Heat transfer studies on solar air heaters for performance improvement

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HEAT TRANSFER STUDIES ON SOLAR AIR HEATERS FOR PERFORMANCE IMPROVEMENT

DIGPAL KUMAR

DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

NOVEMBER 2020

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©Indian Institute of Technology Delhi (IITD), New Delhi, 2020

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HEAT TRANSFER STUDIES ON SOLAR AIR HEATERS FOR PERFORMANCE IMPROVEMENT

by

Digpal Kumar

Department of Mechanical Engineering

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy

to the

Indian Institute of Technology Delhi

NOVEMBER 2020

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Dedicated to My Parents and Friends

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Certificate

This is to certify that the thesis entitled “Heat Transfer Studies on Solar Air Heaters for Performance Improvement” being submitted by Mr. Digpal Kumar to the Indian Institute of Technology Delhi for the award of the degree of DOCTOR OF PHILOSOPHY is a record of the original bonafide research carried out by him. He has worked under our guidance and supervision and has fulfilled the requirements for the submission of the thesis. The results presented in this thesis have not been submitted in part or full to any other University or Institute for award of any degree or diploma.

Prof. B. Premachandran

Professor

Department of Mechanical Engineering Indian Institute of Technology Delhi Hauz Khas, New Delhi-110 016, India

New Delhi

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Acknowledgements

First and foremost, I am grateful to the merciful Almighty for his uncountable blessings.

I would like to express my heartfelt gratitude to my supervisor, Prof. B. Premachandran, for all his invaluable guidance, endless assistance, and encouragement during this dissertation work.

He has been constantly encouraged and motivated me in every step right from the beginning.

His constant zeal for work and enthusiasm have always kept me involved in this work and motivated me to strive for excellence.

I am thankful to Prof. M. R. Ravi, Prof. P. Talukdar and Prof. V. Buwa as my committee members. Their educational guidance, questions and incentive through valuable advice relating my research during my presentations, were very useful to my thought process. I would like to thank the technical staff of Heat Transfer Research laboratory, Mr. Rajender Singh, who helped me in the establishment of the experimental set ups and in extending all the facilities required.

The ideas and inspiration drawn from my friends have been equally important during this period. I hereby express my gratitude towards my lab mats Dr. Sourav Kumar, Mr. Nikhil Kumar Singh, Dr. Sharad N. Pachpute, Dr. B. M. Ningegowda, Dr. Kulpdip Singh, Mr. Thamil Kumaran, Mr. Rohit Kumar and Mr. Giridhar Jambre. I would like to take this opportunity to thank Mr. Kaushlendra Dubey, Mr. Nikhil Kumar, Mr. Mahendra Gupta and Abhishek sit whose association during my PhD work made memorable.

I am deeply indebted to my spiritual Guru, Sri Yogi Anand Kumar for his blessings.

Finally, I would like to thank my family for their support and faith in me. They have always been a source of encouragement and have helped me at every stage of my academic and personal life. I would like to thank my beloved parents, sisters and brothers for their life-long support, everlasting love, and sacrifices, which sustained my interest in research and motivated me towards the successful completion of this study. I owe you all much more than I can possibly express.

New Delhi Digpal Kumar

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Abstract

Solar air heaters (SAHs) are widely used for heating of building and drying of agricultural products. SAHs are mainly based on force convection or natural convection. For a force convection based SAH, a blower is required to blow the air through the air heater channel. In the natural convection based SAHs, flow of air inside the air heater channel occurs due to buoyancy force and no blower is required. In many applications, free convection based solar air heaters are preferred as there is no requirement of blower and easy maintenance.

Furthermore, it is easy to fabricate, noise-free, durable and require low maintenance cost.

Despite extensive studies on natural convection based solar air heaters, several issues have not been properly addressed such as flow transition in inclined channel, effect of atmospheric wind, detailed flow and heat transfer analysis with different fin configurations and porous medium at the outlet.

The following four problems have been investigated in the present study: (i) the effect of atmospheric wind on the performance of natural convection based solar air heaters, (ii) the effect of fins on the bottom side of the absorber plate and the identification of an optimum arrangement of fins for higher heat transfer with less material (iii) the effect of flow resistance at the exit of the channel on the natural convection heat transfer inside the solar air heaters, (iv) laminar, transition and turbulent regimes in a natural convection based solar air heater. In the present work, numerical and experimental investigations have been performed for the natural convection based solar air heaters. Numerical simulations have been carried out by using the Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulations (LES) models. To perform the experiments, an experimental set-up has been fabricated.

A detailed numerical investigation has been carried out in this work to understand the effect of atmospheric wind on heat transfer in natural convection based solar air heaters. A 3D

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inclined rectangular channel has been considered for the numerical simulations. The top wall of the channel is maintained at constant heat flux condition, and the other walls of the channel are assumed to be adiabatic in all the simulations. For heat transfer calculations, combined convection and surface radiation is considered in the present study. All the inner surface of the walls of the channel are assumed to be black and the emissivity, 𝜀 of the plates are taken to be 0.95. The numerical simulations are carried out by varying the values of heat flux, 𝑞^′′ = 250 W/m², 500 W/m²and 750 W/m², velocity of the atmospheric wind, Vwind = 0.0, 0.2, 0.6, and 1.0 m/s, and the inclination angle of the channel, 𝜃 =15°, 30, 45, and 60. In the parametric study, various directions of free stream flow are also considered such as cross flow over the channel, along the main flow direction of the channel and the diagonal to the channel. It is shown that the mass flow rate starts to drop beyond an angle of inclination of 45 degrees in the presence of atmospheric wind, which is not the case for still conditions with no wind.

To obtain an optimum fin arrangement in a natural convection based solar air heater with a rectangular fin array attached to the bottom side of the absorber for better heat transfer and higher mass flow rate of heated air, a numerical study have been performed and the results have been presented for various fin sizes and spacing between the fins. An inclined rectangular channel similar to the dimensions of a typical solar air heater has been considered for this study.

Three different fin configurations viz. continuous long fins for the whole length of the channel, inline interrupted and staggered interrupted arrangements of fins have been studied. The present analysis aims to identify the optimum configuration of the fin array for enhanced heat transfer. The spacing between the fins and the height of the fins are varied to obtain an optimum configuration. The numerical simulations are performed for the heat flux, 𝑞^′′ of 250 W/m², 500 W/m² and 750 W/m² on the absorber plate. The inclination angles of the channel, 𝜃 considered in the parametric study are 15°, 30, and 45 with respect to the horizontal plane.

The results show that with the spacing between fins, S = 5.4 cm performs better in the case of

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longitudinal continuous fin arrangement. On the other hand, a fin spacing of 4.75 cm shows higher heat transfer in the case of staggered fin configuration. Compared to nine long uninterrupted fins, using the staggered arrangement with 15×10 fins saves up to 33% of fin material for same heat transfer.

The effect of flow resistance due to the presence of porous medium representing agricultural products at the exit of free convection based solar air heater has been studied experimentally and numerically. An air heater has been developed as an inclined channel and integrated with a drying chamber to conduct the experiments. Constant heat flux condition is provided by electrical heating on the top absorber plate of the channel. Experiments have been conducted for heat flux ranging from 250 to 750 W/m² for the channel inclination angle of 30^o. The height of porous material bed has also been varied in the drying chamber while the porosity is set at 0.36. In the numerical study, the surface-to-surface radiation model has also been considered for the modelling of heat transfer within the channel. For all the heat flux values considered in the experiments, numerical simulations have been performed for the inclination angles of 15°, 30° and 45°. In this analysis, the temperature distribution in the channel wall, the flow pattern, the difference in the mass flow rate and temperature of the outlet air have been investigated with different heights of the porous medium. For the porous medium thicknesses of 63 mm and 126 mm in the chamber, the mass flow rate is reduced by approximately 20% and 30%, respectively for all the heat flux values considered in this study.

The natural convection flow transition from laminar to turbulent inside a parallel plate channel has been studied numerically at the angles of inclinations of 15°, 30° and 60° with respect to horizontal plane. A numerical study has been carried out using the large eddy simulations (LES) to understand the flow transition from laminar to turbulent. To carry out the numerical investigations, a three dimensional rectangular channel is considered. The top plate of the channel is exposed to the constant heat flux condition of 250 W/m² and the bottom wall

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is assumed to be adiabatic. Periodic boundary conditions are applied to the sides of the channel.

In this study, the main focus is on the effect of the angle of inclination on the flow transition from laminar to turbulent and the development of thermal boundary layer in the channel at different angles of inclination. The results indicate that due to the rapid growth of both the velocity and thermal boundary layers, the early transition occurs at the lower angle of inclination of the channel with respect to horizontal plane. The temperature distributions obtained at various cross sections show that strong mixing occurs at the lower angle of inclination relatively at the early stage of the flow.

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सार

कृषि उत्पाद ों के षिर्ााण और सुखािे के षिए सौर वायु हीटर का व्यापक रूप से उपय ग षकया

जाता है। सौर वायु हीटर र्ुख्य रूप से बि सोंवहि या प्राकृषतक सोंवहि पर आधाररत ह ते हैं। एक बि

सोंवहि आधाररत सौर वायु हीटर के षिए, एयर हीटर चैिि के र्ाध्यर् से हवा क उडािे के षिए एक ब्ल अर की आवश्यकता ह ती है। प्राकृषतक सोंवहि आधाररत सौर वायु हीटर र्ें, वायु हीटर चैिि के

अोंदर हवा का प्रवाह उत्प्लावि बि के कारण ह ता है और षकसी धौोंकिी की आवश्यकता िहीों ह ती है।

कई अिुप्रय ग ों र्ें, प्राकृषतक सोंवहि आधाररत सौर वायु हीटर ों क प्राथषर्कता दी जाती है क् ोंषक ब्ल अर की क ई आवश्यकता िहीों ह ती है। इसके अिावा, यह आसाि है, श र-र्ुक्त, षटकाऊ और कर्

रखरखाव िागत की आवश्यकता है। प्राकृषतक सोंवहि आधाररत सौर वायु हीटर ों पर व्यापक अध्ययि

के बावजूद, कई र्ुद् ों क ठीक से सोंब षधत िहीों षकया गया है जैसे षक झुकाव चैिि र्ें प्रवाह सोंक्रर्ण, वायुर्ोंडिीय हवा का प्रभाव, षवषभन्न षिि कॉन्फ़िगरेशि के साथ षवस्तृत प्रवाह और गर्ी हस्ताोंतरण षवश्लेिण और षिकास र्ें झरझरा र्ाध्यर्।

वतार्ाि अध्ययि र्ें षिम्नषिन्खत चार सर्स्याओों की जाोंच की गई है: (i) प्राकृषतक सोंवहि

आधाररत सौर वायु हीटर ों के प्रदशाि पर वायुर्ोंडिीय पवि का प्रभाव, (ii) अवश िक प्लेट के िीचे की

तरि षिि का प्रभाव और कर् सार्ग्री के साथ उच्च गर्ी हस्ताोंतरण के षिए षिि की एक इष्टतर्

व्यवस्था की पहचाि (iii) सौर हवा के हीटर के अोंदर प्राकृषतक सोंवहि गर्ी हस्ताोंतरण पर चैिि के बाहर षिकििे पर प्रवाह प्रषतर ध का प्रभाव, (iv) एक प्राकृषतक सोंवहि आधाररत सौर वायु हीटर र्ें िैषर्िार, सोंक्रर्ण और अशाोंत क्षेत्र। वतार्ाि काया र्ें, प्राकृषतक सोंवहि आधाररत सौर वायु हीटर ों के षिए सोंख्यात्मक और प्रय गात्मक जाोंच की गई है। रेिॉल्ड्स-एवरेज्ड िेषवयर-स्ट क्स (RANS) और िाजा एड्डी

षसर्ुिेशि (LES) र्ॉडि का उपय ग करके सोंख्यात्मक षसर्ुिेशि षकए गए हैं। प्रय ग ों क करिे के षिए, एक प्रय गात्मक सेट-अप तैयार षकया गया है।

प्राकृषतक सोंवहि आधाररत सौर ऊजाा हीटर ों र्ें गर्ी हस्ताोंतरण पर वायुर्ोंडिीय हवा के प्रभाव क सर्झिे के षिए इस काया र्ें एक षवस्तृत सोंख्यात्मक जाोंच की गई है। सोंख्यात्मक षसर्ुिेशि के षिए एक 3 डी इच्छुक आयताकार चैिि पर षवचार षकया गया है। चैिि की शीिा दीवार क षिरोंतर गर्ी प्रवाह की न्स्थषत र्ें बिाए रखा जाता है, और चैिि की अन्य दीवार ों क सभी षसर्ुिेशि र्ें एषडयाबेषटक र्ािा

जाता है। गर्ी हस्ताोंतरण गणिा के षिए, वतार्ाि अध्ययि र्ें सोंयुक्त सोंवहि और सतह षवषकरण र्ािा

जाता है। चैिि की दीवार ों की सभी आोंतररक सतह क कािा और उत्सजाि र्ािा जाता है, प्लेट ों का ε 0.95 षिया गया है। गर्ी प्रवाह के र्ाि ों क अिग-अिग करके सोंख्यात्मक षसर्ुिेशि षकए जाते हैं,

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𝑞^′′= 250 W/m2, 500 W/m2 और 750 W/m2, वायुर्ोंडिीय हवा का वेग, षवषवड = 0.0, 0.2, 0.6, 0.6 और 1.0 m/s, और चैिि का झुकाव क ण, 𝜃 = 15°, 30, 45, और 60। पैरार्ीषटिक अध्ययि र्ें, फ्री

स्टिीर् प्रवाह की षवषभन्न षदशाओों क भी र्ािा जाता है जैसे चैिि पर क्रॉस फ्ल , चैिि की र्ुख्य प्रवाह षदशा और चैिि के षिए षवकणा। यह षदखाया गया है षक वायुर्ोंडिीय हवा की उपन्स्थषत र्ें द्रव्यर्ाि

प्रवाह दर 45 षडग्री के झुकाव के क ण से परे षगरिा शुरू ह जाती है, ज षक अभी तक क ई हवा िहीों के

साथ न्स्थषत के षिए र्ार्िा िहीों है।

एक बेहतर सोंवहि आधाररत स िर एयर हीटर र्ें एक आयताकार षिि व्यवस्था प्राप्त करिे के

षिए बेहतर गर्ी हस्ताोंतरण के षिए एक आयताकार षिि सरणी के साथ जुडा हुआ है और गर्ा हवा के

उच्च प्रवाह दर, एक सोंख्यात्मक अध्ययि षकया गया है और पररणार् हैं षवषभन्न पोंख ों के आकार और पोंख ों

के बीच अोंतर के षिए प्रस्तुत षकया गया है। इस अध्ययि के षिए एक ठेठ सौर वायु हीटर के आयार् ों के

सर्ाि एक झुकाव आयताकार चैिि पर षवचार षकया गया है। तीि अिग-अिग षिि कॉन्फ़िगरेशि।

चैिि की पूरी िोंबाई के षिए िगातार िोंबे पोंख, इििाइि बाषधत और पोंख ों की कोंषपत व्यवस्था का

अध्ययि षकया गया है। वतार्ाि षवश्लेिण का उद्ेश्य बढाया गर्ी हस्ताोंतरण के षिए षिि सरणी के

इष्टतर् कॉन्फ़िगरेशि की पहचाि करिा है। एक इष्टतर् षवन्यास प्राप्त करिे के षिए पोंख ों और पोंख ों की

ऊोंचाई के बीच अोंतर षभन्न ह ता है। अोंकीय प्लेट पर 250 W/m2, 500 W/m2 और 750 W/m2 की गर्ी

प्रवाह के षिए सोंख्यात्मक षसर्ुिेशि षकए जाते हैं। चैिि के झुकाव क ण, पैरार्ीषटिक अध्ययि र्ें र्ािा

जाता है क्षैषतज षवर्ाि के सोंबोंध र्ें 15°, 30, और 45 हैं। पररणार् बताते हैं षक पोंख ों के बीच ररन्क्त के

साथ, एस = 5.4 सेर्ी अिुदैध्या षिरोंतर षिि व्यवस्था के र्ार्िे र्ें बेहतर प्रदशाि करता है। दूसरी ओर, 4.75 सेर्ी की एक अोंषतर् ररन्क्त कोंषपत षिि कॉन्फ़िगरेशि के र्ार्िे र्ें उच्च गर्ी हस्ताोंतरण षदखाती

है। िौ िोंबे षिबााध पोंख ों की तुििा र्ें, 15×10 पोंख ों के साथ कोंषपत व्यवस्था का उपय ग करिे से सर्ाि

गर्ी हस्ताोंतरण के षिए 33% तक षिि सार्ग्री बचती है।

र्ुक्त सोंवहि आधाररत सौर वायु हीटर के षिकास पर कृषि उत्पाद ों का प्रषतषिषधत्व करिे वािे

झरझरा र्ाध्यर् की उपन्स्थषत के कारण प्रवाह प्रषतर ध का प्रभाव प्रय गात्मक और सोंख्यात्मक रूप से

अध्ययि षकया गया है। एक एयर हीटर क एक झुकाव चैिि के रूप र्ें षवकषसत षकया गया है और प्रय ग ों के सोंचािि के षिए एक सुखािे कक्ष के साथ एकीकृत षकया गया है। चैिि के शीिा अवश िक प्लेट पर षबजिी के हीषटोंग द्वारा िगातार गर्ी प्रवाह की न्स्थषत प्रदाि की जाती है। 30o के चैिि झुकाव क ण के षिए 250 से 750 W/m2 तक के गर्ी प्रवाह के षिए प्रय ग ों का आय जि षकया गया है। शुष्क कक्ष र्ें झरझरा सार्ग्री की ऊोंचाई भी षभन्न-षभन्न रही है, जबषक प रषसटी 0.36 पर सेट है। सोंख्यात्मक

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अध्ययि र्ें, चैिि के भीतर गर्ी हस्ताोंतरण के र्ॉडषिोंग के षिए सतह से सतह षवषकरण र्ॉडि पर भी

षवचार षकया गया है। प्रय ग ों र्ें षवचार षकए गए सभी गर्ी प्रवाह र्ूल् ों के षिए, सोंख्यात्मक षसर्ुिेशि

15°, 30° और 45° के झुकाव क ण के षिए षकए गए हैं। इस षवश्लेिण र्ें, चैिि की दीवार र्ें तापर्ाि

षवतरण, प्रवाह पैटिा, बडे पैर्ािे पर प्रवाह दर और आउटिेट हवा के तापर्ाि र्ें षिद्रपूणा र्ाध्यर् की

षवषभन्न ऊोंचाइय ों के साथ जाोंच की गई है। कक्ष र्ें 63 षर्र्ी और 126 षर्र्ी की झरझरा र्ध्यर् र् टाई के

षिए, इस अध्ययि र्ें षवचार षकए गए सभी गर्ी प्रवाह र्ूल् ों के षिए, क्रर्शः, द्रव्यर्ाि प्रवाह दर िगभग 20% और 30% तक कर् ह जाती है।

क्षैषतज सर्ति के सोंबोंध र्ें 15°, 30° और 60° के झुकाव के क ण पर सोंख्यात्मक प्लेट चैिि के

अोंदर अशाोंत करिे के षिए प्राकृषतक सोंवहि प्रवाह सोंक्रर्ण का सोंख्यात्मक रूप से अध्ययि षकया गया

है। िाषर्िा से अशाोंत करिे के षिए प्रवाह सोंक्रर्ण क सर्झिे के षिए बडे एडी षसर्ुिेशि (एिईएस) का उपय ग करके एक सोंख्यात्मक अध्ययि षकया गया है। सोंख्यात्मक जाोंच करिे के षिए, एक तीि

आयार्ी आयताकार चैिि र्ािा जाता है। चैिि की शीिा प्लेट 250 W/m2 की षिरोंतर गर्ी प्रवाह की

न्स्थषत के सोंपका र्ें है और िीचे की दीवार क एडैबेषटक र्ािा जाता है। चैिि के षकिार ों पर आवषधक सीर्ा की न्स्थषत िागू ह ती है। इस अध्ययि र्ें, र्ुख्य ि कस िाषर्िा से टबुािेंट र्ें प्रवाह सोंक्रर्ण पर झुकाव के क ण और झुकाव के षवषभन्न क ण ों पर चैिि र्ें थर्ाि सीर्ा परत के षवकास पर है। पररणार्

इोंषगत करते हैं षक वेग और थर्ाि सीर्ा परत ों द ि ों के तेजी से षवकास के कारण, क्षैषतज षवर्ाि के सोंबोंध र्ें चैिि के झुकाव के षिचिे क ण पर प्रारोंषभक सोंक्रर्ण ह ता है। षवषभन्न क्रॉस सेक्शि पर प्राप्त तापर्ाि

षवतरण बताते हैं षक प्रवाह के प्रारोंषभक चरण र्ें अपेक्षाकृत झुकाव के षिचिे क ण पर र्जबूत षर्श्रण ह ता है।

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List of Figures

Fig. 1.1 Conventional solar air heater (Bhushan and Singh, 2010) 2 Fig. 2.1 Vertical parallel plate channel with bell mouth shape entrance (Katoh et al.,

1991).

8

Fig. 2.2 Comparison of numerical and experimental wall temperature distributions along the heated vertical wall (Fedorov and Viskanta, 1997).

9

Fig. 2.3 Effect of angle of inclination and Rayleigh number on the Nusselt number distribution with non-dimensional plate spacing (Baskaya et al., 1999).

10

Fig. 2.4 Schematic diagram of solar air heater with sinusoidal wave like absorber plate and a top flat glass cover (Gao et al., 2000).

11

Fig. 2.5 Comparison of normalized vertical velocity for different turbulent model at (a) y/L = 0.77 (b) y/L = 0.53 from the channel inlet (Ben-Mansour et al., 2007).

13

Fig. 2.6 Comparison of normalized temperature for different turbulent model at (a) y/L

= 0.77 (b) y/L = 0.53 from the channel inlet (Ben-Mansour et al., 2007).

13

Fig. 2.7 Fin-array configuration on flat surface studied by Starner and McManus (1963).

16

Fig. 2.8 Schematic diagram of fin array configuration and chosen computational domain (Baskaya et al., 2000).

18

Fig. 2.9 Schematic diagram of the vertically placed fins on the flat plate, (a) continuous rectangular fins (b) interrupted rectangular fin (Ahmadi et al., 2014).

20

Fig. 2.10 Considered geometry for the investigation in Hosseini et al. (2017). 21 Fig. 2.11 Schematic view of the air heater with storage material (Aboul-Enein et al.,

2000). 23 Fig. 2.12 Schematic diagram of indirect type natural convection air heater with storage

material (El-Sebaii et al., 2002).

24

Fig. 2.13 Schematic diagram of natural convection based solar dryer studied by (Pangavhane et al., 2002).

25

Fig. 2.14 Variation of temperature along the channel length at different angle of inclinations (Lau et al., 2012).

28

Fig. 2.15 Computational domain with non-uniformly heated open-ended channel for (a) vertical and (b) inclined channel (Li et al., 2015).

29

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Fig. 2.16 Q criterion shown at value of 0.1 coloured by vorticity in z direction in the region of transition to developed region for parallel plates (Kogawa, 2016).

31

Fig. 3.1 Schematic of the experimental set-up with resistance at the exit of the channel. 36

Fig 3.2 Channel cut section. 37

Fig. 3.3 Images of the experimental set-up for the flow resistance at the exit of the channel (a) experimental set-up (b) stainless steel foil on the absorber plate (c) absorber plate coated with black paint (d) wire mesh of drying chamber and (e) glass balls.

38

Fig. 3.4 Thermocouple positions in both top and bottom plates. 39 Fig. 4.1 A natural convection based air heater for solar energy applications (a)

The geometry and the coordinate system considered for the numerical investigation (b) crosswind over the air heater (c) Axial direction of atmospheric wind (d) diagonal flow of the atmospheric wind (e) computational domain considered in the numerical simulation for accounting external wind.

51

Fig. 4.2 Typical computational mesh used in present study (a) a 3D view of discretized domain (b) mesh pattern in the X-Y plan at the mid of the channel.

55

Fig. 4.3 Results of grid independence study - heat flux 𝒒^′′ = 500 W/m²(GrL = 5.20 × 10¹³) and the inclination angle (𝜽) of 30° (a) temperature along the midline of the top wall (b) Variation of local Nusselt number along the midline of the top wall.

56

Fig. 4.4 Validation of the present numerical model (a) the variation of mean surface temperature along the heated wall of inclined channel with the angle of 30° - experimental and numerical data of Lau et al. (2012) and the present numerical results (b) comparison of the temperature variation across the channel width obtained from the present numerical results with those of Cheng and Muller (1998).

58

Fig. 4.5 Natural convection in a channel for the angle of inclination of 30° and the heat flux of 500 W/m² at the top wall. (a) Streamlines pattern in the channel (b) Temperature distribution over the top wall (c) Temperature distribution over the bottom wall of the channel (d) Temperature

60

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distribution of air at the mid plane of the channel along the flow direction.

Fig. 4.6 The effect of crosswind on heat transfer for the angle of inclination of the channel, = 30°, heat flux, 𝒒^′′ = 500 W/m²(GrL = 5.20 ×10¹³) and the crosswind velocity, Vwind = 0.2 m/s (left), 0.6 m/s (centre), and 1.0 m/s (right).

(a)-(c) streamline patterns (d)-(f) temperature distributions obtained over the top wall (g)-(i) temperature distribution over bottom wall of the channel.

62

Fig. 4.7 The variation of surface temperature of the heated plate for various crosswind velocity for the angle of inclination of the channel of 30°

and the heat flux of 500 W/m²(GrL = 5.20 × 10¹³).

63

Fig. 4.8 Variation of the mass flow rate and the outlet air temperature at different cross wind velocity (a) mass flow rate and (b) outlet air temperature.

64

Fig. 4.9 Comparison of the mean surface temperature along the length of the top wall and the bottom wall of the channel for different angle of inclination at the fixed heat flux (Grashof number-GrL) for 0.6 m/s crosswind velocity.

66

Fig. 4.10 Effect of the angle of inclination on mass flow rate and bulk mean temperature of air at 𝑞^′′ = 500 W/m² (a) variation of mass flow rate (b) variation of outlet bulk mean temperature.

67

Fig. 4.11 Effect of the direction of atmospheric flow on the top and bottom walls of the channel for the angle of inclination () of 45°, the crosswind velocity of 0.6 m/s and the heat flux of 500 W/m²(GrL= 5.20 X 10¹³) (a) natural convection (b) axial direction flow (c) cross flow and (d) diagonal direction flow.

69

Fig. 4.12 Effect of the angle of inclination on mass flow rate and bulk mean temperature of air at 𝑞^′′ = 500 W/m² (a) variation of mass flow rate (b) variation of outlet bulk mean temperature.

72

Fig. 5.1 Schematic of solar air heater (a) Solar air heater with glass plate considering heat losses to the ambient (b) solar air heater without glass plate neglecting all heat losses.

77

Fig. 5.2 A natural convection based air heater and different fin configurations (a) adopted geometry for the numerical study (b) longitudinal fin array

78

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(c) in-line interrupted fin configuration (d) staggered interrupted fin configuration (e) computational domain.

Fig. 5.3 Comparison of results at different grid sizes (a) Variation of velocity along the centreline of the outlet (b) Variation of temperature at the centreline along the length of the top wall.

82

Fig. 5.4 (a) Typical 3 D computational mesh used in present study and mesh pattern in the X-Y plan at the mid of the channel (b) mess pattern near the fin in longitudinal case.

82

Fig. 5.5 Model validation (a) comparison of the temperature rise of the top heated plate of the inclined channel with the Lau et al. (2012a), (b) comparison of surface temperature rise of the heated wall of the vertical channel obtained from the present study with the experimental data of Katoh et al. (1991).

84

Fig. 5.6 Line average (spanwise) temperature distribution of top heated plate and bottom plate along the channel length for different number of fins for 750 W/m²of heat flux and different angle of inclination (a) – (b) 15°, (c) – (d) 30°, and (e) – (f) 45°.

86

Fig. 5.7 Temperature contours at the (a-f) top heated plate and (g-l) bottom plate for different numbers of longitudinal fins for 30° inclination angle and 750 W/m²of heat flux.

87

Fig. 5.8 Variation of span-wise average temperature of the top heated plate along the channel length at different fin height for 12 longitudinal fins across the width for different orientation of the channel and heat flux value (a) 15º and 750 W/m²(b) 30º and 750 W/m²(c) 45º and 750 W/m² (d) 30º and 250 W/m²and (e) 30º and 500 W/m².

89

Fig. 5.9 Comparison of top heated surface temperature in case of in-line and staggered fin arrangement.

91

Fig. 5.10 Velocity contours at the mid plane (0.5 Hfin) of the air heater for the staggered arrangement and different fin length for the spacing between the fins of 8.75 cm.

92

Fig. 5.11 Line average (span-wise) temperature profile of the top heated surface along the length of the channel for different fin length.

94

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Fig. 5.12 Comparison of staggered fin arrangement with uninterrupted fin arrangement.

96

Fig. 6.1 Computational domain taken into consideration in the numerical studies.

100

Fig. 6.2 Grid independence study for the numerical model (a) Variation of top plate temperature along the length of the channel (b) change in the velocity at the centerline of the exit of the rectangular channel.

102

Fig. 6.3 Comparison of the temperatures distributions of the channel walls obtained from numerical simulations and experiments for the angle of inclination θ of 30° (a) – (c) top plate and (d) – (f) Bottom plate.

105

Fig. 6.4 Streamlines patterns for the case of 30° of the inclination angle and

500 W/m² of heat flux value (a) hp = 0 (no porous material), (b) hp = 126 mm.

106

Fig. 6.5 Temperature distribution along the heated plate with different porous conditions for 𝑞^′′ = 500 W/m² at various angles of inclination, θ obtained from the numerical study (a) θ = 15°, (b) θ = 30° and (c) θ = 45°.

107

Fig. 6.6 Temperature distribution of the top plate at different porous conditions for θ = 15° and 𝑞^′′ = 750 W/m² obtained from the numerical study (a) hp = 0 (no porous material), (b) hp = 63 mm and (c) hp = 126 mm.

108

Fig. 6.7 The change in the mass flow rate at different angles of inclination with different porous conditions obtained from the numerical study (a) θ

= 15°, (b) θ = 30° and (c) θ = 45°.

110

Fig. 6.8 The change in the outlet bulk mean temperature at different angles of inclination with different porous conditions (a) θ = 15°, (b) θ = 30° and (c) θ = 45°.

111

Fig. 6.9 The Nusselt number distribution of the top heated plate for different porous conditions at 𝑞^′′= 500 W/m² (a) θ = 15°, (b) θ = 30°, (c) θ = 45° and (d) comparison of experimental and numerical results for θ = 30° and hp = 63 mm.

112

Fig. 7.1 Natural convection between parallel plates (a) physical geometry (b) computational domain adopted for the LES

117

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Fig. 7.2 (a) A typical computational grid used to perform the LES in the inclined parallel plate channel. Close-up view of the mesh for (b) periodic section of the channel and (c) top (also bottom) wall.

118

Fig. 7.3 Variation of the grid spacing to the Kolmogorov length ratio at y/L=

0.5 for the parallel plate channel.

119

Fig. 7.4 Variation of the mean velocity near upper wall compared with the numerical results of Kim et al. (1987) and the experimental data of Eckelmann (1974).

121

Fig. 7.5 The variations of time averaged rms velocity components at the midline of the channel along the length at different angle of inclinations (a) streamwise component (b) normal component and (c) spanwise component.

123

Fig. 7.6 Contours plots of streamwise rms velocity components (vrms) for different angle of inclinations (a) 15°, (b) 30°, and (c) 60°.

124

Fig. 7.7 The contours of thermal boundary layers at different position of the channel in the streamwise direction (a) position of the chosen planes, (b) θ = 15ô, (c) θ = 30ô, (d) θ = 60ô.

126

Fig. 7.8 The time averaged Nusselt number distributions over the heated plate for the inclination angles of 15°, 30° and 60° along the channel length at the midline of the channel (z/w = 0.5).

128

Fig. 7.9 Position of the probes used for the measurement of the time signal velocity data.

129 Fig. 7.10 The time signals of instantaneous velocity at different locations (a)

center of the channel (b) close to the heated wall.

129

Fig. 7.11 The power spectral density of the three velocity components at (a) location 5, (b) location 6, (c) location 11 and (d) location 12.

131

Fig. 7.12 Auto-correlations function over a time period of 12 sec for three velocity components at (a) location 5, (b) location 6, (c) location 11 and (d) location 12 for parallel plate channel.

132

Fig. 7.13 Iso surface of Q criterion, colored with mean Y velocity for different angle of inclinations (a) θ = 15ô, (b) θ = 30ô and (c) θ = 60ô.

134

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List of Tables

Table 3.1 Uncertainties of the measured parameters. 41

Table 4.1 Details of the parameters considered in the study. 52 Table 5.1 Number of cells used for grid sensitivity analysis. 81 Table 5.2 Outlet air temperature at different fin height. 90 Table 5.3 Details of the fin geometry with equal fin material. 92

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Nomenclature

A Area (mm²)

𝐶₁_,C2,𝐶₃_ Empirical constants in 𝑘 − 𝜀 turbulence model 𝐷_𝑃 Mean particle (glass ball) diameter, mm Fij View factor from i^th element to the j^th element g Gravitational acceleration, m/s²

GrL Grashof number based on channel length

havg Average convective heat transfer coefficient, W/m²K

hp Porous material thickness, mm

Hfin Fin height, mm

I Fin interruption length, mm

𝐽 Radiosity, W/m²

k Turbulent kinetic energy, m²/s²

kf Thermal conductivity of the fluid, W/mK

L Length of the channel, mm

W Width of the channel, mm

H Height of the channel, mm

l Length of the extended domain, mm

w Width of the extended domain, mm

h Height of the extended domain, mm

𝑁𝑢_𝑥_𝑖 Local Nusselt number

NuL Average Nusselt number

P Pressure, N/m²

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Pr Prandtl number

𝑞^′′ Heat flux over the heated plate, W/m²

Ra Rayleigh number

Ra* Modified Rayleigh number

S Fin spacing, mm

T Temperature, K

Ta Ambient temperature, K

Tin Inlet air temperature, K

Tw Surface temperature of heated wall, K 𝑇^′ Fluctuating component of temperature, K 𝑢̅_𝑖 Mean velocity component in 𝑥_𝑖 direction, m/s 𝑢′_𝑖 Fluctuating velocity component in 𝑥_𝑖 direction, m/s

Vwind Wind velocity, m/s

x, y, z Cartesian coordinates

y⁺ Non dimensional wall coordinate, y _w   Greek symbols

β Thermal expansion coefficient, K^-1

µ dynamic viscosity, Pa-s

ρ Mass density of air, kg/m³

𝜇_𝑡 Eddy viscosity, Ns/m²

τ wall shear stress, Pa

ε Emissivity of the channel walls

σk , σε Empirical model constant used in turbulent kinetic energy and turbulent dissipation equation

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τij Reynolds stress tensor

j iu

u , _u_T

 j Subgrid scale stress tensors

ν Kinematic viscosity, m²/s

𝜃 Channel inclination from horizontal, degree (°)

𝜎_𝑡 Turbulent Prandtl number

ϕ Porosity of the packed bed

ij rotation rate tensor

 scalar quantity

 Filter width in LES model

t Time increment, s

Subscripts

avg average

Conv Convection

rad Radiation

𝑓 Fluid

𝑤 wall

mean mean flow

SGS Subgrid scale

Heat transfer studies on solar air heaters for performance improvement

HEAT TRANSFER STUDIES ON SOLAR AIR HEATERS FOR PERFORMANCE IMPROVEMENT

DIGPAL KUMAR

HEAT TRANSFER STUDIES ON SOLAR AIR HEATERS FOR PERFORMANCE IMPROVEMENT

Digpal Kumar

Department of Mechanical Engineering

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy

to the

Indian Institute of Technology Delhi

NOVEMBER 2020

Dedicated to My Parents and Friends

Certificate

Prof. B. Premachandran

Acknowledgements

Abstract

Contents

List of Figures

List of Tables

Nomenclature