any commercial energy.

  
<img src="https://lh6.googleusercontent.com/rQvnoJPNBqlUADhlTQB3NDxF1bnp4SSLnoe15_R_CcsilpJmJGsZ_sH69priR3D8nYkaar4WUM6d3Y16doL1QCRETwoSA8OVsBfzrpl71sQg6BZt7ASVJSMqfzRBUGN39BeEebEe" style="display: block; margin-left: auto; margin-right: auto;">

**Fig 5:** Schematic of Active direct and passive direct evaporative roof cooling systems

### Indirect Evaporative Cooling Systems

Indirect Evaporative Cooling Systems consist of heat exchangers used to cool the air supplied to the living space. The evaporative cooling cycle occurs in the heat exchanger.  

The model outlined in this project utilises passive direct cooling where the roof is covered in water (which has a high latent heat of evaporation) to minimise heat inflow to the building envelope - solar radiation is consumed for the evaporation of this water, keeping the building cool.  

**In this project we have majorly focused on direct evaporative cooling.**

## Qualitative Temperature Profile of Direct Evaporative roof cooling systems

<div class="row" style="display: flex;">  
  <div class="column">  
    <img src = "https://lh3.googleusercontent.com/KHnWUlW0yx6Rv0gVumLC7Mrtc8Mjen-z9dSzrH8-HgdSxzf0TTMtlXGHMxjXxZ0ykp_j3zcOg-O3NquA2D2zS9AOFKLrjTvvKGvX7ywErmy8FZ9wLu8r1y3D_WC_IJKcduW-XxKF">
    <p>
      <b>Fig 6:</b> This is the qualitative temperature profile for the first case when the roof is directly exposed to the radiation
    </p>
  </div>  
  <div style="width:60px"></div>
  <div class="column">  
    <img width=92% src= "https://lh4.googleusercontent.com/JsUlI4sdHPA2T8seAbWvyV1vIa-ti3ZFe7B9qc93enrb-rpviaVatRo8qJHWnQBc7mCAAiK6EdgEOnPLBnEFnCsBgYy6GBtcdrCSsgEFUgnrBUnXch3jCdfffWlPydg9bSBad3AY">
    <p>
      <b>Fig 7:</b> This is the qualitative temperature profile of the second case when there is a layer of water over the roof surface to allow evaporative cooling
    </p>
  </div>
</div>

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<img src= "https://lh4.googleusercontent.com/JsUlI4sdHPA2T8seAbWvyV1vIa-ti3ZFe7B9qc93enrb-rpviaVatRo8qJHWnQBc7mCAAiK6EdgEOnPLBnEFnCsBgYy6GBtcdrCSsgEFUgnrBUnXch3jCdfffWlPydg9bSBad3AY" style="display: block; margin-left: auto; margin-right: auto; width: 50%;">

Fig (7): This is the qualitative temperature profile of the second case when there is a layer of water over the roof surface to allow evaporative cooling -->

<!-- ## Overall Assembly of roof and house

The basic overall assembly of the house consists of walls, roof and floor whose schematic representations are mentioned below. This report or project majorly concerns the heat flux through the roof with and without a layer of water over it. 

Roof contains a three layered plaster of concrete, brick and lime . For the case 1 we have a bare roof while for the case two we have a thin layer of water over the roof.
  
Fig 3:
![](https://lh3.googleusercontent.com/W_MbW8Bm3MkpPCarbrGSaX7FvtsCjrAUGfCJ9gdowXoGqMUbudpL2-KW3YRjvKBg9-y7-RceTQpioApg7MDPdvUHUpnhcXLyGZNUv0OjrPU-m3FVnijM2SxP2ohMYTkTzonhX4-o)

  

A)

![](https://lh6.googleusercontent.com/ZRWXMA0wHTamRXhg-3tLKUaCKxW0APS4ju3FUQngI--jHs_MRhnZ6D5EMl2rNRokDg34sWKQlrv2AvGF-onz2cKfeiFxgV-B6WcE4lWs8x0_CWB1KNv8nMDhyW5cyrJy56MqNeae)

B)

![](https://lh6.googleusercontent.com/2WX87tLSZV2uOq6K9b2-6m67JhujJtVRBkARtFP226ssi65qv6QMtbNh69FVYAdVDOVTZPuRIzy9lizUCU3ZVE82Po5EF3y8KNhWVKX5pKU-XuhkVkRUcHpIdjr8T1rUJjDpHRH-)   ![](https://lh6.googleusercontent.com/r1CCwWKkuzuYjIeUNXjAGFV4oKkc5Jnzj6bBX7XW7kGobCkQeEujwKZylV6FhIgybz-hoexmVPbmTGmdkY6edfwzWHsDBVps0qhpGF0HF8B_h4uUfI1IDDP4XNDaKfYHc7VS_9-j)

  

C)

  

Fig (8) : 

A) Shows the schematic of house explicitly mentioning the various layers of roof and the water layer 

B) Schematic of roof having 3 solid layers with a layer of water on it

C) Schematic of the wall and floor of the house showing it various solid layers

  
  
  
  

## Control Volume Analysis

Case 1: Roof without without
![](https://lh6.googleusercontent.com/ycJEAOTygtX_Rq1lu4k9ZUSYmTlj9oW0WzJkenc5gNlJJCdI_IjIsz_bqS57FtG_bWHWL7BD58tfEVqaS7BcTfaoDt6Q8E7uRl2hRNYdWyx94nCIjwwXoOH1P64vXwlahuSTeiml)

Fig (9): This is control volume and overall assembly of roof for the first case when the roof is directly exposed to sunlight

  

Basic Integral Balance Equation for case 1:

1.  qrad \+ qconv\- qref  = qcond
    

  

2.  qcond  = qin
    

  

Where, 

-   qrad  \- radioactive flux
    
-   qconv \- convective flux
    
-   qnet \- net heat flux
    
-   qcond \- conductive heat flux
    
-    qin -  influx of heat
    

  

Case 2: Roof with a layer of water

  
![](https://lh4.googleusercontent.com/sno2W5Gw_h_a3qgbcAlxS-YXUAtAqF6Ty9HZ_LmuOCheez2QcpFtSka9WOyhe0ImJFpQNxfFQkipfJnq_Ac4u9DX68pEkSsSvy2sZd6WD9nEOuBcVVwOTBpkC6fwqq4AIpjTx-Mo)  
  
  
  
  
  
  
  
  
  
  

(A)

  
![](https://lh4.googleusercontent.com/x7wMy48Y3OQ0vBkn8Fkjgdh46z4zxjVrF_tmfgsI22AVZc99iaWfInPiWIvOMs9NrtFYHIpDiePB1pOIFyplxtRK36o2eCdkvB07EGzW0sp5ZdqGJFT9tBRJI9w1AUkekKxSt1zZ)  
  
  
  
  
  
  
  
  
  
  
  
  

 (B)

Basic integral balance for case II:

  

qnet = qcond = qin 

qnet = qrad \+ qconv \- qref \- qevap

  

Where,

-   qrad  \- radioactive flux
    
-   qconv \- convective flux
    
-   qnet \- net heat flux
    
-   qcond \- conductive heat flux
    
-    qin -  influx of heat
    
-   qevap\- evaporative heat flux
    
-   qref \- reflective heat flux
    

  

### Basic Mathematical Model and Common equations : (Reference Tiwari et. al. , Shrivastava et. al. and Incropera Book)

  

#### Case 1: Without a layer of Water:

  
![](https://lh6.googleusercontent.com/5setx6y7smOe_x7qNsYydouW1y4YNlZ7pD55KScAl_HrYEXPKBRQGmXCOUuZS6Mz5EkJfm8Aa4XAsP65XbvNua4nr7Z-OxH0Er-Ce6igTA2oyUo9lKfWl5JHqjQEedrB43sEAZcX)  

![](https://lh3.googleusercontent.com/_o2U3GQUS3MrUJZ4VR2W3ANnu7lbOpYaMXkYiJYGppEXmUULcaeCSSYuMe98JaBC46nJt21a6KC2AaAUSxNBr-_R7cpjlLVCd9xAORMHXXNS8pjMrp64z3OQZujg1zcflUVF_sC9) 

  

Eq 2.1: Describes the fundamental laws governing conduction in solids

  

BC1 and BC2 : Are the Boundary conditions between the solid layer exposed to inner and outer walls layers and air 

  

3.1 and 3.2: Are the equations of continuity of heat flux and temperature between layers

U is the cumulative heat transfer coefficient for the system

![](https://lh5.googleusercontent.com/2yJ9B6_7Ioh5i72TgPwEtVtZlbz0cwnU3F89FP-cw-JFuWEyyTtXR1RfIvjS11lYciVqP0OuCR15c-JpWMSC3do-5u2Byu3PbJXYfzZXo2x6YHNBn_kT4OZ8ZXEgErJ8uekt-Dg8)

  
  

#### Case 2: Roof with the layer of water 

In this case all the above equations are required along with the equation of heat balance over the water layer.

  

Eq 4.1: Gives the fundamental heat transfer equation for water layer taking into consideration the convection through the air and roof surface as well as the solar radiation.

  

Eq 4.2/ 4.3 /4.4: Describes the total radiative, convective and evaporative heat flux  having specific heat transfer coefficients and their correlations mentioned below obtained from literature and Incropera

  

Finally on simplification we can get the Eq 4.6 as the simplified equation with various parameters

  
  
  

The following sections are the mathematical computations for both cases:

1.  Heat Influx in roof without water layer
2.  Heat Influx in roof with a water layer
    
These cases include all the simplifications, assumptions and conditions used for solving along with the proper references
 -->