Heat Loss from Cavity Receiver for Solar Micro- Concentrating Collector

Similar documents
HEAT LOSS CHARACTERISTICS OF A ROOF INTEGRATED SOLAR MICRO-CONCENTRATING COLLECTOR

Simulation of a linear Fresnel solar collector concentrator

Department of Energy Science & Engineering, IIT Bombay, Mumbai, India. *Corresponding author: Tel: ,

Vertical Mantle Heat Exchangers for Solar Water Heaters

Experimental Evaluation of Natural Heat Transfer in Façade Integrated Triangular Enclosures

Simulation of Free Convection with Conjugate Heat Transfer

EFFECT OF SOME PARAMETERS ON LINEAR FRESNEL SOLAR CONCENTRATING COLLECTORS

Performance Assessment of PV/T Air Collector by Using CFD

CFD ANALYSIS OF TRIANGULAR ABSORBER TUBE OF A SOLAR FLAT PLATE COLLECTOR

Numerical Investigation of Convective Heat Transfer in Pin Fin Type Heat Sink used for Led Application by using CFD

THERMAL PERFORMANCE EVALUATION OF AN INNOVATIVE DOUBLE GLAZING WINDOW

An Evacuated PV/Thermal Hybrid Collector with the Tube/XCPC design

NUMERICAL SIMULATION OF THE AIR FLOW AROUND THE ARRAYS OF SOLAR COLLECTORS

UNIT FOUR SOLAR COLLECTORS

International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN

Natural Convection Heat Loss from A Partly Open Cubic Enclosure Timothy N Anderson 1,a * and Stuart E Norris 2,b

Numerical Analysis of Heat Transfer Performance of Flat Plate Solar Collectors

Experimental study on heat losses from external type receiver of a solar parabolic dish collector

CFD MODELLING OF CONVECTIVE HEAT TRANSFER FROM A WINDOW WITH ADJACENT VENETIAN BLINDS

Performance Analysis of the Solar Linear Fresnel Reflector

Effect of Periodic Variation of Sol-air Temperature on the Performance of Integrated Solar Collector Storage System

2-D CFD analysis of passenger compartment for thermal comfort and ventilation

EXPERIMENTAL STUDY ON A CASCADED PCM STORAGE RECEIVER FOR PARABOLIC DISH COLLECTOR

Optimization of the Air Gap Spacing In a Solar Water Heater with Double Glass Cover

Numerical Study of the Three-dimensional Flow in a Flat Plate Solar Collector with Baffles

Numerical Study of Convective Heat Transfer for Flat Unglazed Transpired Solar Collectors

CFD AND CONJUGATE HEAT TRANSFER ANALYSIS OF HEAT SINKS WITH DIFFERENT FIN GEOMETRIES SUBJECTED TO FORCED CONVECTION USED IN ELECTRONICS COOLING

COMBINED MEASUREMENT OF THERMAL AND OPTICAL PROPERTIES OF RECEIVERS FOR PARABOLIC TROUGH COLLECTORS

COMPUTATIONAL ANALYSIS OF LAMINAR FORCED CONVECTION IN RECTANGULAR ENCLOSURES OF DIFFERENT ASPECT RATIOS

International Journal of Advanced Engineering Technology E-ISSN

Exergy Analysis of Solar Air Collector Having W Shaped Artificial Roughness

HEAT LOSS MEASUREMENTS ON PARABOLIC TROUGH RECEIVERS

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

2012, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial- NoDerivatives 4.0 International

Natural Convection in Parabolic Enclosure Heated from Below

Available online at ScienceDirect. Energy Procedia 69 (2015 )

COVENANT UNIVERSITY NIGERIA TUTORIAL KIT OMEGA SEMESTER PROGRAMME: MECHANICAL ENGINEERING

The energy performance of an airflow window

International Journal of Engineering Research and General Science Volume 3, Issue 6, November-December, 2015 ISSN

Fig 1. Power Tower during Operation

Numerical investigation to study effect of radiation on thermal performance of radiator for onan cooling configuration of transformer

Investigation of Jet Impingement on Flat Plate Using Triangular and Trapezoid Vortex Generators

FLUID FLOW AND HEAT TRANSFER INVESTIGATION OF PERFORATED HEAT SINK UNDER MIXED CONVECTION 1 Mr. Shardul R Kulkarni, 2 Prof.S.Y.

Thermal Analysis of Solar Collectors

Collector test according to EN ,2:2002

Chapter 1 INTRODUCTION AND BASIC CONCEPTS

PERFORMANCE ANALYSIS OF PARABOLIC TROUGH COLLECTOR TUBE WITH INTERNAL INTERMITTENT FINS

A NUMERICAL study of solar chimney power plants in Tunisia

Simplified Collector Performance Model

EXPERIMENTAL INVESTIGATION OF DIFFERENT TRACKING MODES OF THE PARABOLIC TROUGH COLLECTOR

MARYLAND. Fundamentals of heat transfer Radiative equilibrium Surface properties Non-ideal effects. Conduction Thermal system components

COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF A V-RIB WITH GAP ROUGHENED SOLAR AIR HEATER

A. Solar Walls. B. Prototype I

NUMERICAL STUDY OF HEAT TRANSFER IN A FLAT PLAT THERMAL SOLAR COLLECTOR WITH PARTITIONS ATTACHED TO ITS GLAZING. Adel LAARABA.

Construction and performance analysis of a three dimensional compound parabolic concentrator for a spherical absorber

Unsteady effects in direct steam generation in the CLFR

TURBULENCE MODELING OF AIR CIRCULATION IN AN ENCLOSURE WITH MULTIPLE OPENINGS AND LOCAL HEAT SOURCES

Heat Transfer Enhancement of Solar Flat Plate Collector by Using V Corrugated Fins and Various Parameters

N. Lemcoff 1 and S.Wyatt 2. Rensselaer Polytechnic Institute Hartford. Alstom Power

Comparison of heat transfer characteristics of liquid coolants in forced convection cooling in a micro heat sink

EFFECT OF NON-UNIFORM TEMPERATURE DISTRIBUTION ON SURFACE ABSORPTION RECEIVER IN PARABOLIC DISH SOLAR CONCENTRATOR

Numerical simulation of heat transfer and fluid flow in a flat plate solar collector with TIM and ventilation channel

HEAT TRANSFER ENHANCEMENT OF SOLAR FLAT PLATE COLLECTOR BY USING V CORRUGATED FINS AND VARIOUS PARAMETERS

Combined Natural Convection and Thermal Radiation in an Inclined Cubical Cavity with a Rectangular Pins Attached to Its Active Wall

Thermal conversion of solar radiation. c =

Thermal Performance Analysis of Water Heating System for a Parabolic Solar Concentrator: An Experimental Model based design

3D Simulation Study of a Receiver on a Solar Power Tower

Project #1 Internal flow with thermal convection

ANALYSIS OF THERMAL STRESSES OF SOLAR PARABOLIC TROUGH COLLECTOR FOR SOLAR POWER PLANT BY FEM

1D and 3D Simulation. C. Hochenauer

A CFD Analysis Of A Solar Air Heater Having Triangular Rib Roughness On The Absorber Plate

Computational Modeling of a Solar Thermoelectric Generator

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

A CFD Simulation Study on Pressure Drop and Velocity across Single Flow Microchannel Heat Sink

HEAT TRANSFER THERMAL MANAGEMENT OF ELECTRONICS YOUNES SHABANY. C\ CRC Press W / Taylor Si Francis Group Boca Raton London New York

S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100

Chapter 2 HEAT CONDUCTION EQUATION

Numerical analysis of fluid flow and heat transfer in 2D sinusoidal wavy channel

HEAT TRANSFER AND THERMAL STRESS ANALYSIS OF WATER COOLING JACKET FOR ROCKET EXHAUST SYSTEMS

Chapter 2 HEAT CONDUCTION EQUATION

EFFECT OF OPERATING PARAMETERS ON THE PERFORMANCE OF THE HYBRID SOLAR PVT COLLECTOR UNDER DIFFERENT WEATHER CONDITION

HEAT TRANSFER CAPABILITY OF A THERMOSYPHON HEAT TRANSPORT DEVICE WITH EXPERIMENTAL AND CFD STUDIES

A NOVEL IMAGING LIGHT FUNNEL AND ITS COLLECTING HEAT EXPERIMENTS

Natural Convection Inside a Rectangular Enclosure with Two Discrete Heat Sources Placed on Its Bottom Wall

The Peak Flux Constraints on Bladed Receiver Performance in High- Temperature Molten Salt Concentrating Solar Power Systems

STUDY OF A PASSIVE SOLAR WINTER HEATING SYSTEM BASED ON TROMBE WALL

Numerical simulation of fluid flow in a monolithic exchanger related to high temperature and high pressure operating conditions

THERMAL PROFILE EVALUATION OF A SILICON WAFER IN THE APPARATUS FOR RAPID THERMAL CHEMICAL VAPOUR DEPOSITION

LAMINAR NATURAL CONVECTION IN VERTICAL 2D GLAZING CAVITIES

Thermal conductivity measurement of two microencapsulated phase change slurries

EFFECT OF DIFFERENT PARAMETERS ON THE PERFORMANCE OF RIB ROUGHNESS SOLAR DUCT

CFD based design and analysis of micro-structured. surfaces with application to drag and noise reduction

S.E. (Chemical) (Second Semester) EXAMINATION, 2011 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100

Principles of Solar Thermal Conversion

Comparative study of Different Geometry of Ribs for roughness on absorber plate of Solar Air Heater -A Review

Table of Contents. Foreword... xiii. Preface... xv

Study ANTALYA. Abstractt. number. reflecting. any specially an importantt solar thermal. of the aperture area to the

Tuesday, December 11th. To be handed in both as a hard copy (in my mailbox in LGRT 1127A) and on SPARK (as a turnitin assignment).

Estimation of Heat Transfer in Internally Micro Finned Tube

PERFORMANCE OPTIMIZATION OF HYBRID SOLAR HEATING SYSTEM USING THERMOELECTRIC GENERATOR

Transcription:

Heat Loss from Cavity Receiver for Solar Micro- Concentrating Collector Tanzeen Sultana 1, Graham L Morrison 1, Andrew Tanner 2, Mikal Greaves 2, Peter Le Lievre 2 and Gary Rosengarten 1 1 School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia tanzeen.s@student.unsw.edu.au 2 Chromasun, Inc., San Jose, CA 95112, USA ABSTRACT In the past decade there has been a significant increase in the use of linear concentrating Fresnel collectors for large scale steam production. This paper describes a microconcentrating Fresnel collector for use on building rooftops. The modules of this collector system are approximately 3 meters long by 1 meter wide and 0.3 meters high. Applications include domestic hot water, industrial process heat, and solar air conditioning. The absorber is contained in a sealed glass envelop to minimise convective losses. The main heat losses are due to natural convection inside the enclosure and radiation heat transfer from the absorber tube. In this paper, a two-dimensional computational fluid dynamics model for combined natural convection and surface radiation is developed for the micro-concentrator cavity receiver. The influence of operating temperature, emissivity of the surface, orientation and the geometry on the total heat loss from the receiver is investigated. The objective of the investigation is to optimize the design to maximise the overall thermal efficiency of a prototype micro-concentrating collector. Keywords - Cavity receiver, Computational fluid dynamics (CFD), Linear fresnel micro-concentrating collector, Natural convection, Solar energy. INTRODUCTION Linear concentrating solar thermal technologies offer a promising method for large scale solar energy collection. In these technologies, the ratio of thermal energy loss to total solar radiation on the receiver decreases significantly; hence the collector has higher efficiency at high temperatures than non concentrating collectors, and can be used for solar thermal power generation or solar cooling (Zhai et al. 2010). Linear Fresnel solar concentrator can also be used for medium temperature (80 o C-250 o C) applications (Singh et al. 2010). Many researchers have investigated concentrating solar collector systems of different sizes and application types. These systems are able to achieve high outlet temperature at low cost. It is possible to use them in thermal-power plants, hot water production for heating, and also solar air conditioning (Petrakis et al. 2009). Until now, the only commercially available high temperature solar thermal technologies, such as parabolic trough and linear Fresnel, have not integrated well on rooftops, as they have been complex, cumbersome, have high wind loads and are difficult to maintain.

In this research, a new low-cost micro-concentrator (MCT) has been studied, which is designed to operate at temperatures up to 220 C, and be seamlessly integrated into the architecture of buildings. The application of this system ranges from domestic hot water and industrial process heat to solar air conditioning for commercial, industrial and institutional buildings. Rooftop solar cooling technologies need to be very space efficient. Since lower temperatures can only drive single effect chillers, traditional flat panel collectors need more than twice the roof area to produce sufficient cooling for a low rise building. High temperature systems, such as parabolic trough collectors, require more space on the rooftop to avoid shading as they track the sun. In this regard the MCT is considered more efficient compared to both low temperature collectors and more complex high temperature systems. The MCT system module is approximately 3.2 meters long by 1.2 meters wide and 0.3 meters high (Figure 1). Fig. 1: A solar micro-concentrator system (source: Chromasun Inc.) This paper focuses on the MCT absorber and cavity arrangement, and presents the results of a computational investigation of the thermal performance of the cavity receiver. The absorber of a solar concentrating device plays an important role in the collection of solar energy. To achieve high efficiency in a concentrating solar collector, there should be minimum thermal losses from the absorber. Figure 2 shows a schematic of the cavity along with the internal modes of heat transfer. During operation, the absorber tube heats up due to the incident concentrated solar radiation, resulting in emission of long-wavelength radiation into the cavity. This radiation represents a heat loss from the absorber, and thus results in a decrease in collector thermal efficiency. In addition, the emitted radiation is absorbed by the cavity windows and bottom wall, which in turn heat up. This promotes buoyancy-driven flows within the cavity, resulting in convection losses and a further reduction in thermal efficiency. In some systems conduction of heat away from the absorber tube represents a third mode of heat loss (Reynolds et al. 2004). 2

Fig. 2: Cross-section of the receiver cavity of micro-concentrating collector Considerable research effort has gone into understanding the collection of solar radiation and heat loss paths from the absorber of a concentrating thermal receiver (Reynolds et al. 2004). Recently, Facao & Oliveira (2009) studied the overall heat loss coefficient of a trapezoidal cavity for a linear Fresnel receiver using computational fluid dynamics. They analysed two geometrical parameters: receiver depth and insulation thickness. Singh et al. (2010) studied the overall heat loss coefficient of a trapezoidal cavity absorber with a rectangular pipe and round pipe with ordinary black coating and selective surface coatings at different absorber temperatures (up to 175 o C) and developed correlations for the heat loss coefficient. Recently different groups have intensified their work on prototypes and industrial size line focussing Fresnel collectors. The Belgium Company Solarmundo attracted attention with their concept of a Fresnel collector, having built a 2500 m 2 prototype in Liege, Belgium (Haberle, A. et al. 2001, 2002 and 2006). Nevertheless until now, no work has been carried out on compact small scale Fresnel concentrating systems. The current study investigates the role of radiation and natural convection heat transfer inside the cavity, along with heat transfer at the boundaries in order to fully understand the heat loss mechanisms. 3

COMPUTATIONAL MODEL A computational model for the prototype absorber has been developed using ANSYS- CFX (ANSYS 12.1), a commercial computational fluid dynamics software package. For simplicity, a two dimensional geometry with a symmetry plane is created (Figure 3). Fig. 3: Cavity geometry Tab. 1: Boundary conditions for the computational model Property Unit Boundary conditions Absorber tube Glass cover Temperature o C 150 to 300 Convection co-efficient W/m 2 K 10 Ambient temperature o C 20 Long wavelength emissivity 0.05 0.9 The absorber tube is modelled as an isothermal surface. The convective flow and resulting temperature distribution between the absorber tube and the secondary reflector and glass cover are studied for various absorber temperatures, from 150 o C to 300 o C. The absorber tube is coated with a selective surface and the long wavelength emissivity is taken as 0.05. The cover glass at the top and sides of the cavity are modelled as convection boundaries with external heat loss coefficients of 10 W/m 2 K, exchanging heat with an ambient temperature of 20 o C, with internal emissivity of 0.9. The base reflector surface is modelled as an adiabatic surface. The air flow in the cavity is modelled as laminar as the Rayleigh number is in the range of 1.8 X 10 4-2.7 X 10 7. Radiation is modelled using the Monte Carlo simulation method (Wang et al. 2010). All discretization is carried out using second order schemes. Air 4

properties are modelled as an ideal gas. Minimum convergence criteria were set at 10-3 for continuity and velocity, and 10-6 for energy. A hybrid mesh is used with structured quadrilateral elements forming the wall zones and unstructured triangular elements used in the central zones of the collector cavities. The resulting mesh size is approximately 2 mm, with 97788 mesh points in total. A grid dependency study has been undertaken to ensure the adequacy of this mesh density. RESULTS AND DISCUSSION The natural convection and surface radiation heat losses from the cavity receiver are determined for different absorber temperatures. The air flow patterns in the receiver cavity of the collector are shown in Figures 4 & 5. These figures demonstrated that radiation heat exchange plays an important role in the convection in the cavity receiver. The process of internal heat transfer is dominated by radiation effects. This is because the absorber temperature is much higher than that of the other surfaces in the cavity. Locations where fluid motion is fastest are down along the glass side walls, then along the base surface. The next fastest fluid motion is a layer along the upper glass cover, with the fluid dropping down into the cavity from the glass at the symmetry plane. Heating of the base of the cavity by the long wave radiation from the absorber drives convection cells in the bottom with a rising plume up the symmetry plane. Although the bottom convective cells cover most of the cavity they do not significantly effect convection around the absorber. For the boundary conditions specified in Table 1; the results show significant thermal gradients in the cavity only around the absorber and secondary reflector. Fluid flow around the absorber tube is entrapped by the secondary reflector which minimises the convective heat loss from the absorber tube to the cavity (Figures 8 & 9). Due to the mixing caused by the bottom convection cell there is a relatively constant temperature in the cavity below the level of the absorber tube and a higher temperature convection cell under the top glass surface as shown in Figures 12 & 13. In this study the secondary reflector around the absorber tube was considered to be a thin aluminium sheet. It may be possible to reduce the strength of the upper convection cell by using an insulated reflector. Heat loss results are shown in Tables 2 & 3 for cases with and without radiation heat loss effects. The long wavelength emissivity of the absorber selective coating is taken as 0.05 (Chromasun Inc.). Due to the low emissivity of the selective coating the radiation heat loss is only 15% to 20% of the convective heat loss. The total heat loss at 220 C is approximately 50W per meter length of tube compared to an expected solar input of approximately 300W to 400W per meter length. At this stage of the project conduction heat loss through supporting structure for the absorber has not been included. In order to validate the heat loss result it is necessary to perform a systematic comparison of CFD simulation results with experimental data. The geometries considered in the present study are relatively new and no experimental data is currently available for this or a similar geometry. Therefore, validation has not been carried out at the time of writing this paper however an extensive program of experimental measurement is planned. 5

Fig. 4: Velocity streamlines in the cavity receiver (without radiation heat loss, absorber tube temperature 200 o C) Fig. 5: Velocity streamlines in the cavity receiver (with radiation heat loss, absorber tube temperature 200 o C) Fig. 6: Temperature contours in the cavity receiver (without radiation heat loss, absorber tube temperature 200 o C) Fig. 7: Temperature contours in the cavity receiver (with radiation heat loss, absorber tube temperature 200 o C) Fig. 8: Velocity magnitude contours and vectors in the cavity receiver (without radiation heat loss, absorber tube temperature 200 o C) Fig. 9: Velocity magnitude contours and vectors in the cavity receiver (with radiation heat loss, absorber tube temperature 200 o C) 6

Tab. 2: Heat loss flux results without radiation heat loss Heat loss flux (W/m 2 ) Absorber temperature # C Absorber tube 150 516 200 827 220 953 240 1138 280 1429 300 1542 Tab. 3: Heat loss flux results with radiation heat loss Absorber temperature # o C Heat loss flux (W/m 2 ) Radiative heat loss flux (W/m 2 ) Absorber tube Convective heat loss flux (W/m 2 ) 150 585 67 518 200 978 117 860 220 1109 144 965 240 1286 172 1114 280 1650 242 1408 300 1802 281 1526 Fig. 10: Absorber heat flux (W/m 2 ) showing the effect of radiation heat loss 7

Fig. 11: Absorber heat flux per unit of absorber area (W/m 2 ) for different absorber temperatures Fig. 12: Temperature profile within the cavity for absorber tube temperature of 200 o C (with and without radiation heat loss) 8

Fig. 13: Velocity profile within the cavity for absorber tube temperature of 200 o C (with and without radiation heat loss) CONCLUSION AND FUTURE WORK Preliminary results have been obtained for the performance of a new cavity receiver concept for a linear Fresnel micro-concentrator collector. The performance was numerically simulated using computational fluid dynamics package, ANSYS-CFX. To analyse the thermal performance of the collector, a simple 2-D numerical analysis has been carried out with steady-state laminar model and heat loss results are obtained. In future, an experimental investigation of performance will be carried out to assess the validity of the CFD results. REFERENCES 1. ANSYS CFX Help Manual 12.1. www.ansys.com 2. Chromasun, Inc., San Jose, CA 95112, USA, www.chromasun.com 3. FACAO, J. & OLIVEIRA, A.C. 2009. Numerical simulation of a linear Fresnel solar collector concentrator. 8 th International Conference on Sustainable Energy Technologies,.Aachen, Germany. pp. 1-6. 4. HABERLE, A., ZAHLER, C., LALAING, J., VEN, J., SUREDA, J., GRAF, W., LERCHENMULLER, H. & WITTWER, V. 2001.The Solarmundo Project- Advance Technology for Solar Thermal Power Generation. Solar World Congress, International Solar Energy Soceity Conference. Adelaide, Australia. 5. HABERLE, A., ZAHLER, C., LERCHENMULLER, H., MERTINS, M., WITTWER, C, TRIEB, F. & DERSCH, J. 2002.The Solarmundo line focussing Fresenl Collector. Optical and thermal performance and cost calculations. Proc. Int. Symp. on Concentrated Solar Power and Chemical Energy Technologies, Solarpaces. Zurich, Germany. 6. HABERLE, A., BERGER, M., LUGINSLAND, F., ZAHLER, C., BAITSCH, M., HENNING, H. & ROMMEL, M. 2006. Linear Concentrating Fresnel Collector for 9

Process heat Applications, Proc. 13th Int. Symp. on Concentrated Solar Power and Chemical Energy Technologies, Spain. 7. PETRAKIS, M., BARAKOS, G. & KAPLANIS, S. 2009. Roof integrated miniparabolic solar collectors. Comparison between simulation and experimental results. Open Fuels and Energy Science Journal, 2, 71-81. 8. REYNOLDS, D. J., JANCE, M. J., BEHNIA, M. & MORRISON, G. L. 2004. An experimental and computational study of the heat loss characteristics of a trapezoidal cavity absorber. Solar Energy, 76, 229-234. 9. SINGH, P. L., SARVIYA, R. M. & BHAGORIA, J. L. 2010. Heat loss study of trapezoidal cavity absorbers for linear solar concentrating collector. Energy Conversion and Management, 51, 329-337. 10. ZHAI, H., DAI, Y. J., WU, J. Y., WANG, R. Z. & ZHANG, L. Y. 2010. Experimental investigation and analysis on a concentrating solar collector using linear Fresnel lens. Energy Conversion and Management, 51, 48-55. 11. WANG, Y., DONG, X. & WEI, JIN, H. 2010. Numerical simulation of the heat flux distribution in a solar cavity receiver. Journal of Frontiers of energy and power engineering in China,Research article, 1673-7393 (print). BIOGRAPHY OF PRESENTER Ms Tanzeen Sultana, a PhD candidate in the School of Mechanical & Manufacturing Engineering at the University of New South Wales (UNSW), holds an Austrian Postgraduate Award (APA) and an Engineering Research Award (ERA). Currently she also holds an Associate Lecturer position in the School of Mechanical & Manufacturing Engineering, UNSW. Her research interest includes: solar thermal design and optimization, engineering heat transfer and renewable energy. 10