Experimental Investigation of Mixed Convection …ijens.org/Vol_18_I_01/182501-3939-IJMME-IJENS.pdfchlorinated polyvinyl chloride CPVC pipe and chlorinated polyvinyl chloride CPVC

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:01 25

182501-3939-IJMME-IJENS © February 2018 IJENS I J E N S

Experimental Investigation of Mixed Convection

Heat Transfer in a Vertical and Horizontal Annulus

with Rotating Inner Cylinder

Akeel Abdulallah Mohammed, Ayad Tareq Mustafa*, Huda Ali Ibrahim Mechanical Department, College of Engineering, Al-Nahrain University, Jadiriya P.O. Box 64040, Baghdad, Iraq

[email protected], [email protected]*, [email protected]

Abstract—An experimental study for heat transfer process by

mixed convection in the entrance region of annulus with

uniformly heated stationary outer cylinder and rotating inner

shaft has been carried out. The present study aimed to investigate

the local and average heat transfer along the axial distance of

outer cylinder in horizontal and vertical positions. The

experimental setup consists of an annulus with a radius ratio of

0.37 and outer cylinder with a heated length of 1.12m. The

experimental investigation was achieved within Reynolds number

ranges from 1000 to 2400 and Taylor number values of 0, 158933,

225269, and 506856. Moreover, the Richardson number ranges

between 1.09 (mixed convection) to 0.104 (forced convection) in

vertical position, and between 1.05 (mixed convection) to 0.113

(forced convection) in horizontal position. The results showed

that the local Nusselt number values increase when the heat flux,

Reynolds number and Taylor number increase. It is found that

the values of local Nusselt number converge with each other

down stream. Two empirical relationships have been deduced for

the average Nusselt number as a function of Taylor number (Ta)

and Richardson number (Ri) for vertical and horizontal

positions.

Index Term— Annulus; convection heat transfer; rotating

inner cylinder; experimental investigation; heat flux

I. INTRODUCTION Convection heat transfer includes natural and forced

convection depending on how the fluid motion is initiated. In natural convection, the fluid motion is caused by the buoyancy effect. Whereas in forced convection, the fluid is forced to flow over a surface or in a tube by external means such as a pump or fan. For study analysis, natural convection is characterized by Grashof number and the forced convection is characterized by Reynolds number [1]. In an annulus with rotating inner cylinder, the motion of flow resulted from rotating inner cylinder will be added to the motion of mixed convection flow, which is characterized by Taylor number. In most applications, both modes are present and the relative magnitude of these two forces determines whether the flow is pure forced, mixed forced and free, or pure free convection.

The investigation of a laminar mixed convection in concentric tubes with a rotating inner tube leads to understanding the fluid motion through the gap between rotating and stationary machine parts. Hence improving the design of such equipment and minimizing the influence that may occur [2]. Several researches were carried out to study experimentally the behavior of heat transfer between fixed outer cylinder and rotating inner cylinder in the vertical

position. In case of uniformly heated the inner rotating cylinder and cooled the outer cylinder; Aoki et al. [3] examined the heat transfer process by natural convection in an annulus with the working fluids at zero axial flow of air, water, iso-buthyl alcohol and spindle oil. Results show that the Nusselt number increased suddenly at modified critical Tylor number. While, Ball, et al. [4] carried out experiments to examine the convective heat transfer process in the annular gap. It is found that if the hydrodynamic instabilities is exist in rotating systems, this leads to a variety of secondary flows. In case of uniformly heated the outer fixed cylinder and rotating inner cylinder; Tachibana et al. [5] examined the convection heat transfer between two cylinders with working fluids of air, spindle oil, and mobile oil. The parameters changes in this study are varying cylinder diameters, widths of gap, and angular velocity of inner cylinder. It is found that the characteristics of the flow and heat transfer had two regions: laminar region and vortex region. Becker and Kaye [6] studied the phenomena that control the heat transfer rate in an annular gap. Experimental data for adiabatic flow in an annulus were discussed and deduced to empirical equations, and then compared with the results of previous studies. Kim and Hwang [7] studied the heat transfer process in concentric annulus with a radius ratio of 0.52. Pressure losses were measured for fully developed flows of water and 0.4% aqueous solution sodium carboxyl methyl cellulose (CMC), respectively. The results show that the change of skin friction coefficient is large for the laminar flow regime, and becomes smaller as Reynolds number increases for the transitional flow regime. While Mauwafak et al. [8] studied the vibration effect on the mixed convection heat transfer in the entrance region of concentric vertical annulus with radius ratio of 0.365. The ranges of Reynold number, Taylor number, heat flux, and frequency were 514≤Re≤1991, 10.44×104≤Ta≤82.23×104, (468≤q≤920) W/m2, and Fr=32 & 77 Hz; respectively. Results show that the values of local Nusselt number increase as the heat flux increases at the natural frequency.

The previous studies focus on the experiments of the convection heat transfer process in the vertical annulus with rotating inner cylinder. Therefore, the present study aimed to investigate experimentally the behavior of the heat transfer process by mixed convection in the vertical and horizontal positions for uniformly heated outer fixed cylinder with rotating inner shaft. Applications related to present topic are included several modes, such as electrical motors, turbines, chemical mixing process, swirl nozzles, combustion chambers,

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drying machinery, oil exploration drills, and rotating-tube heat exchangers.

II. EXPERIMENTAL SETUP

The parts of experimental setup are shown schematically in Figure 1 and really in Figure 2. It consists essentially of a cylindrical concentric annulus and the test section as a part of an open air loop, mounted on iron frame (I) around rotating shaft (K). The test section consists of 5 mm wall thickness, 60 mm outside diameter and 1.12 m long outer cylinder made of aluminum. The cylinder was electrically heated by using heating element wire (Nickel-Chromium wire). The outside of the test section was then thermally insulated, covered with 30 mm approximately as thickness of asbestos rope layer. The cylinder surface temperatures were measured by thirteen thermocouples (type K) arranged along the cylinder. An open air circuit was used, which included an air blower (B), chlorinated polyvinyl chloride CPVC pipe and chlorinated polyvinyl chloride CPVC control valve (C), flexible hose (D), hotwire anemometer and settling chamber (F). The air is driven by air blower which can be regulated by using a control valve and electrical regulator switch. A symmetric flow and a uniform velocity profile produced by a well-designed Teflon bell mouth (H) which was fitted at the beginning of the aluminum cylinder (N) and bolted in the other side inside the settling chamber (F). Another Teflon piece (H) was fitted at the cylinder exit. The Teflon was chosen due to its low thermal conductivity to reduce the heat loss from the aluminum cylinder ends. The inlet air temperature was measured by the hotwire anemometer before the settling chamber (F), while the outlet air temperature was measured by two thermocouples located in the Teflon exit piece. The local bulk air temperature was calculated by using a straight line interpolation between the measured inlet and outlet bulk air temperature. To determine the heat loss from the test section ends, three thermocouples were fixed on the asbestos insulation. By knowing the distance between these thermocouples and the thermal conductivity of the asbestos insulation, then the heat loss at ends can be calculated. The heater circuit of the heating element consists of a Variac (Variable Transformer) (type Phillips-8.5 Amperes) to adjust the heater input power as required, while a digital multimeter (type TAIFA DP3-72) is used to measure the voltage and current of the heater.

The experiments were carried out through the following procedure: (1) the air blower, heater and the motor for the rotating shaft are switched on. (2) The apparatus left more than three hours to reach the steady state condition at maximum required voltage then switched to the next voltage at least the lower one (to reduce the required time to reach the steady state condition). (3) The measuring parameters collected during each test are; thermocouples temperatures in °C, the heater current in amperes, the heater voltage in volts. (4) Same steps were recurred with applying new values of Reynolds number, heat flux, and angular velocity for inner shaft.

Fig. 1. Schematic Diagram of Experimental Setup

Fig. 2. Experimental Setup

III. DATA ANALYSIS

Simplified steps were used to analyze the heat transfer for the air flow in a cylinder when its surface was subjected to a uniform heat flux. The total input power supplied to the cylinder can be calculated by:

B D

N

P

Variac

Thermocouples

Digital Reader



𝑄𝑡 = 𝑉 × 𝐼 (1) The convection and radiation heat transferred from the

cylinder is: 𝑄𝑐𝑟 = 𝑄𝑡 − 𝑄𝑐𝑜𝑛𝑑 (2) Where Qcond is the conduction heat loss which was found

from the following equation:

𝑄𝑐𝑜𝑛𝑑 =∆𝑇𝑜𝑖

𝑙𝑛𝑟𝑜𝑟𝑖

2𝜋𝐾𝑎𝐿⁄ (3)

Where: ∆Toi = To - Ti

To = average outer lagging surface temperature Ti = average inner lagging surface temperature ro = the distance from center of cylinder to the outer

lagging surface ri = the distance from center of cylinder to the beginning

lagging (radius of outer cylinder surface) L = length of cylinder Ka = thermal conductivity of asbestos, which is equal

(0.161 W/m°C) The convection-radiation heat flux can be represented by: 𝑞𝑐𝑟 = 𝑄𝑐𝑟 𝐴𝑜⁄ (4) Where: Ao is outer surface area of cylinder and equal

(2𝜋𝑟2𝐿) The local radiation heat flux can be calculated from the

expression [9]

qr = F1−2 ε σ[((𝑇𝑠)𝑥 + 273)4 − ((𝑇�̅�)𝑥 + 273)4] (5) Where: (𝑇𝑠)𝑥= local temperature of cylinder. (𝑇�̅�)𝑥= average temperature of cylinder. σ = Stefan-Boltzmann constant = 5.66×10-8 W/m2 K4

ε = emissivity of the polished aluminum surface=0.09. F1-2= radiation view factors ≈ 1. Hence, the convection heat flux at any position is: 𝑞 = 𝑞𝑐𝑟 − 𝑞𝑟 (6) The radiation heat flux is very small and can be neglected.

Therefore, the convection-radiation heat can be equated to the convection heat flux, q.

The local heat transfer coefficient can be obtained by:

hz =q

(Ts)x−(Tb)x (7)

(Tb)x= Local bulk air temperature. All the air properties are evaluated at the mean film air

temperature [10].

(Tf)x = (Ts)x−(Tb)x

2 (8)

𝑇𝑓 = Local mean film air temperature.

The local Nusselt number (Nux) can be calculated:

𝑁𝑢𝑥 = hx Dh

K (9)

Where: K = thermal conductivity of air = 0.6099 W/m2°C The average values of Nusselt number Num can be

calculated by:

𝑁𝑢𝑚 =1

𝐿∫ 𝑁𝑢𝑥𝑑𝑥

𝐿

0 (10)

The average values of the other parameters can be calculated based on calculation of average cylinder surface temperature and average bulk air temperature as follows

�̅�𝑠 =1

𝐿∫ (𝑇𝑠)𝑥𝑑𝑥

𝑥=𝐿

𝑥=0 (11)

�̅�𝑏 =1

𝐿∫ (𝑇𝑏)𝑥𝑑𝑥

𝑥=𝐿

𝑥=0 (12)

�̅�𝑓 =�̅�𝑠+�̅�𝑏

2 (13)

All thermodynamics air properties of ρ, μ, ν, and k were

evaluated at the average mean film temperature (�̅�𝑓).

IV. RESULTS AND DISCUSSIONS

A. Temperature Distribution

The effect of heat flux, Reynolds number, and Taylor number on the temperature variation along the outer cylinder of annulus at vertical position is plotted for selected runs in Figures 3, 4, and 5. As can be seen from these figures that at constant heat flux, the surface temperature increases at entrance of the annular gap and attains a maximum point, after which the surface temperature begins to decrease. The rate of surface temperature increases with increasing of the wall heat flux. This can be attributed to the increasing of the thermal boundary layer faster due to buoyancy effect as the heat flux increases at the same Reynolds number. The point of maximum temperature on the curve represents actually the starting of thermal boundary layer fully developed. The region before this point is called the thermal entrance of annulus.

It is obvious that the increasing of the Reynolds number reduces the surface temperature as heat flux kept constant. As can be shown from these Figures the heat transfer process enhances as Taylor number increase. The increasing of angular velocity of the inner cylinder may create air vortices around and along the outer wall of the inner cylinder, which intern improve the heat transfer process. The behavior of temperature distribution along the outer cylinder of annulus with rotating inner cylinder at horizontal position is the same as that in vertical position as shown in Figures 6 and 7.

Fig. 3. Variation of the Surface Temperature with the Axial Distance at Re=1000 and Ta=158933 (vertical position)



Fig. 4. Variation of the Surface Temperature with the Axial Distance at q=557 W/m2 and Ta=158933 (vertical position)

Fig. 5. Variation of the Surface Temperature with the Axial Distance at q=728 W/m2 and Re=2400 (vertical position)

Fig. 6. Variation of the Surface Temperature with the Axial Distance at Re=1000 and Ta=225269 (horizontal position)

Fig. 7. Variation of the Surface Temperature with the Axial Distance at q=728 W/m2 and Ta=225269 (horizontal position)

B. Effect of Annulus Position on Temperature Distribution

Figure 8 represents comparison between the vertical and horizontal positions for the local surface temperature along the axial distance of outer cylinder surface for Re=1000, q=557 W/m2 with non-rotating inner cylinder (Ta=0). As can be seen from this Figure the values of temperature for horizontal position are higher than that for vertical position. This behavior is reversed if the inner cylinder is rotated with Ta=158933 because the vortex generated from rotating inner cylinder and secondary flow are higher in the case of horizontal position (The secondary flow is perpendicular to the main flow) than in vertical position (the natural convection currents are parallel to the main flow) as shown in Figure 9.

Fig. 8. Variation of the Surface Temperature with the Axial Distance at Re=1000, q=557 W/m2 and Ta=0



Fig. 9. Variation of the Surface Temperature with the Axial Distance at Re=1000, Ta=158933 and q=557 W/m2

C. Local Nusselt Number (Nux)

Figure 10 shows the effect of heat flux on the local Nusselt number along the dimensionless axial distance (inverse Graetz number,Gz−1 ) at Re=1700 and Ta=158933 at vertical position. It is noticed that the local Nusselt number values increase when increasing the heat flux, and the values of local Nusselt number converge with each other down stream. This may be ascribed to the secondary flow super imposed on the forced convection effect leading to higher heat transfer coefficients. The distance from beginning enter the flow to the point at which the values of local Nusselt number increase greatly downstream is called the thermal boundary layer length or the thermal entrance region. Figure 11 shows the effect of Reynolds number on the local Nusselt number along the dimensionless axial distance at q=916 W/m2, Ta=506856 at vertical position. It can be seen that values of the local Nusselt number increase as Reynolds number increases because of the dominant forced convection on the heat transfer process. It is obvious also for constant heat flux that the deviation of Nux value moves towards the left and increases as the Reynolds number increases due to a decrease in the inverse Greatz number value. Figure 12 represents the effect of Taylor number on the behavior of local Nusselt number for q=728 W/m2, Re=1000 at vertical position. It is shown that the values of local Nusselt number increase with increasing of Taylor number because the super imposed flow resulting from rotating inner cylinder into main flow leads to increasing the strength of the generated vortex which improves the heat transfer coefficient. The behavior and trend of local Nusselt number values along the outer cylinder of annulus with rotating inner cylinder at horizontal position is the same as that in the vertical position as shown in Figures 13, 14, and 15 for the same ranges of heat flux, Reynold number and Taylor number.

Fig. 10. Local Nusselt number Versus Dimensionless Axial Distance at Re=1700 and Ta=158933 (vertical position)

Fig. 11. Local Nusselt number Versus Dimensionless Axial Distance at q=916 W/m2 and Ta=506856 (vertical position)

Fig. 12. Local Nusselt number Versus Dimensionless Axial Distance at q=728 W/m2 and Re=1000 (vertical position)



Fig. 13. Local Nusselt number Versus Dimensionless Axial Distance at Re=1000 and Ta=225269 (horizontal position)

Fig. 14. Local Nusselt number Versus Dimensionless Axial Distance at q=728 W/m2 and Ta=158933 (horizontal position)

Fig. 15. Local Nusselt number Versus Dimensionless Axial Distance at q=728 W/m2 and Re=1000 (horizontal position)

D. Effect of Annulus Position on Local Nusselt Number (Nux)

The local Nusselt number along the outer surface cylinder for selected runs is plotted in Figures 16 and 17 for comparison between the vertical and horizontal position for the same value of heat flux, Reynolds number and Taylor numbers. It can be concluded the following points:

1. The value of local Nusselt number for horizontal position are higher than that in vertical position for Re=2400, q=916 W/m2, and Ta=225269; as shown in Figure 16 because of strong vortex generated in horizontal position which increase as Reynolds number, heat flux, and Taylor number increase.

2. If the values of Reynolds number and Taylor number reduced to Re=1700 and Ta=158933, the behavior will be reversed and the value of local Nusselt number at vertical position are higher than that at horizontal position because of decreasing the value of Reynold number leads to decreasing the forced convection dominant as shown in Figure 17.

Fig. 16. Variation of Local Nusselt number Versus Dimensionless Axial Distance Re=2400, q=916 W/m2 and Ta=225269

Fig. 17. Variation of Local Nusselt number Versus Dimensionless Axial Distance Re=1700, q=916 W/m2 and Ta=158933

E. Average Nusselt Number

Two empirical relationships for vertical and horizontal positions as a function of Taylor number and Richardson



number have been deduced for mean Nusselt number at the outer cylinder surface with rotating inner cylinder. The relationships were deduced within effective values of Reynolds number (1000, 1700, and 2400), Taylor number (158933, 225269, and 506856), and Grashof number (636552, 840395, and 1079604). Figures 18 and 19 show the relation between Log(Num) against Log(Ta/Ri) for vertical and horizontal position, respectively. The empirical relationship in vertical position is:

𝑁𝑢𝑚 = 2.77 (𝑇𝑎

𝑅𝑖)

0.047

For 1.09 ≤ 𝑅𝑖 ≤ 0.104 (14)

And in horizontal position is:

𝑁𝑢𝑚 = 2.53 (𝑇𝑎

𝑅𝑖)

0.096

For 1.05 ≤ 𝑅𝑖 ≤ 0.113 (15)

The errors resulted from equations (14) and (15) are 8.7% and 7.2%; respectively.

Fig. 18. Average Nusselt number Versus the Ratio (Ta/Ri) for Vertical Position

Fig. 19. Average Nusselt number Versus the Ratio (Ta/Ri) for Horizontal Position

F. Comparison with Previous Experimental Work

The variations of local Nusselt number with the dimensionless axial distance for the present experimental results (Re2/Ta=6.2, Re=1000, Ta=158933, q=916 W/m2) is compared with the experimental data by Mauwafak et al.

(2015) [8] (Re2/Ta=7.9, Re=913, Ta=104400, q=920 W/m2) as shown in Figure 20. It is found that the behavior and trend of Nux with (Gz-1) for the two works are the same. The difference between the two experimental results may be referred to the experimental errors and the difference in the values ratio of L/Dh.

Fig. 20. Results Comparison between the Present Work and Mauwafak et al. (2015) [8]

V. CONCLUSIONS

An experimental study for annulus with uniformly heated stationary outer cylinder and rotating inner shaft has been carried out in horizontal and vertical positions. The fabrication of the experimental setup and the measurement procedure has been elaborated. The conclusions drawn from the investigations results are as follow:

1. The significance of the obtained results is to improving the design of most common conventional rotating machinery and selects the suitable position that produces higher heat transfer coefficient.

2. Variation of surface temperature along the outer cylinder surface increases when Reynolds number and Taylor number decrease, and heat flux increases.

3. The local Nusselt number value increases when increasing Reynolds number, Taylor number, and the heat flux.

4. The values of local temperature along the axial distance of outer cylinder surface for the vertical position are lower than that in the horizontal position. This behavior is reversed in the case of rotate inner cylinder, which dates back to the effect of vortex field. This vortex field in the vertical position is lower than that in the horizontal position.

5. The values of local Nusselt number for high Reynold number and heat flux with rotating inner cylinder in the vertical position are lower than that in the horizontal position. These values are obtained due to the vortex field generation in the horizontal position which increases as Reynolds number, heat flux, and Taylor number increase. This behavior is reversed when Reynold number and Taylor number decrease



for the same heat flux. The values of local Nusselt number in the horizontal position are lower than that in the vertical position due to Reynolds number decreases, which leads to decreasing the forced convection dominant.

6. Two empirical relationships of the average Nusselt number as a function of Taylor number and Richardson number has been deduced for vertical and horizontal positions.

7. The present study can be extended to future work by study the effect of flow direction on the heat transfer process at different inclination angles, study the convection heat transfer in an eccentric annulus, or study the surface effect of rotating inner shaft on the convection heat transfer, such as rough surface shaft, screw shaft, and finned surface shaft.

NOMENCLATURE

�̇�𝑐𝑜𝑛𝑣 convection heat loss, (W) 𝑄𝑐𝑜𝑛𝑑 conduction heat loss, (W) 𝑄𝑡 total heat power, (W) n heat transfer coefficient, (W/m2.ºC) Ts cylinder surface temperature, (ºC) K thermal conductivity, (W/m.ºC) r1 inner radius of cylinder, (m) r2, outer radius of cylinder, (m) Dh, hydraulic diameters, 2(r2-r1), (m) Cf skin friction coefficient, (m) u axial velocity , (m/s) q heat flux, (W/m2) Cp specific heat at constant pressure, (kJ/kg.K) g gravity acceleration, (m/s2) I current, (ampere) L length, (m) Ao outer surface area of cylinder, (m2)

�̇� volumetric flow rate, (m3/s) T temperature, (oC) V voltage, (volt) x axial coordinate Creak Symbols ν kinematic viscosity, (m2/s) ω Angular velocity of inner cylinder, (rad./s) η Radius ratio, r1/r2 μ Dynamic viscosity, (kg/m.s) β Coefficient of volume expansion, (1/K) ρ Density, (kg/m3) Δ Difference between two values Dimensionless Groups Pr Prandtl number (𝜇. 𝐶𝑝/𝐾) Nu Nusselt number (ℎ. 𝐷ℎ/𝐾) Gr Grashof number (𝑔. 𝛽. 𝑞. 𝑟1

4 𝐾. 𝑣2⁄ ) Ta Taylor number [2𝜔2. 𝑟1

2. 𝑏3 𝑣2(𝑟1 + 𝑟2)⁄ ] Re Reynolds number (𝑢. 𝐷ℎ 𝑣⁄ ) Ra Rayligh number (𝐺𝑟. 𝑃𝑟) Ri Richardson number (𝐺𝑟 𝑅𝑒2⁄ ) Gz-1 Inverse Graetz number (𝑧 𝑅𝑒. 𝑃𝑟. 𝐷ℎ⁄ )

Subscript b bulk f film I entrance x local o exit m mean

REFERENCES [1] Hashimoto, K., N. Akino, and H. Kawamura, Combined

forced-free laminar heat transfer to a highly heated gas in a vertical annulus. International journal of heat and mass transfer, 1986. 29(1) p. 145-151.

[2] Kreith, F., Convection heat transfer in rotating systems. Advances in heat transfer, 1969. 5 p. 129-251.

[3] Hiroshi, A., H. NOHIRA, and A. Hajime, Convective heat transfer in an annulus with an inner rotating cylinder. Bulletin of JSME, 1967. 10(39) p. 523-532.

[4] Ball, K., B. Farouk, and V. Dixit, An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder. International Journal of Heat and Mass Transfer, 1989. 32(8) p. 1517-1527.

[5] Tachibana, F., S. FUKUI, and H. MITSUMURA, Heat transfer in an annulus with an inner rotating cylinder. Bulletin of JSME, 1960. 3(9) p. 119-123.

[6] Becker, K.M. and J. Kaye, Measurements of diabatic flow in an annulus with an inner rotating cylinder. Journal of heat transfer, 1962. 84(2) p. 97-104.

[7] Kim, Y.-J. And Y.-K. Hwang, Experimental study on the vortex flow in a concentric annulus with a rotating inner cylinder. KSME international journal, 2003. 17(4) p. 562-570.

[8] Tawfik, M.A., A.A. Mohammed, and H.Z. Zain, Effect of Vibration on the Heat Transfer Process in the Developing Region of Annulus with Rotating Inner Cylinder. Eng. &Tech.Journal, 2015. 33(3).

[9] Holman, J.P., Experimental Method for Engineers. McGraw-Hill, 4th Edition, 1984, Tokyo, Japan.

[10] J.Grimson, Advance fluid dynamic and heat transfer. McGraw-Hill, 1971, England.

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Experimental Investigation of Mixed Convection …ijens.org/Vol_18_I_01/182501-3939-IJMME-IJENS.pdfchlorinated polyvinyl chloride CPVC pipe and chlorinated polyvinyl chloride CPVC