Performance Analysis of LFR Solar Water Heater

A Project Synopsis Submitted in Partial Fulfilment of the Requirements for the

Degree of

BACHELOR OF TECHNOLOGY
in
MECHANICAL ENGINEERING

Submitted by-
Dhruv Kaushik (2100910400014)
Kartik Singh (2100910400017)
Naitik Singh (2100910400021)
Nitish Chauhan (2100910400025)

Under the Supervision Of

Dr. Neelam Khandelwal
(Assistant Professor)

JSS ACADEMY OF TECHNICAL EDUCATION, NOIDA

DR. APJ ABDUL KALAM TECHNICAL UNIVERSITY
(FORMERLY UTTAR PRADESH TECHNICAL UNIVERSITY)
LUCKNOW
January 2025
 CHAPTER - 1
1.1 Introduction:

The current global energy situation illustrates that most countries worldwide are very
dependent on fossil fuels (oil, gas, and coal) to meet their needs. Hydrocarbons, the
dominant energy source, cover 80 % of global energy production. At this speed of
exploration and exploitation, the situation of hydrocarbon reserves is exceptionally
worrying, and their environmental impact is very alarming. Today, energy resources
conservation has become a priority on the planetary scale and given the dizzying
demand for energy, which has pushed specialists to find new suitable techniques by
exploiting renewable energies such as solar energy, hydro power, wind power,
geothermal energy, biomass energy, and new hydrogen energy. Therefore, the thermal
energy production from solar energy has many applications due to their innumerable
economic and environmental interests, where many solar collectors can be used to
exploit the sun’s energy either thermally or as photovoltaic, as needed. According to
the literature, the solar collector performances can be improved by utilizing the
nanofluid technologies by enhancing the thermal co-efficient of the working fluid
used by adding nanoparticles to the base fluid. Solar energy has several advantages
such as renewable, clean that allows environmental preservation, easily exploitable,
inexpensive, and saves energy conventionally, which amounts to saving currency for
the country.

Globally, one of the most critical areas that are known to be widely used in homes and
industrial facilities is water heating. In the case of Algeria, the domestic water heating
is provided by conventional energy such as the use of electricity, natural gas, and fuel.
These forms of energy have several drawbacks, the reserves of which are limited.
New forms of renewable energy are gradually being used to overcome this drawback,
such as solar energy. For this, many types of solar collectors can be used, such as flat
solar collectors, evacuated tube reflectors, parabolic trough collectors, and linear
Fresnel reflectors. Linear Fresnel reflectors have been developed for heat generation
at low or medium temperatures, where the heat generated has wide applications in
water heating, air conditioning and heating of buildings, heat supply in industrial
processes, water treatment, and various other applications. Its concept is simple and
easy compared to other concentrating solar collectors, flat or slightly curved mirrors
are used to make it and is less expensive than the other types of concentrating
collectors.

Several reasons make Algeria a very favourable site for extensive use of solar energy,
such as the importance of the annual potential of solar energy, the large population
living in isolated places deprived of electricity and gas, and the increase in the price of
conventional energy in recent times. This experimental and numerical study aims to
examine the optical and thermal behaviour of a solar water heater that depends on the
linear Fresnel reflector (LFR) in the Blida region at Algeria. Linear Fresnel collectors
are more often designed to produce medium-temperature heat for large-scale
industrial heat processes or commercial power generation. The use of this solar
concentrator for hot water production by small prototypes is an increasingly attractive
solution. Therefore, this work is devoted to examining a linear Fresnel reflector solar
water heater, where this analysis was carried out through an experimental and
numerical study of a small solar prototype based on Fresnel linear technology. The
cost factor is in the parabolic trough collector (PTC) technology based on the shaping
of the glass to obtain its parabolic shape. A possible alternative consists of
approximating the parabolic shape of the collector by a succession of plane mirrors.
This is the linear Fresnel collector principle, where each of the mirrors can pivot by
following the sun path to redirect and permanently concentrate the beam radiation
towards a fixed tube, but unfortunately, its optical performance is about 30 % lower
compared to PTC reflectors. However, its advantages are very beneficial since LFR
technology uses plane mirrors, which are simpler to manufacture and less expensive
than those of other types. Without forgetting that its infrastructure is less complicated
where the lighter support elements and the number of alignment motors reduced and
that there is less wind resistance and therefore light foundations without concrete are
sufficient. Besides, this technology is also an environmental companion, as the use of
water as a working fluid as an alternative of heat oil in the PTC technology to avoid
the pollution risk, fire, and fluid degradation.

In the literature, many discreet scientific studies have dealt with the use of water as a
heat transfer fluid with the linear Fresnel reflectors. Among these studies, Bellos et al.
conducted a numerical and experimental work on water LFR with a thermal
performance estimated at 25% guides for use in cooling, heating, and partial demand
for electricity. Also, Marefati and Mehrpooya have carried out a numerical work on
water steam LFR with a thermal efficiency between 18.88 and 27.83 % intended to
use in combined heat and power process. Moreover, Oscar et al. performed a CFD
modeling study on water LFR with a thermal performance between 25 and 37%
intended to use in water heating and low-temperature steam generation. Besides,
Jaramillo et al. performed numerical and experimental work on water LFR with a
thermal performance assessed at about 45% guides for use in water heating and low-
temperature steam generation. Also, Babu et al. conducted experimental work on a
water LFR with a thermal efficiency estimated at 41.2% planned to use in heating
water. Likewise, Gang et al. al. had experimented on a seawater LFR with a thermal
performance assessed at 41.2% planned to use in desalination. Also, Zhu performed a
numerical study on a water LFR with an optical efficiency estimated at 69.9%
intended to use in electricity production and industrial processes. Also, Chaitanya
Prasad et al. have carried out a numerical study on a water steam LFR with a thermal
performance assessed at 69.9% intended for direct production of superheated steam in
the power stations.

Moreover, Sharma et al. performed a numerical work on a water steam LFR with a
thermal efficiency assessed at 30.4% planned to use in electricity production. Besides,
Morin et al. performed a numerical study on a water steam LFR with a thermal
efficiency assessed at 32% intended to use in electricity production. Also, Qiu et al.
conducted a numerical study on a water steam LFR with a thermal performance
between 48.3 and 72 % intended for the industrial process. Besides, Sahoo et al. have
carried out an experimental work on water steam LFR with a thermal efficiency
between 35 and 50% intended for a direct steam generation. Moreover, Sahoo et al.
performed the numerical works on water steam LFR with a thermal performance
between 85 and 91% intended for electricity production and industrial process
heating. Besides, Ghodbane et al. performed an experimental, numerical, and CFD
modeling work on a small water LFR intended for heating water, where the thermal
performance of the studied prototype exceeded 29%. Likewise, Said et al. conducted a
numerical and experimental work on a small water LFR with a thermal performance
between 19.87 and 29.13% proposed to heating water, whereas this study has dealt
intensely with the optical side of the studied LFR. Moreover, Ghodbane et al.
performed a numerical work on a water steam LFR with a thermal efficiency
estimated at 37.5% intended to use in electricity production. This is a set of scientific
works on the use of water as a working fluid in linear Fresnel reflector, as it varies
between experimental, numerical and CFD modeling study.

The main objective of this experimental and numerical study is to demonstrate the
effectiveness of a MATLAB program developed to track the optical and heat
comportment of a small LFR collector that is intended for heating water in the Blida
region at Blida on January 22, 2015 and February 19, 2015. In a previous study by
Ghodbane et al., the weather data have been entered into the simulation code as an
estimated equation vs. time, i.e., the numerical solution based on the use of the
approximate equations of weather data (NAE) as program data. For the current study,
the weather data have been entered into the program in real-time real values, i.e., the
numerical solution based on the use of the real values of climatic conditions (NRWD)
as program data. Weather data such as direct solar radiation, air temperature, and wind
speed directly affect the numerical results obtained, and entering these data with their
real-time values will determine the effectiveness and accuracy of the numerical
program accomplished. It will also increase the accuracy of the results obtained. Also,
the modified program has been updated to calculate the exergy efficiency, pressure
drop, entropy generation, which will allow very accurate and detailed tracking of the
thermal comportment of the studied LFR system.

Fig.1.1.1

Fresnel collectors have two types: the linear Fresnel reflector (LFR) and the Fresnel
lens collector (FLC). The linear Fresnel mirror concentrator technology is still young
and has taken place in the field of concentrating solar systems, this technology was
conceived by the French physicist Augustin-Jean FRESNEL (1788–1827), he was
used this technique in the optical system of the marine indication headlights. The
work of Alessandro Battaglia is the origin of the concentration technique by linear
Fresnel reflector. The Italian mathematician Giovanni Francia (1911–1980), designed
the first prototype of linear Fresnel concentrator with the downward facing aperture
covered with glass honeycomb tubes at Marseille built in 1962, he got on the
performance equal to 60% and steam water temperature equivalent to 450 °C. In the
general case and according to the literature searches, the performance of this type of
concentrator is varied between 30% and 40%.

In this day of many international institutions are investing and working to develop this
technology, for instance at Almeria in Spain, the German company NOVATEC
BIOSOL built the first commercial linear Fresnel reflector plant in the world. This
electric station has a capacity of 1.4 MW, and since March 2009, their power supplies
the local electricity power lines. In France and since August 2010, CNIM group
invested the only module of its Linear Fresnel solar concentrator at the site of
Lagoubran to generate electricity from a steam turbine. In Australia, the company
Areva has developed the technology of a linear Fresnel concentrator for electricity
generation, Australia has two central, the first is Kimberlina in Bakersfield, California
with a rated power of 24 MW, the second central will be built in Kogan Creek near
Dalby at Australia, where their capacity equal to 44 MW.

There are many studies, addressed to use of the technology of linear Fresnel reflector,
including the study conducted by Choudhury et al., they made a design and analysis
of a linear Fresnel Reflector (LFR), where they got the concentration ratio of 18%
with two-thirds of the periphery of a tubular receiver of 0.025 m in diameter, their
concentration can produce temperatures above 350 °C. Singh et al., who studied the
performance of the linear Fresnel solar concentration device with a single absorber
tube of an aluminium which contains Hytherm-500 oil as heat carrier fluid. Mills et
al., they evaluated concept of a compact linear Fresnel (CLFR), assuming that the size
of the solar field will be great, because it must be designed for the production of
electricity across MW. In the field of water heating in the range between 60 and
95 °C, Singh et al., studied the thermal performance of the linear Fresnel concentrator
which contains a trapezoidal cavity with two types of absorber tubes (rectangular and
circular). The reflector performance of their collectors is varied between 16% and
64%, depending on the shape of the absorber tubes and the quality of the selective
surface. Moghimi et al. used the Computational Fluid Dynamics (CFD) to estimate
the optical efficiency of linear Fresnel reflector, their study is considered a new or
innovative computational approach for an accurate assessment of the contributions of
heat loss in a multi-tube trapezoidal cavity receiver. In another study, Moghimi et al.
conducted a mathematical optimization on the trapezoidal cavity absorber for the
Linear Fresnel Reflector In order to get the optimal designs of the cavity, the
objectives of their study are finding the most appropriate architecture to reduce heat
losses and side wind load.

1.2 Objectives:
1. The main objective is experimental and numerical analysis to demonstrate the
effectiveness of LFR solar system for heating water.
2. To develop a scalable LFR system that optimizes the use of solar energy for
thermal applications, ensuring high efficiency and maximum energy
absorption.
3. To Fabricate a solar water heating system that is affordable, with a focus on
reducing manufacturing and operational costs, making it accessible to a wider
audience.
4. To analyse the environmental impact by reducing reliance on fossil fuels and
promoting the use of renewable solar energy.
5. To assess the performance of the LFR Solar Water Heater under varying
weather conditions.

1.3 Problem Statement:

1. The increasing demand for hot water in residential, commercial, and industrial
sectors has led to a reliance on conventional water heating methods, such as
electric and gas heaters. These methods are not only expensive to operate but
also contribute significantly to environmental issues, including greenhouse gas
emissions and resource depletion.
2. While solar water heaters are a sustainable alternative, existing technologies
like flat-plate collectors and evacuated tube systems often face limitations in
terms of efficiency, cost, and scalability. Linear Fresnel Reflector (LFR)
technology offers a potential solution due to its ability to efficiently
concentrate solar energy using cost-effective and compact designs. However,
the lack of optimization in design, limited awareness, and absence of field
validation hinder its widespread implementation.
3. This project seeks to address these challenges by developing and evaluating a
practical, efficient, and scalable LFR solar water heating system to meet
modern energy demands sustainably and economically.
4. Linear Fresnel Reflector (LFR) technology offers a promising solution by
utilizing simple, cost-effective reflectors to concentrate sunlight for heating
water. However, challenges remain in optimizing the system's efficiency,
scalability, and affordability for widespread adoption. This project addresses
these issues by developing and testing an LFR-based solar water heating
system to provide a sustainable, efficient, and economically viable alternative
to conventional methods.
 CHAPTER – 2

2.1 Literature Review:

 H.J. Mosleh, A. Hakkaki-Fard, M. DaqiqShirazi, A year-round dynamic
simulation of a solar combined, ejector cooling, heating and power generation
system, Appl. Therm. Eng. 153 (2019).

 M. Ghodbane, B. Boumeddane, A parabolic trough solar collector as a solar

system for heating water: a study based on numerical simulation, International
Journal of Energetica (IJECA) 2 (2) (2017).

 M. Ghodbane, et al., Optical numerical investigation of a solar power plant of

parabolic trough collectors, J. Therm. Eng. 7 (3) (2021).

 R. Zhar, et al., Parametric analysis and multi-objective optimization of a

combined organic Rankine cycle and vapor compression cycle, Sustainable
Energy Technologies and Assessments 47 (2021).
 T. Hu, Z. Yue, Potential applications of solar refrigeration systems for
permafrost cooling in embankment engineering, Case Studies in Thermal
Engineering 26 (2021).

 Y. Cao, et al., Single solar chimney technology as a natural free ventilator;

energy-environmental case study for Hong Kong, Case Studies in Thermal
Engineering 26 (2021).

 R. Chauhan, et al., Experimental investigation and multi objective

optimization of thermal-hydraulic performance in a solar heat collector, Int. J.
Therm. Sci. 147 (2020).

 S.K. Natarajan, et al., Numerical investigations of solar cell temperature for

photovoltaic concentrator system with and without passive cooling
arrangements, Int. J. Therm. Sci. 50 (12) (2011).

 Z. Said, et al., Heat transfer, entropy generation, economic and environmental

analyses of linear Fresnel reflector using novel rGO-Co3O4 hybrid nanofluids,
Renew. Energy 165 (1) (2021).

 A.A. Hachicha, et al., A review study on the modeling of high-temperature

solar thermal collector systems, Renew. Sustain. Energy Rev. 112 (2019).

 Singh P.L., Sarviya R.M., and Bhagoria J.L., 2010, "Heat loss study of
trapezoidal cavity absorbers for linear solar concentrating collector," Energy
Conversion and Management, 51,

 O.A. Jaramillo, et al., A modular linear fresnel reflecting solar concentrator

for low-enthalpy processes, in: A. Sayigh (Ed.), Renewable Energy in the
Service of Mankind Vol II: Selected Topics from the World Renewable Energy
Congress WREC 2014, Springer International Publishing, Cham, 2016.
 M. Babu, S.S. Raj, A. Valan Arasu, Experimental analysis on Linear Fresnel
reflector solar concentrating hot water system with varying width reflectors,
Case Studies in Thermal Engineering 14 (2019).

 G.S. Chaitanya Prasad, K.S. Reddy, T. Sundararajan, Optimization of

solar linear Fresnel reflector system with secondary concentrator for uniform
flux distribution over absorber tube, Sol. Energy 150 (2017).

 M. Ghodbane, et al., Evaluating energy efficiency and economic effect of

heat transfer in copper tube for small solar linear Fresnel reflector, J. Therm.
Anal. Calorim. 143 (6) (2020).

 M. Marefati, M. Mehrpooya, Introducing and investigation of a combined

molten carbonate fuel cell, thermoelectric generator, linear fresnel solar
reflector and power turbine combined heating and power process, J. Clean.
Prod. 240 (2019).

 G.S. Chaitanya Prasad, K.S. Reddy, T. Sundararajan, Optimization of

solar linear Fresnel reflector system with secondary concentrator for uniform
flux distribution over absorber tube, Sol. Energy 150 (2017).

 S.S. Sahoo, S. Singh, R. Banerjee, Steady state hydrothermal analysis of the

absorber tubes used in Linear Fresnel Reflector solar thermal system, Sol.
Energy 87.
 CHAPTER - 3
3.1 Research Methodology
Research Methodology for Linear Fresnel Reflector (LFR) Solar Water Heater

1. Introduction

The research methodology outlines the systematic approach for studying and
analyzing the performance, design, and feasibility of a Linear Fresnel Reflector (LFR)
solar water heater. This methodology involves experimental testing, simulation, data
analysis, and evaluation to ensure comprehensive results.

2. Research Objectives

The primary objectives of the study are:

1. To evaluate the thermal performance and efficiency of the LFR solar water
heater.

2. To identify the impact of key design parameters on system performance.

3. To assess the cost-effectiveness and environmental benefits of the system.

4. To compare the LFR system with other solar water heating technologies.

3. Literature Review
Conduct a thorough review of:

1. Existing Research Papers: Study prior work on LFR technology, solar water
heaters, and concentrated solar systems.

2. Patents and Innovations: Analyze patents related to LFR designs and

improvements.

3. Design Principles: Understand the optical, thermal, and mechanical principles

governing LFR systems.

4. Gaps in Research: Identify areas where current knowledge is limited, such as

system scalability or optimization for specific climates.

4. Research Design

4.1 Experimental Design

An experimental setup will be constructed to study the performance of an LFR solar

water heater.

Steps:

1. Prototype Construction:

o Construct an LFR system with key components such as flat or slightly

curved mirrors, a receiver tube, a support structure, and a thermal
storage tank.

o Use materials like highly reflective aluminum for mirrors and copper
or steel for the receiver tube.

2. Instrumentation:

o Install sensors to measure:

 Solar irradiance (using pyranometers).

 Inlet and outlet water temperatures.

 Ambient temperature and wind speed.

 Flow rate of the working fluid.

3. Control Variables:
 o Maintain controlled conditions such as flow rates and initial water
temperatures.

o Test the system under varying solar radiation and environmental

conditions.

4. Testing:

o Record system performance over a typical day.

o Measure the amount of water heated, energy collected, and thermal

losses.

4.2 Simulation Design

Simulations will complement experimental work to explore additional scenarios.

Steps:

1. Use simulation software such as TRNSYS, ANSYS, or MATLAB.

2. Create a model of the LFR system with:

o Optical modeling for solar radiation concentration.

o Thermal modeling for heat transfer and fluid dynamics.

3. Simulate:

o Seasonal performance in different geographic locations.

o Effects of varying design parameters (e.g., mirror tilt angle, receiver

height).

4. Validate simulation results with experimental data.

5. Data Collection

5.1 Parameters to Measure

 Solar Parameters:

o Solar irradiance and angle of incidence.

  Thermal Parameters:

o Inlet and outlet fluid temperatures.

o Heat transfer efficiency of the receiver.

 Flow Parameters:

o Volume and flow rate of water.

 Environmental Parameters:

o Ambient temperature, wind speed, and humidity.

5.2 Tools and Equipment

 Pyranometers and thermocouples for solar and temperature measurements.

 Flow meters for water circulation measurements.

 Data acquisition systems for continuous monitoring.

6. Analysis Methods

6.1 Thermal Performance Analysis

1. Efficiency Calculation:

o Thermal efficiency (η): η = (m × Cp × ∆T) / (A × G)

 m: Mass flow rate of water.

 Cp: Specific heat of water.

 ∆T: Temperature rise of water.

 A: Aperture area of mirrors.

 G: Solar irradiance.

2. Heat Losses:

o Quantify losses due to convection and radiation from the receiver.

6.2 Simulation Analysis

 Compare simulated performance under ideal conditions to real-world data.

  Use sensitivity analysis to study the impact of design variables.

6.3 Comparative Analysis

 Compare the performance of the LFR system to other technologies (e.g.,

parabolic trough, flat-plate collectors) based on efficiency, cost, and feasibility.

7. Cost and Environmental Assessment

7.1 Economic Feasibility

1. Cost Analysis:

o Initial investment costs.

o Maintenance and operational costs.

o Payback period estimation.

2. Cost-Effectiveness:

o Calculate cost per unit of energy (e.g., $/kWh).

7.2 Environmental Impact

 Measure the reduction in carbon emissions by replacing conventional water

heating methods.

 Assess the lifecycle environmental footprint of the LFR system.

8. Validation and Verification

 Cross-verify experimental results with simulation outcomes.

 Ensure consistency with data from previous studies and field trials.

9. Reporting and Documentation

1. Present findings through:

o Graphs and charts showing performance metrics.

o Tables summarizing data and comparisons.

2. Discuss:

o Key insights and implications for the solar energy sector.

 o Recommendations for improving LFR technology.

This research methodology ensures a rigorous, systematic approach to studying the

design, performance, and feasibility of LFR solar water heaters, paving the way for
advancements in solar thermal technologies.

3.2 Progress of work:

Thermal Modelling:
The solar reflector is composed of five elements, they are as follows:
Exterior support frame: it's used to support the weight of the horizontal base with its
reflecting mirrors and the absorber tubes with all its components. It is made of four
angle section metal bars (Length=1000 mm, Width=30 mm, Height=30 mm and
thickness=02 mm).

Interior support frame: it's one of the most important components in this device
because it bears the reflecting mirrors. It is consisted of four hollow square metal bars
(Length=800 mm, Width=30 mm, Height=30 mm and Thickness=1 mm).

Reflecting mirrors: the experimental device contains eleven reflective mirrors strips
(700 mm×80 mm) to redirect and concentrate the direct solar radiation towards a
fixed absorber tube.

Trapezoidal cavity: the trapezoidal cavity is a folded galvanized sheet

(Length=1200 mm, Width=500 mm and thickness=1.5 mm) in the form of (U). The
vacuum inside it was filled with polystyrene (Length=1500 mm, Width=500 mm and
thickness=50 mm). The white Formica plates (Length=850 mm, Width 1=100 mm,
Width 2=125 mm and thickness=3 mm) was glued on polystyrene with silicone and
double-sided sellotape. The all gave us a trapezoidal shape presents the dimensions of
trapezoidal cavity with the four absorber tubes.

Absorber tubes: they are made of a copper pipe (Ø20/22 mm and length (L) equal to
1600 mm) and placed in the cavity, there are four tubes; they are plated with painted
black and covered by selective suitable surface. The selective layer was used on the
absorber to increase its operation temperature and efficiencies.
 Fig. 3.2.1

The absorber tubes are made of copper covered with an adapted a selective coating;
they are placed along the focal line of the linear Fresnel concentrator. The heat
exchange existing in the system takes place between the heat transfer fluid and the
absorber tubes.

These the several simplifying assumptions were used during the calculation:

 The fluid flow is one-dimensional.

 The all properties of the fluid (water) depend on the temperature.
 The temporal variation in the thickness of the absorber tubes is negligible.
 The exchange by conduction in the absorber is negligible.
 The thermal flux is uniformly distributed on the level of the absorber tubes.
 Fig. 3.2.2

Heat exchange between the absorber and the fluid

The temperature modeling is based on the energy balances, which are characterized
by the differential equations of fluid temperatures (TF) and absorber temperature
(TA). presents the thermal power emitted by the sun and received by absorber tubes

qabsorbed=0.7αρmγSeDNI√1−cos2(δ)sin2(h)

Factor α is the absorption coefficient of the absorber tubes, ρm is the reflectance

factor of the mirror, γ is the interception factor and DNI is the direct solar radiation, δ
is declination angle, h is the sun altitude.

The declination angle (δ) is the angle between the terrestrial equator planes and the
earth-sun direction. This angle varies throughout the year symmetrically of –23°26′ to
23°26′ . The declination (δ) is the point's latitude of the earth which are achieved by
the midday sun (noon-solar), it is directly related to the number of day (j) of the year
as it turns out in the.

δ=23,45°sin[0,980°(j+284)]

But the height of the sun (h) is the angle that the sun direction with its projection on
the ground, it varies from 0° to 90° in the southern hemisphere (Nadir), vanishes at
sunrise and sunset and is maximal in the south-solar. It's in term of the latitude (ϕ) and
the hour angle (ω)

h=arcsin(cosφcosδcosω+sinφsinδ)

Se is the effective surface of mirror aperture; this surface can calculate by the
following equation :

Se=∑kn=1W.cos(θt−θn)

Where W is the mirror width, θt is the angle in the transversal plane and θn is the slope
angle of an nth mirror element. enables us to calculate the heat flux exchanged by
convection between the cylindrical absorbent tubes and fluid (water).

qgain=hFAA,int(TA−TF)

It was observed that associated with the coefficient of heat exchange by convection
(hF), this coefficient related to the mode of fluid flow. So, h F given by the following
expression:

hF=Nu×KFDA,int

Where KF presents the thermal conductivity of the fluid.

In this study the flow regime of the water is laminar (Re<2300), the Nusselt
Number (Nu) in type of flow is given

Nu=3.66+0.0668ReFPrDA,intL1+0.04(ReFPrDA,intL)23

The factor (ReF) presents Reynolds number which is expressed by the following
relation :

ReF=4×ρF×QVπ×DA,int×μF

which indicates the dynamic viscosity of the fluid, where the analogy of Reynolds
number is established by the intimate bond viscosity phenomena and heat transfer.
The Prandtl number (Pr) will be written in the following form

PrF=νFαFPrF=νFαF

νF is the kinematic viscosity, it's defined by

νF=μFρFνF=μFρF
The fluid thermal diffusivity (αF) is defined by

αF=KFρF×CFαF=KFρF×CF

The energy balance for the heat transfer fluid circulating in the absorber tubes is
expressed by the following relationship

ρF×CF×π×DA,int∂TF(X,t)∂t=qgain−ρF×CF×QV∂TF(X,t)∂XρF×CF×π×DA,int∂TF(X
,t)∂t=qgain−ρF×CF×QV∂TF(X,t)∂X

The initial conditions and boundary conditions of are

{TF(0,t)=TF,inlet(t)=Tamb(t)TF(X,0)=TF,initial(t)=Tamb(0)
{TF(0,t)=TF,inlet(t)=Tamb(t)TF(X,0)=TF,initial(t)=Tamb(0)

Heat exchange between the absorber and the ambient:

The energy balance for the absorber tube is given by the following equation

ρA×CA×π×(DA,ext−DA,int)∂TF(X,t)∂t=qabsorbed(t)−qout(X,t)
−qgain(X,t)ρA×CA×π×(DA,ext-DA,int)∂TF(X,t)∂t=qabsorbed(t)−qout(X,t)
−qgain(X,t)With, (qout) is the heat quantity at the output of the absorber tube element.
(15)qout(X+ΔX,t)=ρF×CF×QV×ΔX×TF(X+ΔX,t)qout(X+ΔX,t)=ρF×CF×QV×ΔX×T
F(X+ΔX,t)

presents the initial conditions of

TA(X,0)=TA,initial(t)=Tamb(0)TA(X,0)=TA,initial(t)=Tamb(0)

illustrated the global heat exchange between the absorber and the environment.

qext=qext,conv+qext,rayqext=qext,conv+qext,ray

The convection exchange between the absorber and the environment (q ext, conv ) can
account by using

qext,conv=hwAA,ext(TA−Tamb)qext,conv=hwAA,ext(TA−Tamb)

According to McAdams (1954) [22], the heat transfer coefficient of wind (h w) is given
by

hw=5.7+3.8Vwhw=5.7+3.8Vw
The radiation exchange between the absorber tubes and the environment (q ext, ray) can
calculate by

qext,ray=εAσAA,ext(T4A−T4amb)qext,ray=εAσAA,ext(TA4−Tamb4)

For the analysis and dissemination of equations, the finites differences method was
used to discretize the principal equations of the phenomenon. and present the
equations of the unknowns (TA) and (TF) after deployment and analysis of the
previous equations.

TF,j(t)=−QVπ×DA,int×ΔXTF,j(t)+(ρF×CF)|TF,j−1×QV(ρF×CF)|
TF,j×π×DA,int×ΔXTF,j−1(t)+1(ρF×CF)|
TF,j×π×DA,int×ΔXhF×π×DA,int(TA,j−TF,j)TF,j(t)=−QVπ×DA,int×ΔXTF,j(t)+
(ρF×CF)|TF,j−1×QV(ρF×CF)|TF,j×π×DA,int×ΔXTF,j−1(t)+1(ρF×CF)|

To solve this system reformulates of all relations, can be written in the form of a
matrix as follows: [A].[T]=[B], where [A] represents the coefficient matrix, [T] is the
vector of unknowns and [B] is the vector of the second member (B is not null). The
method of Gauss-Seidel with total pivot was adapted for the resolution of this system,
because this method converges rapidly and removes the matrix inversion.

The thermal losses coefficient:

Solar energy which descends on the absorber tubes is not entirely transmitted to the
fluid; a part is dissipated in the form of thermal losses between the absorber and
ambient air. The thermal loss coefficient is given by the following relation :

UL=εAσ(T2A+T2amb)(TA+Tamb)

With (σ) is Stefan-Boltzmann constant (σ=5.66897 10–8 W/m2 K4).

Thermal efficiency:

The thermal efficiencies of our concentrator are given by the following equation

η=ηopt−ULAA,ext(TA−Tamb)DNI×AC

Where ηopt is the optical efficiencies of the collector (LFR), it can be calculated by

ηopt=0.7αρmγ√1−cos2(δ)sin2(h)
The thermal efficiency decreases when the solar insolation increases, this decrease is
due to thermal losses that believe with rising water temperatures respectively at the
inlet and outlet of the absorber tube.

So, the thermal losses increase rapidly when:

 The temperature of the inlet water increases.

 The temperature of the absorber tubes increases.

Using an absorber tube with selective surface allows very significant reduction of
these losses. In our case, the emissivity of our absorber tubes in the vicinity of 0.12,
this value of emissivity could reduce greatly the thermal losses by radiation. In order
to reduce heat loss, the transparent cover can be used around the absorber, because the
transparent cover (glass tubes) is used to reduce convection losses between the
absorber tubes and ambient air through the restraint of the stagnant air layer between
the absorber tubes and the glass tubes. Also, it reduces radiation losses from the
collector because the glass tubes are transparent to the shortwave radiation received
by the sun, but it is nearly opaque to long-wave thermal radiation emitted by the
absorber tubes (infrared greenhouse effect). the usage of glass tube around the
absorber tubes in parabolic trough concentrator was used in a previous work this
technique gives very good results, where the efficiency of the concentrator exceeded
60%.

There is another method to reduce losses by convection by creating vacuum

(technique of suppressing convection) between the absorber tube and glass tube;
where the vacuum envelope reduces convection and conduction losses between them.
Methodology:
 CHAPTER – 4

4.1 Expected Outcomes:

• Using MATLAB Software we will be analyzing the Numerical Simulation
using in which weather data is entered into the MATLAB code as an
approximate Function vs. Time and not in their real terms.

• Compare the heat storage capacity for different heat transfer fluids.

• Analyse the small LFR solar water heater to store the hot water from the
captured solar energy.

• A key outcome of the project will be the development of a sustainable water

heating solution that reduces the reliance on fossil fuels, contributing to a
reduction in greenhouse gas emissions.

• Reduction in installation and operational costs through the use of simple

reflector designs and locally available materials.

4.2 Future Scope:

1. Large-Scale Deployment:
As the technology proves effective at small and medium scales, future efforts can
focus on scaling up the LFR solar water heater for large-scale applications, such
as district heating, industrial process heating, and commercial complexes, which
would allow for a significant reduction in energy consumption.

2. Integration with Hybrid Systems:

Future projects could explore integrating LFR systems with other renewable
energy sources, such as photovoltaic (PV) panels or wind power, to create hybrid
energy systems that ensure stable energy production even during cloudy or low-
wind conditions.

3. Improved Materials and Design:

Continued research into advanced materials for reflectors, receivers, and storage
systems can enhance the efficiency, durability, and cost-effectiveness of LFR
systems. For example, the development of lightweight, corrosion-resistant
 materials or advanced reflective coatings can reduce maintenance needs and
increase system longevity.

4. Automation and Smart Controls:

Incorporating IoT (Internet of Things) technology and advanced control systems
could help monitor and optimize LFR systems in real time. Automated tracking,
remote diagnostics, and predictive maintenance could significantly improve the
system’s overall performance and reliability.

5. Thermal Storage Systems:

Research into more efficient and cost-effective thermal energy storage solutions,
such as phase-change materials (PCMs) or advanced molten salt storage, could
make LFR solar water heaters more reliable during periods of low sunlight,
improving their applicability for 24-hour heating.

6. Customization for Different Climates:

Future projects can focus on adapting LFR systems to operate efficiently in
different geographical and climatic conditions, considering variations in sunlight
intensity, temperature, and humidity. Systems could be tailored to optimize energy
production based on location-specific data.

7. Cost Reduction and Commercialization:

As the technology matures, efforts to reduce manufacturing and installation costs
can lead to a broader market adoption, making LFR solar water heaters a more
affordable option for both residential and commercial consumers.

8. Integration with Building Systems (BIPV/BIST):

LFR systems could be integrated with building architecture, such as in the form of
Building-Integrated Solar Thermal (BIST) systems, where the solar collectors are
incorporated into the building’s structure, improving space utilization and
aesthetics.

9. Global Expansion:
Expanding LFR solar water heaters to regions with high solar radiation but low
access to conventional energy sources could provide a sustainable, off-grid
solution to meet heating demands, especially in developing countries.
10. Policy and Market Development:
Future work could involve advocating for supportive policies and incentives to
promote the use of LFR solar water heaters, thus creating a favourable
environment for their widespread adoption and driving market growth.

4.3 Schedule of activity of next semester:

References:
1. Nixon J.D., Dey P.K., and Davies P.A., 2013, "Design of a novel solar thermal
collector using a multi-criteria decision-making methodology," Journal of
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performance evaluation of a linear fresnel reflector solar concentrator," Solar
& Wind Technology, 6, pp. 589-593.
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Renewable Energy, 39, pp. 198-206.
8. [8] Yanhua L., Gu S., Mingxin L., Zhen D., Shuping C., and Chunyuan M.,
2011, "Thermal performance analysis of linear fresnel reflector concentrator
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 9. Reynolds D.J., Jance M.J., Behnia M., and Morrison G.L., 2004, "An
experimental and computational study of the heat loss characteristics of a
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10. Burkholder F., and Kutscher C., 2009, "Heat Loss Testing of Schott's 2008
PTR70 Parabolic Trough Receiver," NREL Report No. TP-550-45633.

Submitted by:
S. No. Students Names Roll No. Signature

1. DHRUV KAUSHIK 2100910400014

2. KARTIK SINGH 2100910400017

3. NAITIK SINGH 2100910400021

4. NITISH CHAUHAN 2100910400025

Comment of Supervisor:

Name of Supervisor(s): Signature of Supervisor(s)

Projector Coordinators: Head of the Department:

Dr. Neelam Khandelwal Dr. Prashant Chauhan