Entropy generation is squarely linked with irreversibility, and consequently with exergy destruction within a thermal system. This study concerns with the temperature distribution, and local and volumetric averaged entropy generation rates within a cylindrical system with two solid co-rotating inner and outer parts and the middle nanofluid flow part. Temperature-dependent thermal conductivities for solid materials are included within the modeling. To obtain the temperature formula within all three sections, a combined analytical–numerical solution technique is applied. An exact analytical solution is also obtained, when constant thermal conductivities for solid materials are assumed. The resultant data from the analytical–numerical solution technique is verified against the investigated exact solution. Thereafter, the velocity and temperature fields from the combined analytical–numerical solution technique are incorporated into the entropy generation formulations to obtain the local and volumetric averaged entropy generation rates. Using abovementioned procedure, the effects of thermophysical parameters such as nanoparticles volume concentration, Brinkman number, thermal conductivity parameter ratios, outer temperature boundary condition, internal heat generation rates and velocity ratios on the temperature field, and entropy generation rates are investigated.
Issue Section:
Forced Convection
References
1.
Bejan
, A.
, 1995
, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes
, CRC Press
, Boca Raton, FL.2.
Torabi
, M.
, and Zhang
, K.
, 2014
, “Temperature Distribution and Classical Entropy Generation Analyses in an Asymmetric Cooling Composite Hollow Cylinder With Temperature-Dependent Thermal Conductivity and Internal Heat Generation
,” Energy
, 73
, pp. 484
–496
.10.1016/j.energy.2014.06.0413.
Torabi
, M.
, and Aziz
, A.
, 2012
, “Entropy Generation in a Hollow Cylinder With Temperature Dependent Thermal Conductivity and Internal Heat Generation With Convective–Radiative Surface Cooling
,” Int. Commun. Heat Mass Transfer
, 39
(10
), pp. 1487
–1495
.10.1016/j.icheatmasstransfer.2012.10.0094.
Torabi
, M.
, and Zhang
, K.
, 2014
, “Classical Entropy Generation Analysis in Cooled Homogenous and Functionally Graded Material Slabs With Variation of Internal Heat Generation With Temperature, and Convective–Radiative Boundary Conditions
,” Energy
, 65
, pp. 387
–397
.10.1016/j.energy.2013.11.0205.
Mahmoudi
, A. H.
, Pop
, I.
, Shahi
, M.
, and Talebi
, F.
, 2013
, “MHD Natural Convection and Entropy Generation in a Trapezoidal Enclosure Using Cu–Water Nanofluid
,” Comput. Fluids
, 72
, pp. 46
–62
.10.1016/j.compfluid.2012.11.0146.
Mahmoudi
, A. H.
, Shahi
, M.
, and Talebi
, F.
, 2012
, “Entropy Generation due to Natural Convection in a Partially Open Cavity With a Thin Heat Source Subjected to a Nanofluid
,” Numer. Heat Transfer, Part A
, 61
(4
), pp. 283
–305
.10.1080/10407782.2012.6479907.
Mahian
, O.
, Mahmud
, S.
, and Heris
, S. Z.
, 2012
, “Analysis of Entropy Generation Between Co-Rotating Cylinders Using Nanofluids
,” Energy
, 44
(1
), pp. 438
–446
.10.1016/j.energy.2012.06.0098.
Liu
, L. H.
, and Chu
, S. X.
, 2006
, “On the Entropy Generation Formula of Radiation Heat Transfer Processes
,” ASME J. Heat Transfer
, 128
(5
), pp. 504
–506.10.1115/1.21906959.
Makhanlall
, D.
, Munda
, J. L.
, and Jiang
, P.
, 2013
, “Entropy Generation in a Solar Collector Filled With a Radiative Participating Gas
,” Energy
, 60
, pp. 511
–516
.10.1016/j.energy.2013.08.04310.
Aziz
, A.
, and Torabi
, M.
, 2013
, “Transient Response and Entropy Generation Minimisation of a Finite Size Radiation Heat Shield With Finite Heat Capacity and Temperature-Dependent Emissivities
,” Int. J. Exergy
, 12
(1
), pp. 87
–108.10.1504/IJEX.2013.05254511.
Ibáñez
, G.
, López
, A.
, and Cuevas
, S.
, 2012
, “Optimum Wall Thickness Ratio Based on the Minimization of Entropy Generation in a Viscous Flow Between Parallel Plates
,” Int. Commun. Heat Mass Transfer
, 39
(5
), pp. 587
–592
.10.1016/j.icheatmasstransfer.2012.03.01112.
Arikoglu
, A.
, Ozkol
, I.
, and Komurgoz
, G.
, 2008
, “Effect of Slip on Entropy Generation in a Single Rotating Disk in MHD Flow
,” Appl. Energy
, 85
(12
), pp. 1225
–1236
.10.1016/j.apenergy.2008.03.00413.
Sheikholeslami
, M.
, Gorji-Bandpy
, M.
, and Ganji
, D. D.
, 2013
, “Numerical Investigation of MHD Effects on Al2O3–Water Nanofluid Flow and Heat Transfer in a Semi-Annulus Enclosure Using LBM
,” Energy
, 60
, pp. 501
–510
.10.1016/j.energy.2013.07.07014.
Turkyilmazoglu
, M.
, 2012
, “Exact Analytical Solutions for Heat and Mass Transfer of MHD Slip Flow in Nanofluids
,” Chem. Eng. Sci.
, 84
(17
), pp. 182
–187
.10.1016/j.ces.2012.08.02915.
Bejan
, A.
, 1979
, “A Study of Entropy Generation in Fundamental Convective Heat Transfer
,” ASME J. Heat Transfer
, 101
(4
), pp. 718
–725
.10.1115/1.345106316.
Choi
, S. U. S.
, and Eastman
, J. A.
, 1995
, “Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, Nov. 12–17.17.
Singh
, P. K.
, Anoop
, K. B.
, Sundararajan
, T.
, and Das
, S. K.
, 2010
, “Entropy Generation Due to Flow and Heat Transfer in Nanofluids
,” Int. J. Heat Mass Transfer
, 53
(21–22
), pp. 4757
–4767
.10.1016/j.ijheatmasstransfer.2010.06.01618.
Shalchi-Tabrizi
, A.
, and Seyf
, H. R.
, 2012
, “Analysis of Entropy Generation and Convective Heat Transfer of Al2O3 Nanofluid Flow in a Tangential Micro Heat Sink
,” Int. J. Heat Mass Transfer
, 55
(15–16
), pp. 4366
–4375
.10.1016/j.ijheatmasstransfer.2012.04.00519.
Mahian
, O.
, Mahmud
, S.
, and Wongwises
, S.
, 2013
, “Entropy Generation Between Two Rotating Cylinders With Magnetohydrodynamic Flow Using Nanofluids
,” J. Thermophys. Heat Transfer
, 27
(1
), pp. 161
–169
.10.2514/1.T390820.
Mahian
, O.
, Mahmud
, S.
, and Heris
, S. Z.
, 2012
, “Effect of Uncertainties in Physical Properties on Entropy Generation Between Two Rotating Cylinders With Nanofluids
,” ASME J. Heat Transfer
, 134
(10
), p. 101704
.10.1115/1.400666221.
Rashidi
, M. M.
, Abelman
, S.
, and Mehr
, N. F.
, 2013
, “Entropy Generation in Steady MHD Flow Due to a Rotating Porous Disk in a Nanofluid
,” Int. J. Heat Mass Transfer
, 62
(1
), pp. 515
–525
.10.1016/j.ijheatmasstransfer.2013.03.00422.
Cho
, C.-C.
, Chen
, C.-L.
, and Chen
, C.-K.
, 2013
, “Natural Convection Heat Transfer and Entropy Generation in Wavy-Wall Enclosure Containing Water-Based Nanofluid
,” Int. J. Heat Mass Transfer
, 61
, pp. 749
–758
.10.1016/j.ijheatmasstransfer.2013.02.04423.
Sohel
, M. R.
, Saidur
, R.
, Hassan
, N. H.
, Elias
, M. M.
, Khaleduzzaman
, S. S.
, and Mahbubul
, I. M.
, 2013
, “Analysis of Entropy Generation Using Nanofluid Flow Through the Circular Microchannel and Minichannel Heat Sink
,” Int. Commun. Heat Mass Transfer
, 46
, pp. 85
–91
.10.1016/j.icheatmasstransfer.2013.05.01124.
Ting
, T. W.
, Hung
, Y. M.
, and Guo
, N.
, 2014
, “Entropy Generation of Nanofluid Flow With Streamwise Conduction in Microchannels
,” Energy
, 64
, pp. 979
–990
.10.1016/j.energy.2013.10.06425.
Khorasanizadeh
, H.
, Nikfar
, M.
, and Amani
, J.
, 2013
, “Entropy Generation of Cu–Water Nanofluid Mixed Convection in a Cavity
,” Eur. J. Mech.: B/Fluids
, 37
, pp. 143
–152
.10.1016/j.euromechflu.2012.09.00226.
Sarkar
, S.
, Ganguly
, S.
, and Dalal
, A.
, 2014
, “Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder
,” ASME J. Heat Transfer
, 136
(6
), p. 062501
.10.1115/1.402647027.
Parvin
, S.
, and Chamkha
, A. J.
, 2014
, “An Analysis on Free Convection Flow, Heat Transfer and Entropy Generation in an Odd-Shaped Cavity Filled With Nanofluid
,” Int. Commun. Heat Mass Transfer
, 54
, pp. 8
–17
.10.1016/j.icheatmasstransfer.2014.02.03128.
Parvin
, S.
, Nasrin
, R.
, and Alim
, M. A.
, 2014
, “Heat Transfer and Entropy Generation Through Nanofluid Filled Direct Absorption Solar Collector
,” Int. J. Heat Mass Transfer
, 71
, pp. 386
–395
.10.1016/j.ijheatmasstransfer.2013.12.04329.
Bianco
, V.
, Manca
, O.
, and Nardini
, S.
, 2013
, “Second Law Analysis of Al2O3-Water Nanofluid Turbulent Forced Convection in a Circular Cross Section Tube With Constant Wall Temperature
,” Adv. Mech. Eng.
, 2013
, p. 920278
.10.1155/2013/92027830.
Bianco
, V.
, Manca
, O.
, and Nardini
, S.
, 2014
, “Entropy Generation Analysis of Turbulent Convection Flow of Al2O3–Water Nanofluid in a Circular Tube Subjected to Constant Wall Heat Flux
,” Energy Convers. Manage.
, 77
, pp. 306
–314
.10.1016/j.enconman.2013.09.04931.
Mahian
, O.
, Kianifar
, A.
, Kleinstreuer
, C.
, Al-Nimr
, M. A.
, Pop
, I.
, Sahin
, A. Z.
, and Wongwises
, S.
, 2013
, “A Review of Entropy Generation in Nanofluid Flow
,” Int. J. Heat Mass Transfer
, 65
, pp. 514
–532
.10.1016/j.ijheatmasstransfer.2013.06.01032.
Ibáñez
, G.
, Cuevas
, S.
, and de Haro
, M. L.
, 2003
, “Minimization of Entropy Generation by Asymmetric Convective Cooling
,” Int. J. Heat Mass Transfer
, 46
(8
), pp. 1321
–1328
.10.1016/S0017-9310(02)00420-9 33.
Strub
, F.
, Castaing-Lasvignottes
, J.
, Strub
, M.
, Pons
, M.
, and Monchoux
, F.
, 2005
, “Second Law Analysis of Periodic Heat Conduction Through a Wall
,” Int. J. Therm. Sci.
, 44
(12
), pp. 1154
–1160
.10.1016/j.ijthermalsci.2005.09.00434.
Aziz
, A.
, and Khan
, W. A.
, 2011
, “Classical and Minimum Entropy Generation Analyses for Steady State Conduction With Temperature Dependent Thermal Conductivity and Asymmetric Thermal Boundary Conditions: Regular and Functionally Graded Materials
,” Energy
, 36
(10
), pp. 6195
–6207
.10.1016/j.energy.2011.07.04235.
Aziz
, A.
, and Khan
, W. A.
, 2012
, “Entropy Generation in an Asymmetrically Cooled Hollow Sphere With Temperature Dependent Internal Heat Generation
,” Int. J. Exergy
, 10
(1
), pp. 110
–123
.10.1504/IJEX.2012.04506436.
Fénot
, M.
, Bertin
, Y.
, Dorignac
, E.
, and Lalizel
, G.
, 2011
, “A Review of Heat Transfer Between Concentric Rotating Cylinders With or Without Axial Flow
,” Int. J. Therm. Sci.
, 50
(7
), pp. 1138
–1155
.10.1016/j.ijthermalsci.2011.02.01337.
Goshima
, T.
, and Miyao
, K.
, 1991
, “Transient Thermal Stresses in a Hollow Cylinder Subjected to γ-Ray Heating and Convective Heat Losses
,” Nucl. Eng. Des.
, 125
(2
), pp. 267
–273
.10.1016/0029-5493(91)90083-T38.
Ünal
, H. C.
, 1987
, “Temperature Distributions in Fins With Uniform and Non-Uniform Heat Generation and Non-Uniform Heat Transfer Coefficient
,” Int. J. Heat Mass Transfer
, 30
(7
), pp. 1465
–1477
.10.1016/0017-9310(87)90178-539.
Razelos
, P.
, and Satyaprakash
, B. R.
, 1996
, “Analysis and Optimization of Convective Trapezoidal Profile Pin Fins With Internal Heat Generation
,” Int. Commun. Heat Mass Transfer
, 23
(5
), pp. 643
–654
.10.1016/0735-1933(96)00047-440.
Aziz
, A.
, and Bouaziz
, M. N.
, 2011
, “A Least Squares Method for a Longitudinal Fin With Temperature Dependent Internal Heat Generation and Thermal Conductivity
,” Energy Convers. Manage.
, 52
(8–9
), pp. 2876
–2882
.10.1016/j.enconman.2011.04.00341.
Kundu
, B.
, and Das
, P. K.
, 2005
, “Optimum Profile of Thin Fins With Volumetric Heat Generation: A Unified Approach
,” ASME J. Heat Transfer
, 127
(8
), pp. 945
–948.10.1115/1.192978442.
Torabi
, M.
, and Zhang
, Q. B.
, 2013
, “Analytical Solution for Evaluating the Thermal Performance and Efficiency of Convective–Radiative Straight Fins With Various Profiles and Considering all Non-Linearities
,” Energy Convers. Manage.
, 66
, pp. 199
–210
.10.1016/j.enconman.2012.10.01543.
Aziz
, A.
, Torabi
, M.
, and Zhang
, K.
, 2013
, “Convective–Radiative Radial Fins With Convective Base Heating and Convective–Radiative Tip Cooling: Homogeneous and Functionally Graded Materials
,” Energy Convers. Manage.
, 74
, pp. 366
–376
.10.1016/j.enconman.2013.05.03444.
Sheikholeslami
, M.
, Ganji
, D. D.
, and Ashorynejad
, H. R.
, 2013
, “Investigation of Squeezing Unsteady Nanofluid Flow Using ADM
,” Powder Technol.
, 239
, pp. 259
–265
.10.1016/j.powtec.2013.02.00645.
Sheikholeslami
, M.
, Bandpy
, M. G.
, Ellahi
, R.
, Hassan
, M.
, and Soleimani
, S.
, 2014
, “Effects of MHD on Cu–Water Nanofluid Flow and Heat Transfer by Means of CVFEM
,” J. Magn. Magn. Mater.
, 349
, pp. 188
–200
.10.1016/j.jmmm.2013.08.04046.
Sheikholeslami
, M.
, and Ganji
, D. D.
, 2013
, “Heat Transfer of Cu-Water Nanofluid Flow Between Parallel Plates
,” Powder Technol.
, 235
, pp. 873
–879
.10.1016/j.powtec.2012.11.03047.
Bianco
, V.
, Manca
, O.
, and Nardini
, S.
, 2011
, “Numerical Investigation on Nanofluids Turbulent Convection Heat Transfer Inside a Circular Tube
,” Int. J. Therm. Sci.
, 50
(3
), pp. 341
–349
.10.1016/j.ijthermalsci.2010.03.00848.
Sarkar
, S.
, Ganguly
, S.
, and Dalal
, A.
, 2013
, “Buoyancy Driven Flow and Heat Transfer of Nanofluids Past a Square Cylinder in Vertically Upward Flow
,” Int. J. Heat Mass Transfer
, 59
, pp. 433
–450
.10.1016/j.ijheatmasstransfer.2012.12.03249.
Sarkar
, S.
, Ganguly
, S.
, and Biswas
, G.
, 2012
, “Mixed Convective Heat Transfer of Nanofluids Past a Circular Cylinder in Cross Flow in Unsteady Regime
,” Int. J. Heat Mass Transfer
, 55
(17–18
), pp. 4783
–4799
.10.1016/j.ijheatmasstransfer.2012.04.04650.
Ganguly
, S.
, and Chakraborty
, S.
, 2009
, “Effective Viscosity of Nanoscale Colloidal Suspensions
,” J. Appl. Phys.
, 106
(12
), p. 124309
.10.1063/1.327042351.
Ganguly
, S.
, Sikdar
, S.
, and Basu
, S.
, 2009
, “Experimental Investigation of the Effective Electrical Conductivity of Aluminum Oxide Nanofluids
,” Powder Technol.
, 196
(3
), pp. 326
–330
.10.1016/j.powtec.2009.08.01052.
Goodarzi
, M.
, Safaei
, M. R.
, Vafai
, K.
, Ahmadi
, G.
, Dahari
, M.
, Kazi
, S. N.
, and Jomhari
, N.
, 2014
, “Investigation of Nanofluid Mixed Convection in a Shallow Cavity Using a Two-Phase Mixture Model
,” Int. J. Therm. Sci.
, 75
, pp. 204
–220
.10.1016/j.ijthermalsci.2013.08.00353.
Göktepe
, S.
, Atalık
, K.
, and Ertürk
, H.
, 2014
, “Comparison of Single and Two-Phase Models for Nanofluid Convection at the Entrance of a Uniformly Heated Tube
,” Int. J. Therm. Sci.
, 80
, pp. 83
–92
.10.1016/j.ijthermalsci.2014.01.01454.
Malvandi
, A.
, Ganji
, D. D.
, Hedayati
, F.
, and Rad
, E. Y.
, 2013
, “An Analytical Study on Entropy Generation of Nanofluids Over a Flat Plate
,” Alexandria Eng. J.
, 52
(4
), pp. 595
–604
.10.1016/j.aej.2013.09.00255.
Sheikholeslami
, M.
, and Ganji
, D. D.
, 2015
, “Entropy Generation of Nanofluid in Presence of Magnetic Field Using Lattice Boltzmann Method
,” Phys. A
417
(1), pp. 273–286.56.
Malvandi
, A.
, and Ganji
, D. D.
, 2014
, “Brownian Motion and Thermophoresis Effects on Slip Flow of Alumina/Water Nanofluid Inside a Circular Microchannel in the Presence of a Magnetic Field
,” Int. J. Therm. Sci.
, 84
, pp. 196
–206
.10.1016/j.ijthermalsci.2014.05.01357.
Ganji
, D. D.
, and Malvandi
, A.
, 2014
, “Natural Convection of Nanofluids Inside a Vertical Enclosure in the Presence of a Uniform Magnetic Field
,” Powder Technol.
, 263
, pp. 50
–57
.10.1016/j.powtec.2014.04.08958.
Malvandi
, A.
, and Ganji
, D. D.
, 2014
, “Mixed Convective Heat Transfer of Water/Alumina Nanofluid Inside a Vertical Microchannel
,” Powder Technol.
, 263
, pp. 37
–44
.10.1016/j.powtec.2014.04.08459.
Alvariño
, P. F.
, Jabardo
, J. M. S.
, Agras
, J. D. P.
, and Simón
, M. L. S.
, 2013
, “Heat Flux Effect in Laminar Flow of a Water/Alumina Nanofluid
,” Int. J. Heat Mass Transfer
, 66
, pp. 376
–381
.10.1016/j.ijheatmasstransfer.2013.07.03560.
Zaimi
, K.
, Ishak
, A.
, and Pop
, I.
, 2014
, “Unsteady Flow due to a Contracting Cylinder in a Nanofluid Using Buongiorno's Model
,” Int. J. Heat Mass Transfer
, 68
, pp. 509
–513
.10.1016/j.ijheatmasstransfer.2013.09.04761.
Mahian
, O.
, Mahmud
, S.
, and Pop
, I.
, 2012
, “Analysis of First and Second Laws of Thermodynamics Between Two Isothermal Cylinders With Relative Rotation in the Presence of MHD Flow
,” Int. J. Heat Mass Transfer
, 55
(17–18
), pp. 4808
–4816
.10.1016/j.ijheatmasstransfer.2012.04.04862.
Yazdi
, M. H.
, Abdullah
, S.
, Hashim
, I.
, and Sopian
, K.
, 2011
, “Entropy Generation Analysis of Open Parallel Microchannels Embedded Within a Permeable Continuous Moving Surface: Application to Magnetohydrodynamics (MHD)
,” Entropy
, 14
(12
), pp. 1
–23
.10.3390/e1401000163.
Kreyszig
, E.
, 2011
, Advanced Engineering Mathematics
, Wiley
, Hoboken, NJ.64.
Mahian
, O.
, Pop
, I.
, Sahin
, A. Z.
, Oztop
, H. F.
, and Wongwises
, S.
, 2013
, “Irreversibility Analysis of a Vertical Annulus Using TiO2/Water Nanofluid With MHD Flow Effects
,” Int. J. Heat Mass Transfer
, 64
, pp. 671
–679
.10.1016/j.ijheatmasstransfer.2013.05.001Copyright © 2015 by ASME
You do not currently have access to this content.
