- Email: [email protected]
On the notion of the Amlouk–Boubaker optothermal expansivity ψAB
Materials Science in Semiconductor Processing 16 (2013) 111–112
Contents lists available at SciVerse ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
On the notion of the Amlouk–Boubaker optothermal expansivity cAB Yin-Jie Chen Xinjiang University, College of Chemistry and Chemical Engineering, Urumqi 830046, China
a r t i c l e i n f o
abstract
Available online 27 October 2012
In Section 3.4.2 of the commented paper, a new physical parameter: the Amlouk– Boubaker optothermal expansivity, cAB, has been defined as the ratio of the thermal diffusivity to the effective absorptivity. This parameter has been assimilated to a threedimensional expansion velocity of the transmitted heat inside the material, and thus, has been considered a relevant aggregate for evaluating the thermal and optical performance of materials. In this paper, accuracy, correctness and relevance of this parameter are discussed on the basis of precedent definitions. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Amlouk–Boubaker optothermal expansivity Boubaker Polynomials Expansion Scheme (BPES) Crystal growth Thermal analysis Thin films
where a l~
1. Introduction
Eg
In previous studies, the Amlouk–Boubaker optothermal expansivity, cAB, has been defined by [1–4]:
cAB ¼ D=a^
ð1Þ
where D is the layer material thermal diffusivity and a^ is the already defined effective absorptivity. The unit of this parameter, which is expressed in m3/s, has been assimilated to a three-dimensional expansion velocity of the transmitted heat inside the material. Although the definition of the thermal diffusivity, D, is universal and substantially clear, there are issues concerning the definition of the socalled effective absorptivity a^ .
2. Definitions and background Ben Mahmoud and Amlouk [3] have stated that the effective absorbance is defined as the mean absorbance pondered by the solar spectrum irradiance R1 ~ R lmax ~ ~ 0 Iðl ÞAM1:5 a l E dl lmin IðlÞAM1:5 aðlÞEg dl g a^ ¼ R lmax ¼ ð2Þ R1 ~ ~ IðlÞAM1:5 dl 0 Iðl ÞAM1:5 dl l
profile, l~ is the normalized wavelength, and I(l)AM1.5 is solar spectral irradiance. In the same study, the Eg-dependent absorbance profile, for a specific layered material, was determined from the measured transmittance T l~ and reflectance R l~ spectra, and the layer thickness by a smoothening protocol using the 4n-Boubaker polynomials expansion " # N0 1 X a l~ ¼ a0 x0n :B4n l~ rn ð3Þ Eg 2N0 n ¼ 1 where B4n are the 4n-order Boubaker polynomials [5–28], rn are B4n minimal positive roots, N0 is a prefixed integer, xn0 n ¼ 1::N0 are unknown pondering real coefficients, and a0 is the reference absorptivity. The effective absorptivity a^ can hence be calculated using (Eq. (4)): 1 2N0
0
N0 P
n¼1
~ xn :B4n lb n 1 2N 0
N0 P
¼
1369-8001/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2012.06.005
R1
a^ ¼
min
E-mail address: [email protected]
is the material Eg-dependent absorbance
n ¼ 1,m ¼ 1 N0 P n¼1
N0 R1 P 0
n¼1
0 xn :xm Jn,m
xn In
n¼1
~ xn0 :B4n lb n
dl~
~ ~ xn :B4n lb n dl
;
P N0
Jn,m ¼
R1 0
~ ~ ~ B4n lb n B4m lbm dl
112
In ¼
Y.-J. Chen / Materials Science in Semiconductor Processing 16 (2013) 111–112
Z
1 0
~ ~ B4n lb n dl
ð4Þ
where Jn,m and In are calculated using the 4n-Boubaker polynomial proprieties [7–23]. Ambiguity arises from the inconsistency of both definitions. Although the first definition, as used later by Khe´lia et al. [29] emphasizes the response to the standardised solar spectral spectrum, the final one seems to be more linked to the material as stated by Pawley [30] and Biteen et al. [31]. 3. Conclusion In this paper, a new physical parameter: the Amlouk– Boubaker optothermal expansivity, cAB, defined as the ratio of the thermal diffusivity to the effective absorptivity is discussed. This parameter has been assimilated to a three-dimensional expansion velocity of the transmitted heat inside the material, and thus, has been considered a relevant aggregate for evaluating the thermal and optical performance of materials. We have discussed the relevance and correctness of this parameter on the basis of precedent definitions. Some effort is needed to make this parameter accurate, correct and relevant. References [1] B. Ouni, A. Boukhachem, S. Dabbous, A. Amlouk, K. Boubaker, M. Amlouk, Materials Science in Semiconductor Processing 13 (2010) 281–287. [2] S. Fridjine, K. Boubaker, M. Amlouk, Functional Materials Letters 2 (2009) 41–44. [3] K.B. Ben Mahmoud, M. Amlouk, Materials Letters 63 (2009) 991–994. [4] S. Fridjine, M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179–2182. [5] H. Labiadh, M. Dada, O.B. Awojoyogbe, K.B. Ben Mahmoud, A. Bannour, Journal of Differential Equations and Control Processes 1 (2008) 51–66. [6] J. Ghanouchi, H. Labiadh, K. Boubaker, Int. J. of Heat and Technology 26 (2008) 49–52.
[7] S. Slama, M. Bouhafs, K.B. Ben Mahmoud, Int. J. of Heat and Technology 26 (2) (2008) 141–146. [8] K. Boubaker, The Boubaker polynomials, F. E. J. of App. Math 31 (2008) 299–311. [9] S. Slama, J. Bessrour, K. Boubaker, M. Bouhafs, Eur. Phys. J. Appl. Phys. 44 (2008) 317–322. [10] T. Ghrib, K. Boubaker, M. Bouhafs, Modern Physics Letters B 22 (2008) 2893–2993. [11] T. Zhao, B.K. Ben Mahmoud, M.A. Toumi, O.P. Faromika, M. Dada, O.B. Awojoyogbe, J. Magnuson, F. Lin, Journal of Differential Eq. and C.P. 1 (2009) 7. [12] S. Slama, J. Bessrour, M. Bouhafs, K.B. Ben Mahmoud, Numerical Heat Transfer, Part A, Applications 55 (2004) 401–411. [13] A. Milgram, J. of Theoretical Biology 271 (2011) 157–158. [14] J. Ghanouchi, H. Labiadh, K. Boubaker, Int. J. of Heat and Technology 26 (2008) 49–53. [15] S. Lazzez, K.B. Ben Mahmoud, S. Abroug, F. Saadallah, M. Amlouk, Current Applied Physics 9 (2009) 1129–1133. [16] T. Ghrib, K. Boubaker, M. Bouhafs, Modern Physics Letters B 22 (2008) 2893–2907. [17] S. Fridjine, K.B. Ben Mahmoud, M. Amlouk, M. Bouhafs, Journal of Alloys and Compounds 479 (2009) 457–461. [18] C. Khe´lia, K. Boubaker, T. Ben Nasrallah, M. Amlouk, S. Belgacem, Journal of Alloys and Compounds 477 (2009) 461–467. [19] M. Dada, O.B. Awojoyogbe, K. Boubaker, Current Applied Physics 9 (2009) 622–624. [20] S. Tabatabaei, T. Zhao, O. Awojoyogbe, F. Moses, Int. J. Heat Mass Transfer 45 (2009) 1247–1255. [21] A. Belhadj, J. Bessrour, M. Bouhafs, L. Barrallier, J. of Thermal Analysis and Calorimetry 97 (2009) 911–920. [22] A. Belhadj, O. Onyango, N.J. Rozibaeva, Thermophys. Heat Transf 23 (2009) 639–642. [23] P. Barry, A. Hennessy, Journal of Integer Sequences 13 (2010) 1–34. [24] M. Agida, A.S. Kumar, El, Journal of Theoretical Physics 7 (2010) 319–326. [25] A. Yildirim, S.T. Mohyud-Din, D.H. Zhang, Computers and Mathematics with Applications 59 (2010) 2473–2477. [26] A.S. Kumar, Journal of the Franklin Institute 347 (2010) 1755–1761. [27] Benhaliliba M., Benouis C.E., Boubaker K., Amlouk M., Amlouk A. The Amlouk-boubaker Optothermal Expansivity cab in the book: Solar Cells-New Aspects and Solutions, (Edited by): Leonid A. Kosyachenko, [ISBN 978-953-307-761-1, by InTech], 2011:27–41. [28] H. Rahmanov, Studies in Nonlinear Sciences 2 (2011) 46–49. [29] C. Khe´lia, K. Boubaker, M. Amlouk, Fizika 18 (2009) 81–88. [30] J.S. Biteen, D. Pacifici, N.S. Lewis, H.A. Atwater, Nano Lett. 5 (9) (2005 Sep;) 1768–1773. [31] J.B. Pawley, Handbook Of Biological Confocal Microscopy, in: B. James (Ed.), Third Edition, Pawley, Springer Science þBusiness Media, LLC, New York, 2006.
Contents lists available at SciVerse ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
On the notion of the Amlouk–Boubaker optothermal expansivity cAB Yin-Jie Chen Xinjiang University, College of Chemistry and Chemical Engineering, Urumqi 830046, China
a r t i c l e i n f o
abstract
Available online 27 October 2012
In Section 3.4.2 of the commented paper, a new physical parameter: the Amlouk– Boubaker optothermal expansivity, cAB, has been defined as the ratio of the thermal diffusivity to the effective absorptivity. This parameter has been assimilated to a threedimensional expansion velocity of the transmitted heat inside the material, and thus, has been considered a relevant aggregate for evaluating the thermal and optical performance of materials. In this paper, accuracy, correctness and relevance of this parameter are discussed on the basis of precedent definitions. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Amlouk–Boubaker optothermal expansivity Boubaker Polynomials Expansion Scheme (BPES) Crystal growth Thermal analysis Thin films
where a l~
1. Introduction
Eg
In previous studies, the Amlouk–Boubaker optothermal expansivity, cAB, has been defined by [1–4]:
cAB ¼ D=a^
ð1Þ
where D is the layer material thermal diffusivity and a^ is the already defined effective absorptivity. The unit of this parameter, which is expressed in m3/s, has been assimilated to a three-dimensional expansion velocity of the transmitted heat inside the material. Although the definition of the thermal diffusivity, D, is universal and substantially clear, there are issues concerning the definition of the socalled effective absorptivity a^ .
2. Definitions and background Ben Mahmoud and Amlouk [3] have stated that the effective absorbance is defined as the mean absorbance pondered by the solar spectrum irradiance R1 ~ R lmax ~ ~ 0 Iðl ÞAM1:5 a l E dl lmin IðlÞAM1:5 aðlÞEg dl g a^ ¼ R lmax ¼ ð2Þ R1 ~ ~ IðlÞAM1:5 dl 0 Iðl ÞAM1:5 dl l
profile, l~ is the normalized wavelength, and I(l)AM1.5 is solar spectral irradiance. In the same study, the Eg-dependent absorbance profile, for a specific layered material, was determined from the measured transmittance T l~ and reflectance R l~ spectra, and the layer thickness by a smoothening protocol using the 4n-Boubaker polynomials expansion " # N0 1 X a l~ ¼ a0 x0n :B4n l~ rn ð3Þ Eg 2N0 n ¼ 1 where B4n are the 4n-order Boubaker polynomials [5–28], rn are B4n minimal positive roots, N0 is a prefixed integer, xn0 n ¼ 1::N0 are unknown pondering real coefficients, and a0 is the reference absorptivity. The effective absorptivity a^ can hence be calculated using (Eq. (4)): 1 2N0
0
N0 P
n¼1
~ xn :B4n lb n 1 2N 0
N0 P
¼
1369-8001/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2012.06.005
R1
a^ ¼
min
E-mail address: [email protected]
is the material Eg-dependent absorbance
n ¼ 1,m ¼ 1 N0 P n¼1
N0 R1 P 0
n¼1
0 xn :xm Jn,m
xn In
n¼1
~ xn0 :B4n lb n
dl~
~ ~ xn :B4n lb n dl
;
P N0
Jn,m ¼
R1 0
~ ~ ~ B4n lb n B4m lbm dl
112
In ¼
Y.-J. Chen / Materials Science in Semiconductor Processing 16 (2013) 111–112
Z
1 0
~ ~ B4n lb n dl
ð4Þ
where Jn,m and In are calculated using the 4n-Boubaker polynomial proprieties [7–23]. Ambiguity arises from the inconsistency of both definitions. Although the first definition, as used later by Khe´lia et al. [29] emphasizes the response to the standardised solar spectral spectrum, the final one seems to be more linked to the material as stated by Pawley [30] and Biteen et al. [31]. 3. Conclusion In this paper, a new physical parameter: the Amlouk– Boubaker optothermal expansivity, cAB, defined as the ratio of the thermal diffusivity to the effective absorptivity is discussed. This parameter has been assimilated to a three-dimensional expansion velocity of the transmitted heat inside the material, and thus, has been considered a relevant aggregate for evaluating the thermal and optical performance of materials. We have discussed the relevance and correctness of this parameter on the basis of precedent definitions. Some effort is needed to make this parameter accurate, correct and relevant. References [1] B. Ouni, A. Boukhachem, S. Dabbous, A. Amlouk, K. Boubaker, M. Amlouk, Materials Science in Semiconductor Processing 13 (2010) 281–287. [2] S. Fridjine, K. Boubaker, M. Amlouk, Functional Materials Letters 2 (2009) 41–44. [3] K.B. Ben Mahmoud, M. Amlouk, Materials Letters 63 (2009) 991–994. [4] S. Fridjine, M. Amlouk, Modern Phys. Lett. B 23 (2009) 2179–2182. [5] H. Labiadh, M. Dada, O.B. Awojoyogbe, K.B. Ben Mahmoud, A. Bannour, Journal of Differential Equations and Control Processes 1 (2008) 51–66. [6] J. Ghanouchi, H. Labiadh, K. Boubaker, Int. J. of Heat and Technology 26 (2008) 49–52.
[7] S. Slama, M. Bouhafs, K.B. Ben Mahmoud, Int. J. of Heat and Technology 26 (2) (2008) 141–146. [8] K. Boubaker, The Boubaker polynomials, F. E. J. of App. Math 31 (2008) 299–311. [9] S. Slama, J. Bessrour, K. Boubaker, M. Bouhafs, Eur. Phys. J. Appl. Phys. 44 (2008) 317–322. [10] T. Ghrib, K. Boubaker, M. Bouhafs, Modern Physics Letters B 22 (2008) 2893–2993. [11] T. Zhao, B.K. Ben Mahmoud, M.A. Toumi, O.P. Faromika, M. Dada, O.B. Awojoyogbe, J. Magnuson, F. Lin, Journal of Differential Eq. and C.P. 1 (2009) 7. [12] S. Slama, J. Bessrour, M. Bouhafs, K.B. Ben Mahmoud, Numerical Heat Transfer, Part A, Applications 55 (2004) 401–411. [13] A. Milgram, J. of Theoretical Biology 271 (2011) 157–158. [14] J. Ghanouchi, H. Labiadh, K. Boubaker, Int. J. of Heat and Technology 26 (2008) 49–53. [15] S. Lazzez, K.B. Ben Mahmoud, S. Abroug, F. Saadallah, M. Amlouk, Current Applied Physics 9 (2009) 1129–1133. [16] T. Ghrib, K. Boubaker, M. Bouhafs, Modern Physics Letters B 22 (2008) 2893–2907. [17] S. Fridjine, K.B. Ben Mahmoud, M. Amlouk, M. Bouhafs, Journal of Alloys and Compounds 479 (2009) 457–461. [18] C. Khe´lia, K. Boubaker, T. Ben Nasrallah, M. Amlouk, S. Belgacem, Journal of Alloys and Compounds 477 (2009) 461–467. [19] M. Dada, O.B. Awojoyogbe, K. Boubaker, Current Applied Physics 9 (2009) 622–624. [20] S. Tabatabaei, T. Zhao, O. Awojoyogbe, F. Moses, Int. J. Heat Mass Transfer 45 (2009) 1247–1255. [21] A. Belhadj, J. Bessrour, M. Bouhafs, L. Barrallier, J. of Thermal Analysis and Calorimetry 97 (2009) 911–920. [22] A. Belhadj, O. Onyango, N.J. Rozibaeva, Thermophys. Heat Transf 23 (2009) 639–642. [23] P. Barry, A. Hennessy, Journal of Integer Sequences 13 (2010) 1–34. [24] M. Agida, A.S. Kumar, El, Journal of Theoretical Physics 7 (2010) 319–326. [25] A. Yildirim, S.T. Mohyud-Din, D.H. Zhang, Computers and Mathematics with Applications 59 (2010) 2473–2477. [26] A.S. Kumar, Journal of the Franklin Institute 347 (2010) 1755–1761. [27] Benhaliliba M., Benouis C.E., Boubaker K., Amlouk M., Amlouk A. The Amlouk-boubaker Optothermal Expansivity cab in the book: Solar Cells-New Aspects and Solutions, (Edited by): Leonid A. Kosyachenko, [ISBN 978-953-307-761-1, by InTech], 2011:27–41. [28] H. Rahmanov, Studies in Nonlinear Sciences 2 (2011) 46–49. [29] C. Khe´lia, K. Boubaker, M. Amlouk, Fizika 18 (2009) 81–88. [30] J.S. Biteen, D. Pacifici, N.S. Lewis, H.A. Atwater, Nano Lett. 5 (9) (2005 Sep;) 1768–1773. [31] J.B. Pawley, Handbook Of Biological Confocal Microscopy, in: B. James (Ed.), Third Edition, Pawley, Springer Science þBusiness Media, LLC, New York, 2006.