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Year 2021, , 934 - 950, 01.05.2021
https://doi.org/10.18186/thermal.930919

Abstract

References

  • [1]. Cleveland Jr. RF. Radio frequency radiation in the environment: sources, exposure standard, and related issue. In: Carpenter DO, Ayrapetyan S, editors. Biological effects of electric and magnetic fields. 1, New York: Academic Press; 1994.
  • [2]. World Health Organization (WHO) and International Programme on Chemical Safety. Electromagnetic fields (‎300 Hz to 300 GHz)/ published under the joint sponsorship of the United Nations Environment Programme, the International Radiation Protection Association, and the World Health Organization. Geneva: World Health Organization; 1993.
  • [3]. Ryan KL, D’Andrea JA, Jauchem JR, Mason PA. Radio frequency radiation of millimeter wave length: potential occupational safety issues relating to surface heating. Health Phys 2008; 78(2): 170-81. doi: 10.1097/00004032-200002000-00006
  • [4]. Durney CH, Massoudi H, Magdy FI. Radio frequency radiation dosimetry handbook. 4th ed. Texas: B rooks Air Force Base; 1986.
  • [5]. Challis LJ. Mechanisms for interaction between RF fields and biological tissue. Bioelectromagnetics Suppl 2005; 7: S98–S106. https://doi.org/10.1002/bem.20119
  • [6]. Stuchly MA. Health Effects of Exposure to Electromagnetic Fields. IEEE Aerospace Applications Conference Proceedings 1995; 351–368. doi: 10.1109/AERO.1995.468891
  • [7]. Adair ER, Adams BW, Akel GM. Minimal changes in hypothalamic temperature accompany microwave-induced alteration of thermoregulatory behavior. Bioelectromagnetics 1984; 5: 13–30. https://doi.org/10.1002/bem.2250050103
  • [8]. Kargel C.Infrared Thermal Imaging to Measure Local Temperature Rises Caused by Handheld Mobile Phones. IEEE Trans Instrum Meas 2005; 54: 1513–1519. doi: 10.1109/TIM.2005.851082
  • [9]. Kodera S, Gomez-Tames J, Hirata A. Temperature elevation in the human brain and skin with thermoregulation during exposure to RF energy. Biomed Eng OnLine 2018; 17:1. https://doi.org/10.1186/s12938-017-0432-x
  • [10]. Ibrahiem A, Dale C, Tabbara W, Wiart J. Analysis of the temperature increase linked to the power induced by RF source. Prog Electromagn Res 2005; 52: 23–46. doi:10.2528/PIER04062501
  • [11]. Bernardi P, Cavagnaro M, Pisa S, Piuzzi E. Specific absorption rate and temperature increases in the head of a cellular-phone user. IEEE Trans Microw Theory Tech 2000; 48: 1118–1126. doi: 10.1109/22.848494
  • [12]. Leeuwen GMJV, Lagendijk JJW, Leersum BJAMV, Zwamborn APM, Hornsleth SN, Kotte ANTJ. Calculation of change in brain temperatures due to exposure to a mobile phone. Phys Med Biol 1999; 44: 2367–2379. DOI: 10.1088/0031-9155/44/10/301
  • [13]. Wang J, Fujiwara O. FDTD computation of temperature rise in the human head for portable telephones. IEEE Trans Microw Theory Tech. 1999; 47: 1528–1534. doi: 10.1109/22.780405
  • [14]. Wessapan T, Srisawatdhisukul S, Rattanadecho P, (2012). Specific absorption rate and temperature distributions in human head subjected to mobile phone radiation at different frequencies. Int J Heat Mass Transf 2012; 55: 347–359. doi: 10.4103/ijpvm.IJPVM_70_17
  • [15]. Liu J, Chen X, Xu LX. New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating. IEEE Trans Biomed Eng 1999; 46: 420– 428. doi: 10.1109/10.752939
  • [16]. Ozen S, Helhel S, Cerezci O. Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT). Burns 2008; 34: 45–9. doi.org/10.1016/J.BURNS.2007.01.009
  • [17]. Liu J, Zhang X, Wang C, Lu W, Ren Z. Generalized time delay bioheat equation and preliminary analysis on its wave nature. Chin Sci Bull 1997; 42: 289–292. https://doi.org/10.1007/BF02882462
  • [18]. Xu F, Lu T, Seffen KA. Dual-phase-lag model of skin bioheat transfer, Proceedings of the 2008 International Conference on BioMedical Engineering and Informatics 2008; 1: 505–511. doi: 10.1109/BMEI.2008.325
  • [19]. Liu KC, Wang YN, Chen YS. Investigation on the bio-heat transfer with the dual-phase-lag effect. International Journal of Thermal Sciences 2012; 58: 29–35. https://doi.org/10.1016/j.ijthermalsci.2012.02.026
  • [20]. Ahmadikia H, Fazlali R, Moradi A. Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue. International Communications in Heat and Mass Transfer 2012; 39: 121–130. https://doi.org/10.1016/j.icheatmasstransfer.2011.09.016
  • [21]. Xu F, Seffen K, Lu T. Non-Fourier analysis of skin biothermomechanics. International Journal of Heat and Mass Transfer 2008; 51: 2237–2259. https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.024
  • [22]. Mitra K, Kumar S, Vedevarz A, Moallemi MK. Experimental evidence of hyperbolic heat conduction in processed meat. J Heat Transfer 1995; 117: 568–573. https://doi.org/10.1115/1.2822615
  • [23]. Banerjee A, Ogale A, Das C, Mitra K, Subramanian C. Temperature distribution in different materials due to short pulse laser irradiation. Heat Transfer Eng 2005; 26: 41–49. https://doi.org/10.1080/01457630591003754
  • [24]. Antaki P. New interpretation of Non-Fourier heat conduction in processed meat. J Heat Transfer 2005; 127(2): 189-193https://doi.org/10.1115/1.1844540
  • [25]. Xu F, Lu T. Analysis of skin bioheat transfer, in: Introduction to Skin Biothermomechanics and Thermal Pain Berlin, Heidelberg: Springer; 2011. https://doi.org/10.1007/978-3-642-13202-5_4
  • [26]. Kaur J, Khan S. Thermal changes in Human Abdomen Exposed to Microwaves: A Model Study. Advanced Electromagnetics 2019; 8(3): 64-75. https://doi.org/10.7716/aem.v8i3.1092
  • [27]. Liu XZ, Zhu Y, Zhang F, Gong XF. Estimation of temperature elevation generated by ultrasonic irradiation in biological tissues using the thermal wave method. Chin Phys B 2013; 22: 024301. doi: 10.1088/1674-1056/22/2/024301
  • [28]. Tullius TK, Bayazitoglu Y. Analysis of relaxation times on the human head using the thermal wave model. Int J Heat Mass Transf 2013; 67: 1007–1013. https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.097
  • [29]. Pennes HH. Analysis of tissue and arterial blood temperature in the resting human forearm. Journal of Applied Physiology 1948; 1: 93–122. https://doi.org/10.1152/jappl.1948.1.2.93
  • [30]. Kaminski W. Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J Heat Transfer 1990; 112: 555–560. https://doi.org/10.1115/1.2910422
  • [31]. Herwig H, Beckert K. Fourier versus non-fourier heat conduction in materials with a nonhomogeneous inner structure. J Heat Transfer 1999; 122: 363–365. https://doi.org/10.1115/1.521471
  • [32]. Kizilova N, Korobov A. (2019). Bioheat equation with Fourier and non-Fourier heat transport laws: applicability to heat transfer in human tissues. Journal of Thermal Engineering 2019; 5(6): 149-161. https://doi.org/10.18186/thermal.653915
  • [33]. Cattaneo C. A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comp Rend 1958; 247: 431–433.
  • [34]. Vernotte P. (1958). Les paradoxes de la theorie continue de l’equation de la chaleur. Comp Rend 1958; 246: 3154–3155.
  • [35]. Sabbah AI, Dib NI, Al-Nimr MA. Evaluation of specific absorption rate and temperature elevation in a multi-layered human head model exposed to radio frequency radiation using the finite-difference time domain method. IET Microw Antennas Propag 2011; 5: 1073-1080. doi: 10.1049/iet-map.2010.0172
  • [36]. International Commission on Non-Ionizing Radiation Protection (ICNIRP). Guidelines for Limiting Exposure to Time-Varying Electric, Magnetic and Electromagnetic Fields (up to 300 GHz). Health Phys 1998; 74: 494–522.
  • [37]. Spiegel RJ. (1984). A review of numerical models for predicting the energy deposition and resultant thermal response of humans exposed to electromagnetic fields. IEEE Transactions on Microwave Theory and Techniques 1984; 32 (8): 730-746. doi: 10.1109/TMTT.1984.1132767
  • [38]. Wessapan T, Rattanadecho P. Temperature induced in human organs due to near-field and far-field electromagnetic exposure effects. International Journal of Heat and Mass Transfer 2018; 119: 65–76. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.088
  • [39]. Hasgall PA, Di Gennaro F, Baumgartner C, Neufeld E, Lloyd B, Gosselin MC, Payne D, Klingenböck A, Kuster N. IT’IS Database for thermal and electromagnetic parameters of biological tissues, Version 4.0, May 15, 2018. Accessed on February 11, 2019.
  • [40]. Wessapan T, Rattanadecho P. Specific Absorption Rate and Temperature Increase in Human Eye Subjected to Electromagnetic Fields at 900 MHz. Int J Heat Transf 2012; 134: 091101-1-11. https://doi.org/10.1115/1.4006243
  • [41]. Shafahi M, and Vafai K. Human Eye Response to Thermal Disturbances. Journal of Heat Transfer 2011; 133: 011009-1-7. https://doi.org/10.1115/1.4002360
  • [42]. Zhao Y, Tang L, Rennaker R, Hutchens C, Ibrahim TS. Studies in RF Power Communication, SAR, and Temperature Elevation in Wireless Implantable Neural Interfaces. PLoS ONE 2013; 8(11): e77759. https://doi.org/10.1371/journal.pone.0077759

INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES

Year 2021, , 934 - 950, 01.05.2021
https://doi.org/10.18186/thermal.930919

Abstract

The electromagnetic energy carried by microwaves interacts with human head and produces thermal changes within the head. Conventionally, Pennes’ bioheat transfer equation (BTE) is employed to investigate the thermal changes in biological tissues. Pennes’ equation assumes infinite speed of propagation of heat transfer, however, heterogeneous structures such as biological tissues exhibit relaxation times, which is the time required for accumulation of enough energy to transfer it to the nearest element. In present study, we utilized thermal wave model of bioheat transfer (TWMBT) which incorporates relaxation times to numerically predict temperature changes in six layers human head. Finite element based numerical simulation package COMSOL Multiphysics is employed for the thermal analysis. Numerical scheme comprises coupling of solution of Maxwell's equation of wave propagation within tissue to TWMBT. Temperatures estimated with various values of relaxation time are compared with that by Pennes’ equation. The results show that the transient temperature within human head estimated with relaxation time 10 s, 20 s, and 30 s can be up to 36%, 54%, and 66% lower than predicted by Pennes’ BTE respectively. At longer microwave exposure the influence of relaxation times becomes insignificant and the steady state temperatures predicted by TWMBT and Pennes’ BTE are identical. The findings suggest that inclusion of relaxation times in thermal analysis is of significant importance if the exposure duration is short. The effect of parameters such as microwave power and user age on the temperatures projected with different relaxation times is also investigated.

References

  • [1]. Cleveland Jr. RF. Radio frequency radiation in the environment: sources, exposure standard, and related issue. In: Carpenter DO, Ayrapetyan S, editors. Biological effects of electric and magnetic fields. 1, New York: Academic Press; 1994.
  • [2]. World Health Organization (WHO) and International Programme on Chemical Safety. Electromagnetic fields (‎300 Hz to 300 GHz)/ published under the joint sponsorship of the United Nations Environment Programme, the International Radiation Protection Association, and the World Health Organization. Geneva: World Health Organization; 1993.
  • [3]. Ryan KL, D’Andrea JA, Jauchem JR, Mason PA. Radio frequency radiation of millimeter wave length: potential occupational safety issues relating to surface heating. Health Phys 2008; 78(2): 170-81. doi: 10.1097/00004032-200002000-00006
  • [4]. Durney CH, Massoudi H, Magdy FI. Radio frequency radiation dosimetry handbook. 4th ed. Texas: B rooks Air Force Base; 1986.
  • [5]. Challis LJ. Mechanisms for interaction between RF fields and biological tissue. Bioelectromagnetics Suppl 2005; 7: S98–S106. https://doi.org/10.1002/bem.20119
  • [6]. Stuchly MA. Health Effects of Exposure to Electromagnetic Fields. IEEE Aerospace Applications Conference Proceedings 1995; 351–368. doi: 10.1109/AERO.1995.468891
  • [7]. Adair ER, Adams BW, Akel GM. Minimal changes in hypothalamic temperature accompany microwave-induced alteration of thermoregulatory behavior. Bioelectromagnetics 1984; 5: 13–30. https://doi.org/10.1002/bem.2250050103
  • [8]. Kargel C.Infrared Thermal Imaging to Measure Local Temperature Rises Caused by Handheld Mobile Phones. IEEE Trans Instrum Meas 2005; 54: 1513–1519. doi: 10.1109/TIM.2005.851082
  • [9]. Kodera S, Gomez-Tames J, Hirata A. Temperature elevation in the human brain and skin with thermoregulation during exposure to RF energy. Biomed Eng OnLine 2018; 17:1. https://doi.org/10.1186/s12938-017-0432-x
  • [10]. Ibrahiem A, Dale C, Tabbara W, Wiart J. Analysis of the temperature increase linked to the power induced by RF source. Prog Electromagn Res 2005; 52: 23–46. doi:10.2528/PIER04062501
  • [11]. Bernardi P, Cavagnaro M, Pisa S, Piuzzi E. Specific absorption rate and temperature increases in the head of a cellular-phone user. IEEE Trans Microw Theory Tech 2000; 48: 1118–1126. doi: 10.1109/22.848494
  • [12]. Leeuwen GMJV, Lagendijk JJW, Leersum BJAMV, Zwamborn APM, Hornsleth SN, Kotte ANTJ. Calculation of change in brain temperatures due to exposure to a mobile phone. Phys Med Biol 1999; 44: 2367–2379. DOI: 10.1088/0031-9155/44/10/301
  • [13]. Wang J, Fujiwara O. FDTD computation of temperature rise in the human head for portable telephones. IEEE Trans Microw Theory Tech. 1999; 47: 1528–1534. doi: 10.1109/22.780405
  • [14]. Wessapan T, Srisawatdhisukul S, Rattanadecho P, (2012). Specific absorption rate and temperature distributions in human head subjected to mobile phone radiation at different frequencies. Int J Heat Mass Transf 2012; 55: 347–359. doi: 10.4103/ijpvm.IJPVM_70_17
  • [15]. Liu J, Chen X, Xu LX. New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating. IEEE Trans Biomed Eng 1999; 46: 420– 428. doi: 10.1109/10.752939
  • [16]. Ozen S, Helhel S, Cerezci O. Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT). Burns 2008; 34: 45–9. doi.org/10.1016/J.BURNS.2007.01.009
  • [17]. Liu J, Zhang X, Wang C, Lu W, Ren Z. Generalized time delay bioheat equation and preliminary analysis on its wave nature. Chin Sci Bull 1997; 42: 289–292. https://doi.org/10.1007/BF02882462
  • [18]. Xu F, Lu T, Seffen KA. Dual-phase-lag model of skin bioheat transfer, Proceedings of the 2008 International Conference on BioMedical Engineering and Informatics 2008; 1: 505–511. doi: 10.1109/BMEI.2008.325
  • [19]. Liu KC, Wang YN, Chen YS. Investigation on the bio-heat transfer with the dual-phase-lag effect. International Journal of Thermal Sciences 2012; 58: 29–35. https://doi.org/10.1016/j.ijthermalsci.2012.02.026
  • [20]. Ahmadikia H, Fazlali R, Moradi A. Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue. International Communications in Heat and Mass Transfer 2012; 39: 121–130. https://doi.org/10.1016/j.icheatmasstransfer.2011.09.016
  • [21]. Xu F, Seffen K, Lu T. Non-Fourier analysis of skin biothermomechanics. International Journal of Heat and Mass Transfer 2008; 51: 2237–2259. https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.024
  • [22]. Mitra K, Kumar S, Vedevarz A, Moallemi MK. Experimental evidence of hyperbolic heat conduction in processed meat. J Heat Transfer 1995; 117: 568–573. https://doi.org/10.1115/1.2822615
  • [23]. Banerjee A, Ogale A, Das C, Mitra K, Subramanian C. Temperature distribution in different materials due to short pulse laser irradiation. Heat Transfer Eng 2005; 26: 41–49. https://doi.org/10.1080/01457630591003754
  • [24]. Antaki P. New interpretation of Non-Fourier heat conduction in processed meat. J Heat Transfer 2005; 127(2): 189-193https://doi.org/10.1115/1.1844540
  • [25]. Xu F, Lu T. Analysis of skin bioheat transfer, in: Introduction to Skin Biothermomechanics and Thermal Pain Berlin, Heidelberg: Springer; 2011. https://doi.org/10.1007/978-3-642-13202-5_4
  • [26]. Kaur J, Khan S. Thermal changes in Human Abdomen Exposed to Microwaves: A Model Study. Advanced Electromagnetics 2019; 8(3): 64-75. https://doi.org/10.7716/aem.v8i3.1092
  • [27]. Liu XZ, Zhu Y, Zhang F, Gong XF. Estimation of temperature elevation generated by ultrasonic irradiation in biological tissues using the thermal wave method. Chin Phys B 2013; 22: 024301. doi: 10.1088/1674-1056/22/2/024301
  • [28]. Tullius TK, Bayazitoglu Y. Analysis of relaxation times on the human head using the thermal wave model. Int J Heat Mass Transf 2013; 67: 1007–1013. https://doi.org/10.1016/j.ijheatmasstransfer.2013.08.097
  • [29]. Pennes HH. Analysis of tissue and arterial blood temperature in the resting human forearm. Journal of Applied Physiology 1948; 1: 93–122. https://doi.org/10.1152/jappl.1948.1.2.93
  • [30]. Kaminski W. Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure. J Heat Transfer 1990; 112: 555–560. https://doi.org/10.1115/1.2910422
  • [31]. Herwig H, Beckert K. Fourier versus non-fourier heat conduction in materials with a nonhomogeneous inner structure. J Heat Transfer 1999; 122: 363–365. https://doi.org/10.1115/1.521471
  • [32]. Kizilova N, Korobov A. (2019). Bioheat equation with Fourier and non-Fourier heat transport laws: applicability to heat transfer in human tissues. Journal of Thermal Engineering 2019; 5(6): 149-161. https://doi.org/10.18186/thermal.653915
  • [33]. Cattaneo C. A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comp Rend 1958; 247: 431–433.
  • [34]. Vernotte P. (1958). Les paradoxes de la theorie continue de l’equation de la chaleur. Comp Rend 1958; 246: 3154–3155.
  • [35]. Sabbah AI, Dib NI, Al-Nimr MA. Evaluation of specific absorption rate and temperature elevation in a multi-layered human head model exposed to radio frequency radiation using the finite-difference time domain method. IET Microw Antennas Propag 2011; 5: 1073-1080. doi: 10.1049/iet-map.2010.0172
  • [36]. International Commission on Non-Ionizing Radiation Protection (ICNIRP). Guidelines for Limiting Exposure to Time-Varying Electric, Magnetic and Electromagnetic Fields (up to 300 GHz). Health Phys 1998; 74: 494–522.
  • [37]. Spiegel RJ. (1984). A review of numerical models for predicting the energy deposition and resultant thermal response of humans exposed to electromagnetic fields. IEEE Transactions on Microwave Theory and Techniques 1984; 32 (8): 730-746. doi: 10.1109/TMTT.1984.1132767
  • [38]. Wessapan T, Rattanadecho P. Temperature induced in human organs due to near-field and far-field electromagnetic exposure effects. International Journal of Heat and Mass Transfer 2018; 119: 65–76. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.088
  • [39]. Hasgall PA, Di Gennaro F, Baumgartner C, Neufeld E, Lloyd B, Gosselin MC, Payne D, Klingenböck A, Kuster N. IT’IS Database for thermal and electromagnetic parameters of biological tissues, Version 4.0, May 15, 2018. Accessed on February 11, 2019.
  • [40]. Wessapan T, Rattanadecho P. Specific Absorption Rate and Temperature Increase in Human Eye Subjected to Electromagnetic Fields at 900 MHz. Int J Heat Transf 2012; 134: 091101-1-11. https://doi.org/10.1115/1.4006243
  • [41]. Shafahi M, and Vafai K. Human Eye Response to Thermal Disturbances. Journal of Heat Transfer 2011; 133: 011009-1-7. https://doi.org/10.1115/1.4002360
  • [42]. Zhao Y, Tang L, Rennaker R, Hutchens C, Ibrahim TS. Studies in RF Power Communication, SAR, and Temperature Elevation in Wireless Implantable Neural Interfaces. PLoS ONE 2013; 8(11): e77759. https://doi.org/10.1371/journal.pone.0077759
There are 42 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Jagbir Kaur This is me 0000-0001-9937-0084

Suyeb Khan This is me 0000-0001-8565-5134

Publication Date May 1, 2021
Submission Date May 10, 2019
Published in Issue Year 2021

Cite

APA Kaur, J., & Khan, S. (2021). INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES. Journal of Thermal Engineering, 7(4), 934-950. https://doi.org/10.18186/thermal.930919
AMA Kaur J, Khan S. INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES. Journal of Thermal Engineering. May 2021;7(4):934-950. doi:10.18186/thermal.930919
Chicago Kaur, Jagbir, and Suyeb Khan. “INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES”. Journal of Thermal Engineering 7, no. 4 (May 2021): 934-50. https://doi.org/10.18186/thermal.930919.
EndNote Kaur J, Khan S (May 1, 2021) INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES. Journal of Thermal Engineering 7 4 934–950.
IEEE J. Kaur and S. Khan, “INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES”, Journal of Thermal Engineering, vol. 7, no. 4, pp. 934–950, 2021, doi: 10.18186/thermal.930919.
ISNAD Kaur, Jagbir - Khan, Suyeb. “INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES”. Journal of Thermal Engineering 7/4 (May 2021), 934-950. https://doi.org/10.18186/thermal.930919.
JAMA Kaur J, Khan S. INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES. Journal of Thermal Engineering. 2021;7:934–950.
MLA Kaur, Jagbir and Suyeb Khan. “INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES”. Journal of Thermal Engineering, vol. 7, no. 4, 2021, pp. 934-50, doi:10.18186/thermal.930919.
Vancouver Kaur J, Khan S. INFLUENCE OF RELAXATION TIMES ON HEAT TRANSFER IN HUMAN HEAD EXPOSED TO MICROWAVE FREQUENCIES. Journal of Thermal Engineering. 2021;7(4):934-50.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK http://eds.yildiz.edu.tr/journal-of-thermal-engineering