A cfd investigation and pressure correlation of solar air heater

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME

401

A CFD INVESTIGATION AND PRESSURE CORRELATION OF

SOLAR AIR HEATER

Anup Kumar*, Anil Kumar Mishra**

* Dept. of Mechanical Engineering, Birla Institute of Technology, Mesra, India

**Dept. of Mechanical Engineering, Birla Institute of Technology, Mesra, India

ABSTRACT

The intent of the present work is to study the behavior of solar air heater with and

without porous media and also to compare their performance under different set of

conditions, obtained by changing various governing parameters like air mass flow rate, inlet

air temperature, spacing between top cover and absorber plate and intensity of solar radiation.

The problems have been solved by the Finite Difference Method. This study presents the

mathematical model for predicting the heat transfer characteristics and the performance of

solar air heater with and without porous media. The solar air heater with porous media gives

higher thermal efficiency than without porous media. The thermal conductivity of porous

media has significant effect on the thermal performance of the solar air heater. The work has

been carried out on GAMBIT and FLUENT software as it is standard tool for flow analysis

and widely acceptable. A double pass flat plate solar air heater model is prepared subjected to

the relative loads and constraints and results are obtained for the proposed models.

Keyword: Solar Air Heater, Porous Media, Pressure Drop, CFD

1. INTRODUCTION

Energy is a vital need in all aspects and increasing demands for energy is not

sufficient for basic requirement. Therefore, human being is looking for renewable source of

energy such as solar energy, geothermal energy, and wind energy. Humans have always used

the Solar energy is the radiation produced by nuclear fusion reactions in the core of the sun.

This radiation travels to earth through space in the form of energy called photons. Solar

energy collectors are special kind of heat exchangers that transform solar radiation energy to

internal energy of the transport medium. The major component of any solar system is the

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING

AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)

ISSN 0976 – 6359 (Online)

Volume 4, Issue 2, March - April (2013), pp. 401-417

© IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com

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402

solar plate collector. This is a device which absorbs the incoming solar radiation converts it

into heat, and transfers this heat to a fluid (usually air, water, or oil) flowing through the

collector. The solar energy thus collected is carried from the circulating fluid either directly

to the hot water or space conditioning equipment or to a thermal energy storage tank from

which can be drawn for use at night and/or cloudy days. Solar collector may be classified

according to their collecting characteristics, and the way in which they are mounted and

depends on the type of working fluid which is employed into the collector. A collector

generally uses liquid or a gas as working medium to transfer heat. The most common liquids

are water or a water-ethylene glycol solution. The most common gas is air.

Figure 1 Exploded view of the Flat plate collector

Depending upon the air passage in the solar air heater the air heaters can be classified in the

following ways-

Single glass cover air heater- In this type of solar heater there is only one glass surface on

the top and the absorber is below the glass plate. The air flows between the glass plate and

the absorber plate. (Figure 2)

Double glass cover air heater- This type of air heater includes two glass cover on the top

surface and the air flows between the glass cover and the absorber plate. (Figure 3)

Double pass air heater without porous matrix- In this type of solar air heater, air flows

between two glass plate in one direction and then between the glass plate and the absorber

plate in the opposite direction. (Figure 4)

Double pass air heater with porous matrix- The constructional part of solar air heater with

porous media same as solar air with non- porous media but only difference is that the porous

material is used in second pass of air flow. Porous materials have become increasingly

attractive for application in high temperature heat exchangers. The high effectiveness of the

heat exchange mechanism is mainly due to the intimate contact in the interstices between the

gas particles and porous plate. (Figure 5)



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A porous medium is a material containing pores (voids). The skeletal portion of the material

is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or

gas). The skeletal material is usually a solid, but structures like foams are often also usefully

analyzed using concept of porous media. A porous medium is most often characterized by its

porosity. It is also observed that thermal efficiency of solar air heater can be increased by

minimizing heat loss from collector to maximize heat transfer from absorber [8]. To provide

a counter flow passage an extra top cover can be provided to increase volumetric heat transfer

co-efficient.

2. MATHEMATICAL FORMULATION

In the present study, at first mathematical model is obtained by the application of the

governing conservation laws. The heat balance is accomplished across each component of

given solar air heater i.e., the glass covers, the air stream and the absorber plate. The heat

balance for the air stream yields the governing differential equations and the associated

boundary conditions. The main idea is to minimize heat losses from the front cover of the

collector and to maximize heat extraction from the absorber. Porous media forms an

extensive area for heat transfer, where the volumetric heat transfer coefficient is very high; it

will enhance heat transfer from the absorber to the airstream. In the design of this type of

collector, this combines double air passage and porous media pressure drop should be

minimized[11]. The basic physical equations used to describe the heat transfer characteristics

Figure 2 Single glass cover air heater Figure 3 Double glass cover air heater

Figure 4 Double pass air heaters without

porous matrix

Figure 5 Double pass air heaters

with porous matrix



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are developed from the conservation equations of energy. The heat and fluid flow are

assumed steady and one dimensional. It is because of the radiation heat exchange terms that

render the problem non-linear hence making the exact solution cumbersome. So a numerical

approach is applied which would give a solution with a fairly good accuracy.

The model is based on the assumption made by Naphon and Kongtragool[2] -

� Flow of air is steady.

� Outside convective heat transfer coefficient is constant along the length of solar air

heater.

� Inside convective heat transfer coefficient is constant along the length of solar air

heater.

� Thermal conductivity of the porous media is constant along the length of solar air

heater.

� The temperatures of the cover and plates vary only in the direction of fluid flow (x-

direction);

� The side losses are negligible and leakage of air to/or from the collectors is negligible.

� Ideal gas with constant specific heat.

� The air flow is forced, steady and one-dimensional and the thermo-physical properties

of air and packed bed are independent of temperature.

� The plug flow condition exists throughout the length of heater, i.e., the air velocity in

the channel at any section is constant.

� The porous absorber and the air stream are in thermal equilibrium because the value

of volumetric heat transfer coefficient in the pores of the porous matrix is very high.

2.1 Factors Affecting Efficiency of flat Plate Solar Air Heater

2.1.1 Porous Medium - The solar air heater with the porous media gives 25.9%

higherthermal efficiency than that without porous media. The thermal conductivity of porous

media has significant effect on the thermal performance of the solar air heater [2].

Asporous mediumis characterized by its porosity or measure of voids and the skeletal portion

of the material is often called the "matrix" or "frame". The measure of void isa fraction of the

volume of voids over the total volume, between 0–1, or as a percentage between 0–100

percent. There is also a concept of closed porosity andeffective porosity, i.e., the pore space

accessible to flow.[7]

2.2.2 Transmissivity-Absorptivity Product-Transmissivity-Absorptivity product is defined

as the ratio of the flux absorbed in the absorber plate to the flux incident on the cover system,

and is denoted by the symbol (τα). Out of fraction τα transmitted through the cover system, a

part is absorbed and a part reflects back diffusively. Out of the reflected part, a portion is

transmitted through the cover system and a portion reflected back to the absorber plate. The

process of absorption and reflection at the absorber plate surface (figure 6) goes on

indefinitely, the quantities involved being successively smaller.

Thus, the net fraction absorbed (τα) = τα�1 � �1 � α�ρ��1 � α�ρ� �]

� τα

� �� α�ρ�(1)



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Figure. 6 Process of Absorption and Reflection

2.2.3 Overall Loss Coefficient- The heat loss from the collector in terms of overall loss

coefficient defined by the equation

q� � U�A��T�� T�� (2)

The heat loss from the collector is the sum of heat loss from the top, bottom and the sides.

Thus q� � q� � q� � q� (3)

q� � U�A��T�� T�� (4)

q� � U�A��T�� T�� (5)

q� � U�A��T�� T�� (6)

U� � U� � U� � U� (7)

2.2.4Top loss coefficient ��- The top loss coefficient is evaluated by considering convection

and radiation losses from the absorber plate in the upward direction. For the purpose of

calculation, it is assumed that the transparent covers and the absorber plate constitute a

system of infinite parallel surfaces and that the flow of heat is one-dimensional and steady. It

is further assumed that the temperature drop across the thickness of the covers is negligible

and the interaction between the incoming solar radiation absorbed by the covers and the

outgoing loss may be neglected. The outgoing re-radiation is of larger wavelength. For these

wavelengths, the transparent cover is assumed to be opaque.Sukhatme [3] suggested thatheat

transferred by convection and radiation at different layers as follows-

(a) The absorber plate and the first cover; �� h� "��T�� T"�� σ �# $% #&�% �� ' ( )� '&( �(8)

(b) The two glass covers; �� h"� "�T"� � T"� � σ �#&�% #&*% �� '&( )� '&( � (9)

(c) The second glass cover and the sky; �� h��T" � T�� σε"�T"+ � T�,-+ � (10)



406

Sukhatme [3] also suggested the empirical relation for the top loss coefficient as-

U� � � ./ 01 $23

1 $415678 9:.<< �

�=5> � � �

σ�# $* )#5*��# $)#5��

ε 7:.::?6��4ε �)*6784�ε& .] (11)

Where, f � �1 � 0.04h� � 0.0005h��1 � 0.091�M

C � 365.9�1 � 0.00883β � .0001298β� M=number of glass covers

2.2.5Heat transfer coefficient at the top cover- The convective heat transfer coefficient

(h�) at the top cover has been calculated from the following empirical correlation suggested

by McAdams [4],

h� � 5.7 � 3.8V (12)

Where, V is the wind speed in m/s.

An another important dimensionless correlation have been suggested by Sparrow and

hiscoworkers [5] given as,

j � 0.86�RePQ � �/ ; (13)

Where, j=j-factor given by =5ρS TPr/W

RePQ= Reynolds number based on the characteristics dimension L � 4A"/C" A"=Collector gross area C"=Circumference associated with the collector gross area.

2.2.6Sky Temperature- As suggested by Sukhatme [3] Sky temperature is usually

calculatedfrom empirical relation in which temperature are expressed in Kelvin

T�,- � T� (14)

2.2.7Bottom loss coefficient(Ub)-The bottom loss coefficient is calculated by considering

conduction and convection losses from the absorber plate in the downward direction[6]. It

will be assumed that the heat flow is one dimensional and steady (Fig.7). In most cases, the

thickness of thermal insulation is provided such that the thermal resistance associated with

conduction dominates. Thus, neglecting the convective resistance at the bottom surface of the

collector casing. U� � KZ/δ�

Where, kZ=Thermal conductivity of the insulation

δ�= Thickness of the insulation.



407

Figure 7. Bottom and side losses from a flat-plate

2.2.8 Side loss coefficient (�\)-The assumptions applied for side loss coefficient is

conduction resistance dominates and that the flow of heat is one dimensional and steady state.

The one-dimensional approximation can be justified on the grounds that U�is always much

smaller than theU�. If the dimensions of the absorber plate are L1 x L2 and the height of the collector is L3 and

assuming that the average temperature drop across the insulation is (T�� T��/2 andthe

thickness of this insulation isδ�.

q� � 2LW�L� � L�kZ�T�� T��2δ�

U� � 2LW�L� � L�kZ�T�� T��L�Lδ�

2.3 Governing Equation Under steady state operating conditions, the energy balance for the conventional and

counter flow collectors as suggested by Mohammad [1] and applying the finite difference

method on the proposed double-pass flat-pate solar air heaters without and with porous media

which are as follows:

For top glass cover:

G.E:Iα" � h��T"� � T�� h^"��T"� � T^�� h_.""�T"� � T"�...(15)

For down flow air stream:

G.D.E.: mc ��8��b � h^"��T"� � T̂ �� h^"�T" � T̂ ��…(16)

For second glass cover

G.E.: Iα"τ" � h_.""�T" � T"�� h^�"�T" � T^�� h^"�T" � T^� � h_.�"�T" � T�� …(17)

For up follow air stream:

G.D.E.: mc �#8*�b � h^�"�T" � T^� � h^��T� � T^�...(18)



408

For absorber plate:

G.E.: Iα�τ" � h^��T� � T^� � h_.�"�T� � T"� � U��T� � T��…(19)

Double-pass flat-pate collector with porous media

For top glass cover:

G.E: Iα" � h��T"� � T�� h^"��T"� � T^�� h_.""�T"� � T"�...(20)

For down flow air stream:

G.D.E.: mc ��8��b � h^"��T"� � T̂ �� h^"�T" � T̂ ��…(21)

For second glass cover

G.E.: Iα"τ" � h_.""�T" � T"�� h^�"�T" � T^�� h^"�T" � T^� � h_.�"�T" � T�� ...(22)

For up flow air stream:

G.D.E.:

mc �#8*�b � Kc^^ �*#8*�b* � h^"�T" � T^� � U��T� � T^� � Iα�τ"τ"...(23)

For the sake of convenience the heat transfer coefficients between the air stream and the

covers and between the air stream and the absorber plate are assumed equal and can be

calculated as follows:

h^�"� � h^�" � h^" � h^� � h^…(24)

The air density: ρ � d5e#5…(25)

Kinematic viscosity: ν � µ

ρ…(26)

Thermal diffusivity: α � ,ρ" …(27)

Prandtl number: P_ � ν

α…(28)

Hydraulic diameter: D= � +�8d � 2D…(29)

Reynolds number: Rc � ρghiµ

� �µ

…(30)

Grashof Number =jk∆m<n* …(31)

Nusselt number; Nu � 0.0333 Rcq.r P_q.WW…(32)



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Convective heat transfer coefficient between any two surfaces

h_� � σ�#�)#*��#�*)#**��ε�) �

ε* �…(33)

When the air flows through the channel in the air heater, due to friction the air pressure drop

along the of the flow channel. This pressure drop across the duct is given by the:

p � f 3�<ρ9 3P<h<9…(34)

Where, f � fq � y�hP) …(3.40)

The value of fq and y are:

fq=24/Re, y=0.9 for Laminar flow (Re<2550) …(34)

fq = 0.0094, y =2.92Re-0.15

for transitional flow (2550<Re<104) …(35)

fq = 0.059 Re-0.2

, y =0.73 for turbulent flow (104<Re<10

5) …(36)

So far as pressure drop (pumping power) is concerned, the counter flow solar air heater has a

U-turn section and extra-length for air passages. Hence the extra pressure drop is introduced

by this design. The pressure drop in the u-section can be calculated as:

u p � v�*ρh*…(37)

K=1forU-section

The pumping power can be calculated asW � �u�ρ

…(38)

3. MODELING AND ANALYSIS

The finite difference method (FDM) is used to solve the differential equations and

hence to simulate a given solar air heater. In FDM technique, the first step involves the

transformation of the actual physical domain into the computational grid. Second step is to

transform the differential equations into difference equations, which along with the equations

obtained by heat balance across the covers and the absorber are the simultaneous nonlinear

algebraic equations. The next step is to solve those numerically using gauss elimination

method. The solution is obtained in the form of nodal temperatures for the covers, the air

streams and the absorber. Study has been extended by changing the various governing

parameters like the air mass flow rate, the inlet air temperature, the depth of the collector duct

and the intensity of solar radiation and finally the performance characteristics have been

obtained. A computer program is developed using Dev C++ programming language based on

algorithm and flow chart.



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3.1 Technical Specifications Input Parameters and Constants for the proposed model.

Sl.No. Input Parameters Values

1. Length of solar air heater, L(m) 2.0

2. Width of solar air heater, w(m) 1.0

3. Depth of upper channel solar air heater, D1(cm) 4.5,5.5,6.5

4. Depth of lower channel solar air heater, D2(cm) 4.5,5.5,6.5

5. Emissivity of glass covers, ε" 0.92

6. Emissivity of absorber plate and packed bed,ε� 0.92

7. Transmissivity of glass cover and absorber,xy z{ x| 0.92

8. Absorptivity of glass cover,α" 0.06

9. Absorptivity of absorber,α� 0.92

10. Inlet air temperature, Ti(K) 288,303

11. Air mass flow rate per unit width, m (kg/m s) 0.01-.2

12. Back insulation thickness(m) 0.05

13. Side insulation thickness(m) 0.05

14. Porosity of Porous medium( Glass wool) 0.8

15. Plate Type Flat Plate

3.2 Proposed Model The design of thermal equipment must focus on a combination of numerical and

experimental techniques hence, a three-dimensional numerical model was developed using

the CFD numerical package FLUENT. The proposed model is modeled by using CATIA V5

R19 which is used for analysis by applying boundary conditions. An analysis of proposed

model is also performed by using CFD package as CFD is concerned with the efficient

numerical solution of the partial differential equations that describe fluid dynamics. A model

for virtual prototyping of thermal equipment must be detailed enough in order to consider all

the main physical phenomena that are taking place as well as giving results in a reasonable

computational time. The mesh size is critical for CFD analysis, especially when dealing with

natural convection.

3.3 Algorithm for Computer Program

Following steps are involved in the simulation of double pass flat plate solar air heater:

Step 1: Enter values of m, L, D, T�, p�, R, h�, µ, U�, α", α�, τ",σ, c�, k^. Step 2: Select the type of heater.

Step 3: Calculateν, P_, Rc, N~, h^. Step 4: Initialize with T^�0> � TZ, h_.""�i> � 5, h_.�"�i> � 5 for all i. Step 5: Solving the finite difference equations for a given solar heater to calculate the nodal

temperatures by using the appropriate boundary conditions and gauss elimination method for

solving the simultaneous equations as described above. After that following parameter are

calculated.

P � f �mWρ��LWDW�

η � mc�∆TIA



411

Step 6: Once all these temperature are obtained, the following performance characteristics are

obtained:

1. ∆P Vs m

2. η vs �|

3. η Vs m

4. �#� Vs m

5. � �� m�

Figure 8. 3-D Model of Solar Air Heater

Figure 9. Mesh generation of 3-D Model



412

3.4 Flowchart for the simulation of double pass flat plate solar air heater

Start

Obtain the following characteristics

1. ΔP Vs m

2. η vs �|

3. η Vs m

4. �#� Vs m

5. � �� m�

End

ΔT� � max�T"��i> � T�� Δ�|� � max ��|��> � ��>� P � f �mW

ρ � �LWDW�

� � ��|��q � �� ;

Obtain:

Input the Values of

�, �, �, �� , �� , �, �� , �, ¡ , ¢y , ¢|, xy , £, �|, ¤�

Substituting these values in the set of equations obtained by

energy balance for a given solar air heater and solving them

simultaneous by gauss-elimination method to evaluate T"�, T", T^�, T^ and T�

n; ρ; ν; ¢; ©̈; �ª;«¬

Calculate



413

4. RESULT AND DISCUSSION

The majority of the heat transfer occurred at the bottom section of the solar air

heater,rather than near the level between the inlet fluid temperature and the fluid inside

thesolar air heater.The variation of pressure drop with different mass flow andefficiency

withmass flow rate, plate temperature, solar radiation for both solar air heater without porous

and with porous media are shown in graph 10, 11, 12, 13 and 14.The pressure drop increases

in both solar air heater without porous and with porous media with increase in mass flow rate.

Figure 10. Variation of Pressure with Mass flow rate

Figure 11. Variation of efficiency with Mass flow rate



414

Figure 12. Variation of efficiency with plate temperature

Figure 13. Variation of efficiency with dT/I

Figure 14. Variation of dT/I with mass flow rate



415

Figure 15. Variation of Pressure Drop across solar Air Heater

Figure 16. Variation of Air Velocity across Solar Air heater

5. CONCLUDING REMARKS

The variations of pressure in solar air heater model with different mass flow rate for

non-porous and porous media are shown in figure 10 for different depth, inlet temperature

and solar radiation. It is concluded that outlet temperature is decreasing with increase in mass

flow rate. It is found that the use of porous media in lower channel increases the outlet

temperature. The use of porous media in solar air heater increases the system efficiency and

outlet temperature. This increase, results an increase in the pressure drop for solar collector

with porous media, which means increasing of the cost of the pumping power expanded in

the collector. But this factor has no significant for low flow rates.



416

Nomenclature Af-Front Area

Cp- Specific heat capacity

D-Depth of the duct

Dh-Hydraulic Diameter

L-Length of the duct

n1-Refractive index

h-Heat transfer coefficient

m- Mass flow rate

k- Thermal conductivity

I- Intensity of solar radiation

U- Overall heat transfer coefficient

T- Temperature

V-Ambient Air velocity

W-Pumping factor

GREEK LETTERS -Emissivity x -Transmissivity ¢- Absorptivity ®-Diffusivity �- Thermal efficiency ¯- Porosity °- Extinction coefficient

∆Difference of two quantities

SUBSCRIPTS

a- Ambient

b- Bottom

c- Cover

e-Effective

f- Fluid

p- Packing plate

t- Top

1- First glass cover

2- Second glass cover

REFERENCE

[1]Mohamad.A.A,“High efficiency solar air heater”, solar energy vol.60 No.2, pp.71-76,

1997.

[2]-Naphonparison,“Effect of porous media on the performance of the double pass flat plate

solar air heater”, solar energy, Vol.12 No.1, pp.90-99, 1996

[3]Sukhatme S.P., “Solar energy”, 3rd ed., 1984, Tata McGraw Hill, New Delhi.

[4] McAdams.W.H, “Heat Transmission”, 3rd ed.., McGraw Hill, New York, 1954.

[5] Sparrow, E.M., and Tien, K.K., “Forced convection heat transfer at an inclined and yawed

square plate application to solar collectors”, Heat transfer, Vol. 99 pp.507-522, 1977



417

[6] Raja shekhar,Y.,Sharma,K.,V.,,Rao,M.,B.,“Evaluation of heat loss coefficients in solar

flat plate collectors”,ARPN Journal, Vo. l4,No.5, pp. 15-19,2009.

[7] Languri,E.,M.,Taherian, H.,“Enhanced double –pass solar air heater with and without

porous medium”, International Journal of green Energy, Vol. 8, pp. 643-654,2011.

[8] Pradharaj,M.,Velmurugan,V., Moorthy, H., “Review on porous and non-porous flat plate

air collector with mirror enclose”, International journal of Engineering and Technology, Vol2

pp.4013-4019,2010

[9] Yousef.BAA, Adam.NM, “Performance analysis for flat plate collector with and without

porous media”, Journal of energy in Southern Africa, vol.19 No.4, pp.32-42, 2008.

[10] Zhao, Q., Salder, G.W., Leonardo, J.J., “Transient simulation of flat-plate solar

collectors”, Solar Energy, Vol.40, pp.167-174, 1988.

[11] Lansing.F.L,Reynold.R, “High performance flat plate solar collector”, solar energy

vol.24 No.2, pp.90-99, 1996.

[12] Ajay Kumar Kapardar and Dr. R. P. Sharma, “Experimental Investigation of Solar Air

Heater using Porous Medium”, International Journal of Mechanical Engineering &

Technology (IJMET), Volume 3, Issue 2, 2012, pp. 387 - 396, ISSN Print: 0976 – 6340,

ISSN Online: 0976 – 6359.

[13] Yogesh C. Dhote and Dr. S.B. Thombre, “Parametric Study on the Thermal Performance

of the Solar Air Heater with Energy Storage”, International Journal of Mechanical

Engineering & Technology (IJMET), Volume 3, Issue 1, 2012, pp. 90 - 99, ISSN Print:

0976 – 6340, ISSN Online: 0976 – 6359.

[14] Ajay Kumar Kapardar and Dr. R. P. Sharma, “Numerical and CFD Based Analysis of

Porous Media Solar Air Heater”, International Journal of Mechanical Engineering &

Technology (IJMET), Volume 3, Issue 2, 2012, pp. 374 - 386, ISSN Print: 0976 – 6340,

ISSN Online: 0976 – 6359.

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A cfd investigation and pressure correlation of solar air heater

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