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Performance of a novel solar assisted Bian stone thermal therapy
International Journal of Heat and Mass Transfer 100 (2016) 445–450
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance of a novel solar assisted Bian stone thermal therapy Cai Wu a, Xiuhua Chen a, Xinping Zhou b,c,⇑ a
The Second Clinical College, Guangzhou University of Chinese Medicine (GUCM), Guangzhou 510405, China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China c Research Institute of Huazhong University of Science and Technology in Shenzhen, Shenzhen 518057, China b
a r t i c l e
i n f o
Article history: Received 11 February 2016 Accepted 21 April 2016 Available online 12 May 2016 Keywords: Solar assisted system Bian stone thermal therapy Heat transfer Human body
a b s t r a c t In this paper, a novel Bian stone thermal therapy assisted by using solar radiation is proposed for safe thermal therapy on patients. A mathematical model is developed based on heat balance, and the performance of heat transfer from the novel Bian stone thermal therapy system to human body is studied. Sensitivity analysis is also performed. Fluid heated by solar radiation is channeled through a pipe to heat the Bian stone. For stronger solar radiation, or smaller or shorter pipe, the Bian stone attains the initial body temperature faster, and the novel thermal therapy system shows better performance and can therefore be used on patients earlier during the day. Early use of the thermal therapy system is a very important factor because the lowest ambient temperature is normally obtained early in the morning. Moderate water flow velocity is suitable by considering good mixing effect and power savings. The stone-body contact surface area has little influence on the critical heating time for the Bian stone to reach the initial body temperature after sunrise. This work lays a solid foundation for safe use of the solar assisted Bian stone thermal therapy. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, fossil fuels have been depleting and air pollution worsening. Fossil fuels are also environmentally unfriendly hence there is need to look for alternative energy sources for various domestic and commercial use. Like wind power, biomass, and gravitational potential energy of water for use [1–3], solar radiation energy has been considered as a reliable and widely available energy source for sustainable use in the near future [4,5]. Additionally, solar radiation energy is safe and environmentally friendly. Bian stone also called bianshi or stone needle is one of the earliest known instruments of therapy in Traditional Chinese Medicine [6]. The Bian stone is used for performing massage, heating, and other physiotherapies (Fig. 1a). Bian stone can be used to help relaxing muscle, relieving pain, promoting blood circulation and so on [7]. The Bian stone therapy has obvious therapeutic effect on many diseases, such as shoulder periarthritis [8], cervical spondylosis [9] and osteoarthritis [10]. Nowadays, the Bian stone’s function of nursing health in daily life is attracting great interest of more and more people [6]. ⇑ Corresponding author at: Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (X. Zhou). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.04.062 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Thermal therapy helps in generating heat in the human body and leads to higher tissue temperature. This rise in temperature produces vasodilation, thus promoting better blood circulation. It also can improve the metabolism of human tissues and organs. Thermal therapy has good effect on some diseases such as, some pains [11], blood vessels [12], nerves [12], myalgia [13], fibromyalgia [13], contracture [13], bursitis [13] and muscle spasms [13]. Electricity is usually used to heat the Bian stone in order to enhance the thermal therapy on patients [14]. However, like for electrothermal blanket [15], there is potential safety risk for the electrothermal Bian stone attached to human bodies when it is used many times. Safety is always one of the most important factors during treatment. Therefore, a major question of how to improve safety during treatment must always be asked using any form of treatment. Previous studies on Bian stone have focused on analyses of the chemical constitute of the materials [16,17]. However, to date, little work on safety of electrothermal Bian stone therapy has been reported. In order to solve the safety problem, this paper explores a new way of using solar radiation to assist in the application of Bian stone thermal therapy. A mathematical model is developed, the heat transfer performance is studied, and the sensitivity analysis is performed.
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are used to link the water heater and the upper surface of Bian stone. A pump is used to force the circulation of water in the two pipes. In order to accelerate the heating rate of water in the pipe and reduce the heat loss through the pipe wall, the water pipe should be as short as possible. Therefore, the pipe can reach the heater through the dish concentrator center, and the table/bed of therapy can be located below the concentrator center. The heat transfer principle used in the system is: flowing water obtains heat from the water heater and releases heat to Bian stone. The continuously heated Bian stone can be used for therapy on patients’ bodies when the stone temperature is over the initial body temperature. One factor that must be considered is that the rate at which Bian stone heats up is slow, therefore, modeling the heating process of Bian stone and body and studying the performance are very important processes. Once the body is heated to a target temperature, any available heat control technology to keep the body at the target temperature can be employed in releasing the redundant heat to other materials or systems. This aspect is not studied in this work. 3. Mathematical model
Fig. 1. (a) Picture of a traditional Bian stone therapy (which is from the Traditional Therapy Center of the Second Affiliated Hospital of GUCM); (b) schematic of solar assisted Bian stone thermal therapy system.
2. Description of Bian stone therapy and novel solar assisted system 2.1. Characteristics of Bian stone therapy Use of Bian stone as an instrument of therapy can be traced back to the New Stone Age about 4000 years ago [6,18]. The Bian stone in the earliest form used for therapy is a piece of polished sharpened flat stone or stone needle used for treating illness by pricking certain parts of the body [19]. The acupuncture originated from the Bian stone therapy [20]. With the development of Traditional Chinese Medicine, stone needles were gradually replaced by needles made of metal used for acupuncture [19,21]. Whatever the case, Bian stone played an important role in ancient therapy and works well in modern therapy. Use of Bian stone for physiotherapy is determined by the material characteristics of Bian stone. Bian stone is composed of numerous calcite microcrystallines [17]. The stone has good capability of heat conduction, storage and radiation due to its high-content microcrystalline calcite with good thermal properties [17,22]. Specifically, Bian stone has high infrared emission rate. Infrared radiation energy can easily be absorbed by human body and is more useful in heating the human body than visible radiation which is strongly reflected by the human body. The good thermal property of Bian stone determines its very good physiotherapeutic effect on the human body. In this case, Bian stone can improve the energy metabolism of human cells and promote microcirculation, thus being very beneficial to alleviating diseases and improving health conditions [22,23]. 2.2. Description of a novel solar assisted Bian stone thermal therapy system A novel Bian stone thermal therapy assisted by using solar radiation is proposed (Fig. 1b). In the solar assisted Bian stone thermal therapy system, a concentrating solar collector, i.e., a parabolic dish concentrator tracking the sun’s beams is installed on the roof of a house to heat the water heater at its center. Two water pipes
A mathematical model based on heat balance is developed for the solar assisted Bian stone thermal therapy system. The following assumptions are made: (1) The power of the pump is enough to force the water to mix fully and quickly. Therefore, the temperature of the working fluid is taken to be constant and uniform to some extent. (2) The heat loss through the body is not considered because the heat penetration depth is assumed to be far smaller than the thickness of the studied part of the body. (3) The heat is transferred from the stone to the body perpendicularly to the stone-body contact surface. By assuming the maximum irradiance of a day to occur at the noon (12:00), solar radiation intensity G at any time t for daylight hours in a day is calculated by [24]
G ¼ Gmax cos ððt=3600 12Þp=DÞ
ð1Þ
where Gmax is the maximum solar radiation in the day and D is the total daylight hours in the day, while for non-daylight hours G = 0. The ambient temperature in the day can be taken as [24]
T 1 ¼ T 1av g þ DT 1 cos ððt=3600 14Þp=12Þ
ð2Þ
where T1avg is the average temperature of the day, and DT1 is the diurnal temperature range, which is equal to the maximum temperature variation in the day, and is assumed to occur at 14:00 p.m. The equation to describe the heat transfer from the solar radiation absorbed by the solar concentrator to the working fluid is given by
aGAcoll U loss ðT f T 1 ÞAp hf ðT f T st ÞAst ¼ mf cpf
dT f dt
ð3Þ
where a is the effective absorptivity of solar radiation G, Acoll is the effective collecting area of solar radiation, Ap is the average heat transfer area of the pipe conveying fluid and the thermal insulating layer, Ast is the area of the stone-body contact surface, mf is the total mass of working fluid in the pipe, cpf is the specific heat capacity of working fluid, Tf is the temperature of working fluid, and Uloss is the effective heat loss coefficient of the working fluid. The heat transferred from the working fluid to the Bian stone is assumed to be stored in the stone and the studied part of the body. The structure of the body including skins, muscles, bones, blood, vessels and so on is very complex. In addition, the Bian stone is assumed to be thin. In order to study the heat transfer in the body
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conveniently, the temperature gradient is assumed to be linear in the body and stone. Therefore, when the Bian stone is in contact with the body, the heat transfer equation can be expressed as
dT av g hf T f T st Ast ¼ ðMst cst þ Mb cb Þ dt
ð4Þ
where Mst is the mass of the Bian stone, and Mb is the mass of the body part influenced by the heat of the stone in contact with the body. The average temperature, Tavg, is given by
T av g ¼
T st þ T b0 2
ð5Þ
where Tb0 is the original temperature of the human body. Substituting Eq. (5) into Eq. (4), we obtain:
1 dT st hf T f T st Ast ¼ ðM st cst þ M b cb Þ 2 dt
ð6Þ
It is known that some time after sunrise, the temperature of the fluid and the Bian stone may still be lower than normal temperature of human body. So the Bian stone is used for therapy on human body only when the fluid temperature is high enough, preferably when the stone’s temperature is above the body temperature. In this case, Eqs. (4)–(6) can be used. If the temperature of the Bian stone is very low, the stone is put into a thermal insulating layer like the water pipe, and then in that case the following equation can be used:
hf ðT f T st Þ U loss2 ðT st T 1 Þ ¼ 0
ð7Þ
where Uloss2 is the effective heat loss coefficient of the working fluid container through the stone and its thermal insulating layer. The effective heat loss coefficient of the working fluid, Uloss, is given by
U loss ¼
1 1 hf
ð8Þ
d
þ h1w þ kpp þ dki i
where dp and kp are the thickness and thermal conductivity of the tube wall, respectively, di and ki are the thickness and thermal conductivity of the thermal insulating layer surrounding the tube conveying fluid, respectively, and hf and hw are the convection heat transfer coefficients from water to the pipe wall and from the thermal insulating layer of the pipe to the ambient winds, respectively. The effective heat loss coefficient of the working fluid through the stone and its thermal insulating layer, Uloss2, is
U loss2 ¼
1 1 hw
ð9Þ
þ dki þ dkstst i
hw can be given by [25]
hw ¼ 5:7 þ 3:8V w
ð10Þ
where Vw is the velocity of air flow around the thermal insulating layer. hf can be expressed as
hf ¼
kf Nu dp
ð11Þ
For a fully developed laminar or turbulent flow in a circular tube, the following equations of Nusselt number Nu can be used, respectively [26]:
Nu ¼
4:36;
laminar
0:023 Re0:8 Pr0:3 ; turbulent
ð12Þ
4. Results and discussion The reference values of the parameters used in conducting the study of the performance of the solar assisted Bian stone thermal
therapy system are presented in Table 1. There is always a suitable temperature range for thermal therapy on patients’ bodies. In this paper, the target average body temperature is set to be 45 °C for the Bian stone thermal therapy. Fig. 2 shows the solar radiation intensity and ambient temperature on a reference day. In this figure, there is zero solar radiation and lowest ambient temperature during the period from 0:00 a.m. to 5:00 a.m. Therefore, the thermal therapy system is assumed to start operation once the solar radiation is received by the solar collector. In the early stage after the thermal therapy system operates, the temperature of the stone may still be lower than normal temperature of human body. It is assumed that once heated to the temperature equal to the normal temperature of human body, the stone parameters shift from being in the thermal insulating layer to working on the body. Fig. 3 shows the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. under the temperature limit of 45 °C. In this figure, the temperature gradually increases after 5:00 a.m. and reaches initial body temperature after 29.9 min. Therefore, it is proposed that the system is used on patients’ bodies after 29.9 min. The average body temperature reaches 45 °C after 57.2 min. Fig. 4 shows that the variations of the stone’s surface temperature and average body temperature with time starting from 5:00 a.m. for various daily maximum solar radiation intensity of 400 W/m2, 600 W/m2 and 800 W/m2. As expected, stronger solar radiation provides more heat and leads to quicker heating of the stone and the body. This subsequently leads to the body attaining the desired temperature in a shorter time. This effect by increasing solar radiation intensity can be considered similar to enlarging the collector area or improving the collector efficiency. Fig. 5 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various pipe diameters. Smaller water volume in the pipe will result in higher water temperature, which determines higher temperature of both the stone and the influenced body due to larger volume and larger thermal storage capacity of water as compared to the stone and body. The critical heating time of
Table 1 Reference values of parameters used. Parameters
Values
Concentrating solar collector area (m2) Effective absorptivity of solar radiation (%) Pipe diameter (m) Pipe length (m) Outside length (m) Inside length (m) Pipe wall thickness (m) Pipe wall heat conductivity (W/(m K)) Water flow velocity in pipe (m/s) Thermal insulating layer thickness (m) Thermal insulating layer heat conductivity (W/ (m K)) Initial body temperature (°C) Ambient wind velocity (m/s) Inside wind velocity (m/s) Body’s density (kg/m3) Body’s specific heat capacity (J/(kg K)) Studied volume of body (L*W*H) Average temperature of the day (°C) Diurnal temperature range (°C) Maximum solar radiation in the day (W/m2) Total daylight hours in the day (h) Bian stone density (kg/m3) Bian stone specific heat capacity (J/(kg K)) Bian stone size (L*W*H) Limit of average temperature of the stone and the influenced part of the body (°C)
20 80 0.04 21.5 17 4.5 0.005 0.14 0.5 0.015 0.05 36 2 0.2 1045 3000 0.2 m * 0.2 m * 0.1 m 30 3 600 14 2800 900 0.2 m * 0.2 m * 0.015 m 45
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Fig. 2. Solar radiation intensity and ambient temperature in a reference day.
Fig. 5. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various pipe diameters.
Fig. 3. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C. Fig. 6. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various thicknesses of thermal insulating layer.
Fig. 4. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various solar radiation intensities.
reaching initial body temperature becomes less for smallerdiameter pipe. This effect of decreasing the pipe diameter can be assumed to be similar to decreasing the pipe length since the most important parameter here is the volume. Fig. 6 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various thermal insulating layer thicknesses of 0.005 m, 0.015 m, and 0.025 m. The thickness of thermal insulating layer between 0.005 m and 0.025 m has little influence on the temperature and the critical heating time of reaching initial body temperature, and the results for the thickness of 0.0015 m are basically
Fig. 7. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various water flow velocities.
the same as those for the thickness of 0.025 m. This is because that the superficial area of the tube is far smaller than effective collecting area of solar collector and the tube wall has high thermal resistance. It is also found out that the thermal insulating layer of the system is high-performance. Fig. 7 shows the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various flow velocities of water of 0.2 m/s, 0.5 m/s and 0.8 m/s.
C. Wu et al. / International Journal of Heat and Mass Transfer 100 (2016) 445–450
Fig. 8. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various areas of stone-body contact surface.
Before reaching the initial body temperature, the temperature is basically the same for the three water flow velocities. After reaching the initial body temperature, with a decrease in water flow velocity, the convective heat transfer rate from the hot water to the stone and body becomes lower. This results in a lower stone and body temperature. The results for the water flow velocity of 0.5 m/s are very close to those of 0.8 m/s, and the difference between the temperature for water flow velocity of 0.2 m/s and temperature for 0.5 m/s is not large. This shows that the water flow velocity has small effect on the temperature variation so long as the velocity is not too low. However very low water flow velocity is not desirable because this will cause poor mixing effect of the water inside the pipe which is contrary to the assumption of the mathematical model. Too high water flow velocity is also not suitable, because water of high flux increases the electricity use of the therapy system and it basically doesn’t enhance the performance of the therapy system. Therefore, a moderate value e.g., of 0.5 m/ s is recommended for the flow velocity of water inside the pipe. Fig. 8 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various stone-body contact surface areas of 0.01 m2, 0.04 m2 and 0.09 m2. In order to enhance the effect of the stonebody contact surface area on temperature variations, the change rates of the three areas are much higher than those for solar radiation intensities, pipe lengths, pipe diameters, thicknesses of thermal insulating layer and water flow velocities. In this figure, as expected, the area of the stone-body contact surface has little effect on the temperature variations because the studied volume of body is assumed to have direct proportion relationship with the area of the stone-body contact surface. Larger stone-body contact surface area determines larger volume of studied body and leads to the slight reduction of the water temperature, thus making the time of reaching the target temperature slightly shorter. In order to use the therapy system early on patients after sunrise, strong solar radiation, and small and short pipe are desirable, moderate water flow velocity is recommended, and the stone-body contact surface area has little influence on the temperature of stone and body as well as the critical time of reaching the target temperature. In order to get stronger solar radiation, the collector area can be increased, or a more efficient collector can be employed.
5. Conclusions Solar radiation energy is considered to be one of the most promising new energy resources and electrothermal Bian stone
449
therapy is a suitable way to treat special diseases. Safety is the most importance factor of therapy. In this paper, a novel solar assisted Bian stone thermal therapy system has been proposed, mathematically modeled and tested. The proposed novel system is safer and can reduce the possibility of accidents as opposed to electrothermal carpets. A mathematical model based on heat balance has been developed. The calculated results and the sensitivity analysis have been demonstrated and some conclusions are drawn as follows. When starting from 5:00 a.m., the Bian stone is gradually heated by solar radiation energy to the initial body temperature after operating for 29.9 min. It is proposed that the Bian stone can then be used on patients’ bodies after this period of 29.9 min. The average body temperature is heated to the target average body temperature of 45 °C after a period of 57.2 min. Stronger solar radiation, or smaller or shorter pipe results in better performance of the novel system. Therefore, the therapy system can be used on patients earlier during the day. Early use of the thermal therapy system is a very important factor because the lowest ambient temperature is normally obtained early in the morning. Higher flow velocity of water leads to slightly better performance of the system at the expense of more electricity use, and very low water flow velocity causes poor mixing effect of the water, so a moderate water flow velocity is more suitable. The stone-body contact surface area has little influence on the temperature of stone and body and the critical time of reaching the target temperature. This work lays a solid foundation for safe use of Bian stone thermal therapy. It is recommended that further researches be focused on the developing of more comprehensive studies of the enhancement performance of the novel solar assisted Bian stone thermal therapy with some improvements.
Acknowledgements This research has been partially supported by Huazhong University of Science and Technology Foundation (No. 2014ZZGH006) and the Special Fund for Strategic New Industry Development of Shenzhen, China (Grant No. JCYJ20140509162710494).
References [1] A.D. Sßahin, Progress and recent trends in wind energy, Prog. Energy Combust. Sci. 30 (2014) 501–543. [2] X.P. Zhou, F. Wang, H.W. Hu, L. Yang, P.H. Guo, B. Xiao, Assessment of sustainable biomass resource for energy use in China, Biomass Bioenergy 35 (2011) 1–11. [3] B. Wagner, C. Hauer, A. Schoder, H. Habersack, A review of hydropower in Austria: past, present and future development, Renewable Sustainable Energy Rev. 50 (2015) 304–314. [4] X.P. Zhou, Y.Y. Xu, Solar updraft tower power generation, Sol. Energy 128 (2016) 95–125. [5] C. Li, Y. Goswami, E. Stefanakos, Solar assisted sea water desalination: a review, Renewable Sustainable Energy Rev. 19 (2013) 136–163. [6] J.B. Meng, Z.J. Meng, Bianshixue, TCM Ancient Books Publishing House, Beijing, 2007. [7] C.Q. Guo, S.N. Han, Illustration of Bian Stone Therapy, China Medical Science Press, Beijing, 2012, p. 2. [8] C.Q. Guo, N. Rui, Y.G. Liu, Y.X. Liu, Y. Sha, G.H. Ma, Multi-central randomized controlled observation on clinical therapeutic effect of the new Bian-stone therapy on scapulohumeral periarthritis, Chin. Acupunct. Moxibust. 27 (2007) 633–637. [9] Y.X. Geng, J. Yu, S.S. Hu, Z.X. Lu, Treatment of 30 cases of cervical spondylosis with Bian stone therapy, Hebei J. Tradit. Chin. Med. 29 (2007) 1109–1110 (in Chinese). [10] Z.W. Hou, P. Zheng, Treatment of 36 cases of degenerative knee osteoarthritis with warm purgative therapy of stone needle, Beijing Univ. Tradit. Chin. Med. (Clin. Med.) 17 (2010) 33–35 (in Chinese). [11] C. Wu, Heat transfer behavior for lower back of human body using Bian stone therapy, in: International Conference and Expo on Novel Physiotherapies, Chicago, Illinois, USA, 2015. [12] Y.W. Ding, G.H. Ding, Application of infrared radiation spectrum to acumoxibustion research, Acupunct. Res. 31 (2006) 252–255 (in Chinese).
450
C. Wu et al. / International Journal of Heat and Mass Transfer 100 (2016) 445–450
[13] P.P. Raj, Practical Management of Pain, third ed., Mosby, Missouri, 2000, ISBN 978-0-8151-2569-3. [14] T. Huang, G. Litscher, L. Wang, W.B. Zhang, Study on effect of lying electrothermal Bian-stone on Dazhui to blood flow velocity of cerebral arteries, Chin. J. Basic Med. Tradit. Chin. Med. 18 (2012) 312–313 (in Chinese). [15] Warshauer-McLaughlin Law Group, P.C. Electric Blanket Fire Causes. Available at
[19] K.-W. Ma, The roots and development of Chinese acupuncture: from prehistory to early 20th century, Acupunct. Med. 10 (1992) 92–99. [20] B. Wang, Huang Di Nei Jing (Yellow Emperor’s Internal Classic), TCM Ancient Books Publishing House, Beijing, 2003. [21] L.X. Lao, Acupuncture techniques and devices, J. Altern. Complement. Med. 2 (1996) 23–25. [22] S. Ge, G.-Z. Chen, S.-H. Liu, Application thinking on Bian-stone of the acoustooptic effect in the treatment of primary dysmenorrhea, in: Proc. of SPIE, vol. 7519, 2009, p. 751908. [23] Q. Qiu, The discovery of Sibin Bian-stone makes old stone needle newborn, in: The Chinese Medicine Research Institute Academy Reports 18, 2002. 4. [24] C.D. Papageorgiou, Floating solar chimney power stations with thermal storage, in: Proceedings of the IASTED Conference on European Power and Energy Systems, Rhodes, Greece, 2006. Also available at. [25] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, fourth ed., Wiley, New York, 2013. [26] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, seventh ed., Wiley, New Jersey, 2011, pp. 337–552.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Performance of a novel solar assisted Bian stone thermal therapy Cai Wu a, Xiuhua Chen a, Xinping Zhou b,c,⇑ a
The Second Clinical College, Guangzhou University of Chinese Medicine (GUCM), Guangzhou 510405, China Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China c Research Institute of Huazhong University of Science and Technology in Shenzhen, Shenzhen 518057, China b
a r t i c l e
i n f o
Article history: Received 11 February 2016 Accepted 21 April 2016 Available online 12 May 2016 Keywords: Solar assisted system Bian stone thermal therapy Heat transfer Human body
a b s t r a c t In this paper, a novel Bian stone thermal therapy assisted by using solar radiation is proposed for safe thermal therapy on patients. A mathematical model is developed based on heat balance, and the performance of heat transfer from the novel Bian stone thermal therapy system to human body is studied. Sensitivity analysis is also performed. Fluid heated by solar radiation is channeled through a pipe to heat the Bian stone. For stronger solar radiation, or smaller or shorter pipe, the Bian stone attains the initial body temperature faster, and the novel thermal therapy system shows better performance and can therefore be used on patients earlier during the day. Early use of the thermal therapy system is a very important factor because the lowest ambient temperature is normally obtained early in the morning. Moderate water flow velocity is suitable by considering good mixing effect and power savings. The stone-body contact surface area has little influence on the critical heating time for the Bian stone to reach the initial body temperature after sunrise. This work lays a solid foundation for safe use of the solar assisted Bian stone thermal therapy. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction In recent years, fossil fuels have been depleting and air pollution worsening. Fossil fuels are also environmentally unfriendly hence there is need to look for alternative energy sources for various domestic and commercial use. Like wind power, biomass, and gravitational potential energy of water for use [1–3], solar radiation energy has been considered as a reliable and widely available energy source for sustainable use in the near future [4,5]. Additionally, solar radiation energy is safe and environmentally friendly. Bian stone also called bianshi or stone needle is one of the earliest known instruments of therapy in Traditional Chinese Medicine [6]. The Bian stone is used for performing massage, heating, and other physiotherapies (Fig. 1a). Bian stone can be used to help relaxing muscle, relieving pain, promoting blood circulation and so on [7]. The Bian stone therapy has obvious therapeutic effect on many diseases, such as shoulder periarthritis [8], cervical spondylosis [9] and osteoarthritis [10]. Nowadays, the Bian stone’s function of nursing health in daily life is attracting great interest of more and more people [6]. ⇑ Corresponding author at: Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China. E-mail address: [email protected] (X. Zhou). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.04.062 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Thermal therapy helps in generating heat in the human body and leads to higher tissue temperature. This rise in temperature produces vasodilation, thus promoting better blood circulation. It also can improve the metabolism of human tissues and organs. Thermal therapy has good effect on some diseases such as, some pains [11], blood vessels [12], nerves [12], myalgia [13], fibromyalgia [13], contracture [13], bursitis [13] and muscle spasms [13]. Electricity is usually used to heat the Bian stone in order to enhance the thermal therapy on patients [14]. However, like for electrothermal blanket [15], there is potential safety risk for the electrothermal Bian stone attached to human bodies when it is used many times. Safety is always one of the most important factors during treatment. Therefore, a major question of how to improve safety during treatment must always be asked using any form of treatment. Previous studies on Bian stone have focused on analyses of the chemical constitute of the materials [16,17]. However, to date, little work on safety of electrothermal Bian stone therapy has been reported. In order to solve the safety problem, this paper explores a new way of using solar radiation to assist in the application of Bian stone thermal therapy. A mathematical model is developed, the heat transfer performance is studied, and the sensitivity analysis is performed.
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C. Wu et al. / International Journal of Heat and Mass Transfer 100 (2016) 445–450
are used to link the water heater and the upper surface of Bian stone. A pump is used to force the circulation of water in the two pipes. In order to accelerate the heating rate of water in the pipe and reduce the heat loss through the pipe wall, the water pipe should be as short as possible. Therefore, the pipe can reach the heater through the dish concentrator center, and the table/bed of therapy can be located below the concentrator center. The heat transfer principle used in the system is: flowing water obtains heat from the water heater and releases heat to Bian stone. The continuously heated Bian stone can be used for therapy on patients’ bodies when the stone temperature is over the initial body temperature. One factor that must be considered is that the rate at which Bian stone heats up is slow, therefore, modeling the heating process of Bian stone and body and studying the performance are very important processes. Once the body is heated to a target temperature, any available heat control technology to keep the body at the target temperature can be employed in releasing the redundant heat to other materials or systems. This aspect is not studied in this work. 3. Mathematical model
Fig. 1. (a) Picture of a traditional Bian stone therapy (which is from the Traditional Therapy Center of the Second Affiliated Hospital of GUCM); (b) schematic of solar assisted Bian stone thermal therapy system.
2. Description of Bian stone therapy and novel solar assisted system 2.1. Characteristics of Bian stone therapy Use of Bian stone as an instrument of therapy can be traced back to the New Stone Age about 4000 years ago [6,18]. The Bian stone in the earliest form used for therapy is a piece of polished sharpened flat stone or stone needle used for treating illness by pricking certain parts of the body [19]. The acupuncture originated from the Bian stone therapy [20]. With the development of Traditional Chinese Medicine, stone needles were gradually replaced by needles made of metal used for acupuncture [19,21]. Whatever the case, Bian stone played an important role in ancient therapy and works well in modern therapy. Use of Bian stone for physiotherapy is determined by the material characteristics of Bian stone. Bian stone is composed of numerous calcite microcrystallines [17]. The stone has good capability of heat conduction, storage and radiation due to its high-content microcrystalline calcite with good thermal properties [17,22]. Specifically, Bian stone has high infrared emission rate. Infrared radiation energy can easily be absorbed by human body and is more useful in heating the human body than visible radiation which is strongly reflected by the human body. The good thermal property of Bian stone determines its very good physiotherapeutic effect on the human body. In this case, Bian stone can improve the energy metabolism of human cells and promote microcirculation, thus being very beneficial to alleviating diseases and improving health conditions [22,23]. 2.2. Description of a novel solar assisted Bian stone thermal therapy system A novel Bian stone thermal therapy assisted by using solar radiation is proposed (Fig. 1b). In the solar assisted Bian stone thermal therapy system, a concentrating solar collector, i.e., a parabolic dish concentrator tracking the sun’s beams is installed on the roof of a house to heat the water heater at its center. Two water pipes
A mathematical model based on heat balance is developed for the solar assisted Bian stone thermal therapy system. The following assumptions are made: (1) The power of the pump is enough to force the water to mix fully and quickly. Therefore, the temperature of the working fluid is taken to be constant and uniform to some extent. (2) The heat loss through the body is not considered because the heat penetration depth is assumed to be far smaller than the thickness of the studied part of the body. (3) The heat is transferred from the stone to the body perpendicularly to the stone-body contact surface. By assuming the maximum irradiance of a day to occur at the noon (12:00), solar radiation intensity G at any time t for daylight hours in a day is calculated by [24]
G ¼ Gmax cos ððt=3600 12Þp=DÞ
ð1Þ
where Gmax is the maximum solar radiation in the day and D is the total daylight hours in the day, while for non-daylight hours G = 0. The ambient temperature in the day can be taken as [24]
T 1 ¼ T 1av g þ DT 1 cos ððt=3600 14Þp=12Þ
ð2Þ
where T1avg is the average temperature of the day, and DT1 is the diurnal temperature range, which is equal to the maximum temperature variation in the day, and is assumed to occur at 14:00 p.m. The equation to describe the heat transfer from the solar radiation absorbed by the solar concentrator to the working fluid is given by
aGAcoll U loss ðT f T 1 ÞAp hf ðT f T st ÞAst ¼ mf cpf
dT f dt
ð3Þ
where a is the effective absorptivity of solar radiation G, Acoll is the effective collecting area of solar radiation, Ap is the average heat transfer area of the pipe conveying fluid and the thermal insulating layer, Ast is the area of the stone-body contact surface, mf is the total mass of working fluid in the pipe, cpf is the specific heat capacity of working fluid, Tf is the temperature of working fluid, and Uloss is the effective heat loss coefficient of the working fluid. The heat transferred from the working fluid to the Bian stone is assumed to be stored in the stone and the studied part of the body. The structure of the body including skins, muscles, bones, blood, vessels and so on is very complex. In addition, the Bian stone is assumed to be thin. In order to study the heat transfer in the body
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conveniently, the temperature gradient is assumed to be linear in the body and stone. Therefore, when the Bian stone is in contact with the body, the heat transfer equation can be expressed as
dT av g hf T f T st Ast ¼ ðMst cst þ Mb cb Þ dt
ð4Þ
where Mst is the mass of the Bian stone, and Mb is the mass of the body part influenced by the heat of the stone in contact with the body. The average temperature, Tavg, is given by
T av g ¼
T st þ T b0 2
ð5Þ
where Tb0 is the original temperature of the human body. Substituting Eq. (5) into Eq. (4), we obtain:
1 dT st hf T f T st Ast ¼ ðM st cst þ M b cb Þ 2 dt
ð6Þ
It is known that some time after sunrise, the temperature of the fluid and the Bian stone may still be lower than normal temperature of human body. So the Bian stone is used for therapy on human body only when the fluid temperature is high enough, preferably when the stone’s temperature is above the body temperature. In this case, Eqs. (4)–(6) can be used. If the temperature of the Bian stone is very low, the stone is put into a thermal insulating layer like the water pipe, and then in that case the following equation can be used:
hf ðT f T st Þ U loss2 ðT st T 1 Þ ¼ 0
ð7Þ
where Uloss2 is the effective heat loss coefficient of the working fluid container through the stone and its thermal insulating layer. The effective heat loss coefficient of the working fluid, Uloss, is given by
U loss ¼
1 1 hf
ð8Þ
d
þ h1w þ kpp þ dki i
where dp and kp are the thickness and thermal conductivity of the tube wall, respectively, di and ki are the thickness and thermal conductivity of the thermal insulating layer surrounding the tube conveying fluid, respectively, and hf and hw are the convection heat transfer coefficients from water to the pipe wall and from the thermal insulating layer of the pipe to the ambient winds, respectively. The effective heat loss coefficient of the working fluid through the stone and its thermal insulating layer, Uloss2, is
U loss2 ¼
1 1 hw
ð9Þ
þ dki þ dkstst i
hw can be given by [25]
hw ¼ 5:7 þ 3:8V w
ð10Þ
where Vw is the velocity of air flow around the thermal insulating layer. hf can be expressed as
hf ¼
kf Nu dp
ð11Þ
For a fully developed laminar or turbulent flow in a circular tube, the following equations of Nusselt number Nu can be used, respectively [26]:
Nu ¼
4:36;
laminar
0:023 Re0:8 Pr0:3 ; turbulent
ð12Þ
4. Results and discussion The reference values of the parameters used in conducting the study of the performance of the solar assisted Bian stone thermal
therapy system are presented in Table 1. There is always a suitable temperature range for thermal therapy on patients’ bodies. In this paper, the target average body temperature is set to be 45 °C for the Bian stone thermal therapy. Fig. 2 shows the solar radiation intensity and ambient temperature on a reference day. In this figure, there is zero solar radiation and lowest ambient temperature during the period from 0:00 a.m. to 5:00 a.m. Therefore, the thermal therapy system is assumed to start operation once the solar radiation is received by the solar collector. In the early stage after the thermal therapy system operates, the temperature of the stone may still be lower than normal temperature of human body. It is assumed that once heated to the temperature equal to the normal temperature of human body, the stone parameters shift from being in the thermal insulating layer to working on the body. Fig. 3 shows the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. under the temperature limit of 45 °C. In this figure, the temperature gradually increases after 5:00 a.m. and reaches initial body temperature after 29.9 min. Therefore, it is proposed that the system is used on patients’ bodies after 29.9 min. The average body temperature reaches 45 °C after 57.2 min. Fig. 4 shows that the variations of the stone’s surface temperature and average body temperature with time starting from 5:00 a.m. for various daily maximum solar radiation intensity of 400 W/m2, 600 W/m2 and 800 W/m2. As expected, stronger solar radiation provides more heat and leads to quicker heating of the stone and the body. This subsequently leads to the body attaining the desired temperature in a shorter time. This effect by increasing solar radiation intensity can be considered similar to enlarging the collector area or improving the collector efficiency. Fig. 5 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various pipe diameters. Smaller water volume in the pipe will result in higher water temperature, which determines higher temperature of both the stone and the influenced body due to larger volume and larger thermal storage capacity of water as compared to the stone and body. The critical heating time of
Table 1 Reference values of parameters used. Parameters
Values
Concentrating solar collector area (m2) Effective absorptivity of solar radiation (%) Pipe diameter (m) Pipe length (m) Outside length (m) Inside length (m) Pipe wall thickness (m) Pipe wall heat conductivity (W/(m K)) Water flow velocity in pipe (m/s) Thermal insulating layer thickness (m) Thermal insulating layer heat conductivity (W/ (m K)) Initial body temperature (°C) Ambient wind velocity (m/s) Inside wind velocity (m/s) Body’s density (kg/m3) Body’s specific heat capacity (J/(kg K)) Studied volume of body (L*W*H) Average temperature of the day (°C) Diurnal temperature range (°C) Maximum solar radiation in the day (W/m2) Total daylight hours in the day (h) Bian stone density (kg/m3) Bian stone specific heat capacity (J/(kg K)) Bian stone size (L*W*H) Limit of average temperature of the stone and the influenced part of the body (°C)
20 80 0.04 21.5 17 4.5 0.005 0.14 0.5 0.015 0.05 36 2 0.2 1045 3000 0.2 m * 0.2 m * 0.1 m 30 3 600 14 2800 900 0.2 m * 0.2 m * 0.015 m 45
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Fig. 2. Solar radiation intensity and ambient temperature in a reference day.
Fig. 5. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various pipe diameters.
Fig. 3. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C. Fig. 6. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various thicknesses of thermal insulating layer.
Fig. 4. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various solar radiation intensities.
reaching initial body temperature becomes less for smallerdiameter pipe. This effect of decreasing the pipe diameter can be assumed to be similar to decreasing the pipe length since the most important parameter here is the volume. Fig. 6 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various thermal insulating layer thicknesses of 0.005 m, 0.015 m, and 0.025 m. The thickness of thermal insulating layer between 0.005 m and 0.025 m has little influence on the temperature and the critical heating time of reaching initial body temperature, and the results for the thickness of 0.0015 m are basically
Fig. 7. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various water flow velocities.
the same as those for the thickness of 0.025 m. This is because that the superficial area of the tube is far smaller than effective collecting area of solar collector and the tube wall has high thermal resistance. It is also found out that the thermal insulating layer of the system is high-performance. Fig. 7 shows the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various flow velocities of water of 0.2 m/s, 0.5 m/s and 0.8 m/s.
C. Wu et al. / International Journal of Heat and Mass Transfer 100 (2016) 445–450
Fig. 8. Stone surface temperature and average body temperature versus time starting from 5:00 a.m. based on target temperature of 45 °C for various areas of stone-body contact surface.
Before reaching the initial body temperature, the temperature is basically the same for the three water flow velocities. After reaching the initial body temperature, with a decrease in water flow velocity, the convective heat transfer rate from the hot water to the stone and body becomes lower. This results in a lower stone and body temperature. The results for the water flow velocity of 0.5 m/s are very close to those of 0.8 m/s, and the difference between the temperature for water flow velocity of 0.2 m/s and temperature for 0.5 m/s is not large. This shows that the water flow velocity has small effect on the temperature variation so long as the velocity is not too low. However very low water flow velocity is not desirable because this will cause poor mixing effect of the water inside the pipe which is contrary to the assumption of the mathematical model. Too high water flow velocity is also not suitable, because water of high flux increases the electricity use of the therapy system and it basically doesn’t enhance the performance of the therapy system. Therefore, a moderate value e.g., of 0.5 m/ s is recommended for the flow velocity of water inside the pipe. Fig. 8 shows that the variations of the stone surface temperature and average body temperature with time starting from 5:00 a.m. for various stone-body contact surface areas of 0.01 m2, 0.04 m2 and 0.09 m2. In order to enhance the effect of the stonebody contact surface area on temperature variations, the change rates of the three areas are much higher than those for solar radiation intensities, pipe lengths, pipe diameters, thicknesses of thermal insulating layer and water flow velocities. In this figure, as expected, the area of the stone-body contact surface has little effect on the temperature variations because the studied volume of body is assumed to have direct proportion relationship with the area of the stone-body contact surface. Larger stone-body contact surface area determines larger volume of studied body and leads to the slight reduction of the water temperature, thus making the time of reaching the target temperature slightly shorter. In order to use the therapy system early on patients after sunrise, strong solar radiation, and small and short pipe are desirable, moderate water flow velocity is recommended, and the stone-body contact surface area has little influence on the temperature of stone and body as well as the critical time of reaching the target temperature. In order to get stronger solar radiation, the collector area can be increased, or a more efficient collector can be employed.
5. Conclusions Solar radiation energy is considered to be one of the most promising new energy resources and electrothermal Bian stone
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therapy is a suitable way to treat special diseases. Safety is the most importance factor of therapy. In this paper, a novel solar assisted Bian stone thermal therapy system has been proposed, mathematically modeled and tested. The proposed novel system is safer and can reduce the possibility of accidents as opposed to electrothermal carpets. A mathematical model based on heat balance has been developed. The calculated results and the sensitivity analysis have been demonstrated and some conclusions are drawn as follows. When starting from 5:00 a.m., the Bian stone is gradually heated by solar radiation energy to the initial body temperature after operating for 29.9 min. It is proposed that the Bian stone can then be used on patients’ bodies after this period of 29.9 min. The average body temperature is heated to the target average body temperature of 45 °C after a period of 57.2 min. Stronger solar radiation, or smaller or shorter pipe results in better performance of the novel system. Therefore, the therapy system can be used on patients earlier during the day. Early use of the thermal therapy system is a very important factor because the lowest ambient temperature is normally obtained early in the morning. Higher flow velocity of water leads to slightly better performance of the system at the expense of more electricity use, and very low water flow velocity causes poor mixing effect of the water, so a moderate water flow velocity is more suitable. The stone-body contact surface area has little influence on the temperature of stone and body and the critical time of reaching the target temperature. This work lays a solid foundation for safe use of Bian stone thermal therapy. It is recommended that further researches be focused on the developing of more comprehensive studies of the enhancement performance of the novel solar assisted Bian stone thermal therapy with some improvements.
Acknowledgements This research has been partially supported by Huazhong University of Science and Technology Foundation (No. 2014ZZGH006) and the Special Fund for Strategic New Industry Development of Shenzhen, China (Grant No. JCYJ20140509162710494).
References [1] A.D. Sßahin, Progress and recent trends in wind energy, Prog. Energy Combust. Sci. 30 (2014) 501–543. [2] X.P. Zhou, F. Wang, H.W. Hu, L. Yang, P.H. Guo, B. Xiao, Assessment of sustainable biomass resource for energy use in China, Biomass Bioenergy 35 (2011) 1–11. [3] B. Wagner, C. Hauer, A. Schoder, H. Habersack, A review of hydropower in Austria: past, present and future development, Renewable Sustainable Energy Rev. 50 (2015) 304–314. [4] X.P. Zhou, Y.Y. Xu, Solar updraft tower power generation, Sol. Energy 128 (2016) 95–125. [5] C. Li, Y. Goswami, E. Stefanakos, Solar assisted sea water desalination: a review, Renewable Sustainable Energy Rev. 19 (2013) 136–163. [6] J.B. Meng, Z.J. Meng, Bianshixue, TCM Ancient Books Publishing House, Beijing, 2007. [7] C.Q. Guo, S.N. Han, Illustration of Bian Stone Therapy, China Medical Science Press, Beijing, 2012, p. 2. [8] C.Q. Guo, N. Rui, Y.G. Liu, Y.X. Liu, Y. Sha, G.H. Ma, Multi-central randomized controlled observation on clinical therapeutic effect of the new Bian-stone therapy on scapulohumeral periarthritis, Chin. Acupunct. Moxibust. 27 (2007) 633–637. [9] Y.X. Geng, J. Yu, S.S. Hu, Z.X. Lu, Treatment of 30 cases of cervical spondylosis with Bian stone therapy, Hebei J. Tradit. Chin. Med. 29 (2007) 1109–1110 (in Chinese). [10] Z.W. Hou, P. Zheng, Treatment of 36 cases of degenerative knee osteoarthritis with warm purgative therapy of stone needle, Beijing Univ. Tradit. Chin. Med. (Clin. Med.) 17 (2010) 33–35 (in Chinese). [11] C. Wu, Heat transfer behavior for lower back of human body using Bian stone therapy, in: International Conference and Expo on Novel Physiotherapies, Chicago, Illinois, USA, 2015. [12] Y.W. Ding, G.H. Ding, Application of infrared radiation spectrum to acumoxibustion research, Acupunct. Res. 31 (2006) 252–255 (in Chinese).
450
C. Wu et al. / International Journal of Heat and Mass Transfer 100 (2016) 445–450
[13] P.P. Raj, Practical Management of Pain, third ed., Mosby, Missouri, 2000, ISBN 978-0-8151-2569-3. [14] T. Huang, G. Litscher, L. Wang, W.B. Zhang, Study on effect of lying electrothermal Bian-stone on Dazhui to blood flow velocity of cerebral arteries, Chin. J. Basic Med. Tradit. Chin. Med. 18 (2012) 312–313 (in Chinese). [15] Warshauer-McLaughlin Law Group, P.C. Electric Blanket Fire Causes. Available at
[19] K.-W. Ma, The roots and development of Chinese acupuncture: from prehistory to early 20th century, Acupunct. Med. 10 (1992) 92–99. [20] B. Wang, Huang Di Nei Jing (Yellow Emperor’s Internal Classic), TCM Ancient Books Publishing House, Beijing, 2003. [21] L.X. Lao, Acupuncture techniques and devices, J. Altern. Complement. Med. 2 (1996) 23–25. [22] S. Ge, G.-Z. Chen, S.-H. Liu, Application thinking on Bian-stone of the acoustooptic effect in the treatment of primary dysmenorrhea, in: Proc. of SPIE, vol. 7519, 2009, p. 751908. [23] Q. Qiu, The discovery of Sibin Bian-stone makes old stone needle newborn, in: The Chinese Medicine Research Institute Academy Reports 18, 2002. 4. [24] C.D. Papageorgiou, Floating solar chimney power stations with thermal storage, in: Proceedings of the IASTED Conference on European Power and Energy Systems, Rhodes, Greece, 2006. Also available at