Abstract-- Extension of the tube wall’s heat transfer area and mixing nanoparticles with working fluids are the most effective and potential techniques to enhance the heat transfer rate, which is required to remove the excessive load of heat from the heat transfer apparatus. These extreme loads are dangerous threats for heat transfer equipment, which may cause several damages. Therefore, a corrugated pipe was studied numerically along with SWCNT-water nano-fluid, to determine the improvement of laminar convective heat transfer rate. Ansys fluent software and steady-state control volume method were applied for simulation purposes. Hence, different volume fractions (1% - 5%) of nanoparticles were considered to mix with water to produce nanofluid. A range of Reynolds numbers from 500 to 1200 with a constant wall heat flux of 1000 W/m2 was considered to calculate the heat transfer rate. Additionally, the corresponding pumping power requirement for such improvements was also calculated. The result demonstrated that by increasing the Reynolds number, the Nusselt number and heat transfer coefficient were raised significantly for a corrugated pipe compared to a plain pipe. Consequently, the presence of nanoparticles in the working fluid also showed more enhancement. For the corrugated pipe, at Re =500, SWCNT-water nanofluid showed a maximum 56.52% enhancement of Nusselt number and heat transfer coefficient. Furthermore, SWCNT-water nanofluid showed a pumping power advantage (92% for 5% volume fraction). Additionally, correlations to calculate the Nusselt number and heat transfer coefficient of nanofluid were also developed, which showed good agreement with numerical results. However, it can be concluded that corrugated channels, along with nanofluid, provide enhancement of heat transfer rate, Nusselt number, and pumping power advantage for the laminar developed region of a pipe.
Keywords-- Nusselt number; nanoparticles; nanofluid; heat transfer coefficient; pumping power.
I. INTRODUCTION
The working fluids that are generally utilized in heat transfer applications often reveal poor heat transfer performance. Therefore, it is crucial to look for enhanced heat transfer techniques. The addition of appropriate metal or their oxide particles undoubtedly raises the heat transfer performance. Moreover, one of the efficient ways in this regard is the utilization of corrugated pipe. Suspension of nanoparticles with base fluid and increment of the area of pipe wall by applying corrugated wall section is more effective for heat transfer applications.
Enhancement of heat transfer utilizing corrugated channels has been investigated broadly in the last few decades. Various studies were undertaken on heat and mass transfer in corrugated channels numerically and experimentally. In the late 19th century, the concept of nanoparticles has become a significant part of modern adventure. At first, Tuckerman and Pease (1981) introduced microchannel technology. Then, a microchannel heat exchanger has been introduced by Choi (1991).
Smaisim (2018) investigated heat transfer in a corrugated tube utilizing a four-start spiral wall and found that the heat transfer was precisely proportional to the index of severity. He also found that the obtained heat transfer was remarkably higher than the pressure loss up to a specific Reynolds threshold. Ehsan et al. (2016) evaluated the enhancement of convective heat transfer in a rough circular tube using Al2O3-water nanofluid. He found that the rate of heat transfer was enhanced when the nanofluid was applied compared to the water flow through a smooth tube, and the growth of Nusselt number was caused by the increment of volume fraction of nanofluid.
Navickaite et al. (2019) analyzed elliptical double corrugated tubes for heat transfer enhancement. His analysis showed that the fluid flow was affected by the double corrugated tubes' novel geometry, which disturbed thermal boundary layers and modified the flow profile in comparison to the straight tube. He also found that the Nusselt number's rise was around 20% for the elliptical corrugated tubes. Omer and Alkhodari (2018) found that nanofluids' enhancement of heat transfer has a little effect on nanoparticle material, and more enhancements were observed in metals rather than metal oxides. His analysis also showed that the increase of inlet Reynolds number resulted in enhancement of convective heat transfer performance and a rise in pumping power requirement with a small penalty. Abbas and Dhaidan (2018) observed that the effect of nanoparticle loading was comparatively more extensive than the size of the nanoparticle, and the pressure drop and heat transfer rate varied a lot with the nanoparticle concentration. Yang et al. (2011) found that the rise of pulsating amplitude resulted in an increased average pressure drop in a corrugated tube compared to the steady-state. In contrast, the pulsating flow initiation made the mean Nusselt number lower in the corrugated tube compared to the steady-state. Ahmed et al. (2015) observed the enhancement of the average Nusselt number and the heat transfer enhancement with the increase of nanoparticles volume fraction. He also found the maximum heat transfer enhancement in the trapezoidal corrugated channel. Kamel et al. (2019) also found a significant improvement in the heat transfer rate by utilizing nanofluids.
Hassanzadeh and Tokgoz (2017) observed thermal and hydraulic characteristics of nanofluids in circular ducts. They found that the turbulent flow was developed in the entire ducts due to periodic corrugations, which produced higher thermal efficiency and flowed mixing compared to the plain duct. Takabi and Salehi (2014) analyzed the performance of heat transfer for a sinusoidal corrugated enclosure. They found that the heat transfer rate was improved due to the application of hybrid nanofluid compared to nanofluid and water for all the observed Rayleigh numbers. Navaei et al. (2015) observed that the nanofluid that contained SiO2 had the maximum Nusselt number in comparison to other types. Chand et al. (2015a) identified destabilizing effects using Darcy and Prandtl numbers and stabilizing effects by utilizing modified diffusivity ratio and Lewis number. Kasmani et al. (2017) found that with the increase of the Soret parameter, both the Dufour parameter and heat transfer rate are decreased. Mohammed et al. (2014) examined buoyancy-opposing laminar mixed convection in a vertical duct and found that SiO2 nanofluid has the highest Nusselt number at the highest buoyancy level. As a result of uncertainty regarding thermal conductivity and complex nanofluid viscosity in limit layer flow and heat transfer characteristics, Ahmed et al. (2014) established impacts in heat source/sink presence due to the permeable stretch tube. To achieve more realistic boundary conditions, Chand et al. (2015b) investigated a linear study of thermal instability for the nanofluid layer in the presence of suspended particles. Those suspended particles have been shown to have an important effect on the fluid layer stability.
Ajeel et al. (2019) compared the thermal performance of semicircle trapezoidal. House-shaped corrugated channel utilizing ZnO nanofluid and observed that the Nusselt number and pressure drop were 1-4 times higher than the straight corrugated profile. To be more specific, the increment of the semicircle's thermal performance, trapezoidal, and house-shaped corrugated profiles were 7.4%, 8.7%, and 4.86%, respectively, more elevated than the straight one. Andrade et al. (2019) observed the internal flow in corrugated tubes for characterizing the heat transfer and pressure drop and found that corrugated tubes' effectiveness for maximum heat transfer augmentation was in the transitional flow regime as the Reynold number was close to 2000. The Nusselt number reached up to 4.7 for the experimental tubes. Karimzadehkhouei et al. (2019) investigated the effect of inlet temperature for alumina-water nanofluid for thermally developing and hydrodynamically developed zone of laminar fluid flow. In contrast, their results indicated that inlet temperature effects for thermally developing regions were more resulted and significant. Meanwhile, Sajid and Ali (2019) reviewed recent heat transfer applications of nanofluids. They found that the boundary layer thickness and particle clustering reduce with nanoparticles, which significantly improves the system's characteristics of heat transfer. He also observed a comparatively higher heat transfer rate in the nanofluids having smaller size nanoparticles. Several recent research papers highlighted the application of nanofluids, including Ali (2020), Gao et al. (2020), Rabby et al. (2020), Choi et al. (2021), Kamel et al. (2021) and Rabby et al. (2021).
Extending the heat transfer area of the tube wall and combining nanoparticles with the working fluids are the most successful and promising approaches for increasing the heat transfer rate necessary to eliminate the heat transfer apparatus's excessive heat load. Extreme loads pose a hazard to heat transfer equipment, resulting in a variety of problems. Thus, the numerical simulation of a corrugated pipe in conjunction with SWCNT-water nanofluid has been used to estimate the improvement in laminar convective heat transfer rate. Besides, very few studies concentrated on the influence of pumping power, which can notably affect thermophysical characteristics and have energy-saving applications. As pumping power is a vital thing to explore, they have been covered in this article. Moreover, correlations for determining the Nusselt number and heat transfer coefficient of nanofluid in corrugated pipe have not been developed enough in the literature. Hence, a correlation is required to compute the Nusselt number and heat transfer coefficient without simulation or experimentation, which this study has fulfilled.
II. METHODS
A. Computational Model
To investigate the heat transfer rate and corresponding pumping power, constant heat flux was applied on both surfaces of a two-dimensional pipe. To investigate the nanofluid performance through a pipe, a numerical analysis has been performed by applying the renowned commercial computational fluid dynamics software ANSYS Fluent. The flow was considered laminar and a two-dimensional circular sharp pipe with 2 mm diameter and 300 mm length. At the pipe wall boundary, a uniform constant 500 W/m2 heat flux was exerted, and the pipe wall was considered to be in no-slip condition. At the pipe inlet, inlet velocity and constant temperature were set as boundary conditions to allow the fluids to flow at a uniform temperature of 303 K. At the pipe outlet, the pressure outlet was considered the boundary condition. The heat exchange parameters and fluid dynamics were released after making thermal and hydrodynamic enhancement of the fluid stream. Measurements were computed beyond the entrance length of x/D=60. To deter-
Figure 1: Computational model of the corrugated pipe
mine the heat transfer characteristics and pumping power, the surface and bulk temperatures were examined at the outlet, and pressures were measured at lines situated around 290 mm and 280 mm from the inlet to calculate the pressure drop. As the region has been considered fully developed, pressure drop does not depend on the distance. Figure 1 represents the computational model of the corrugated pipe.
To discretize the governing equations and boundary conditions, a finite volume approach was utilized. Additionally, second-order upwind and second-order central differencing methods have been used for convective and diffusive terms, respectively. For coupling between pressure and velocity, the SIMPLE procedure has been applied.
B. Assumptions
Nanofluid has been assumed to be thermally and hydrodynamically stable. Besides, the flow has been considered pure forced convection, incompressible, single-phase, and slip less.
C. Governing Equations
For forced convection under the steady-state and laminar flow condition, the expression of governing equations for continuity, momentum, and energy following Patankar (1980) can be written as follows:
Continuity equation: In steady flow, the conservation of mass for nanoparticles can be written as,
(1)
Here, 
and 
are the
velocity of the fluid at 
and 
directions,
respectively.
Momentum equation: For laminar flow, the X-momentum and Y-momentum equations are:
X-momentum equation,
(2)
Y-momentum equation,
(3)
Here, 
is the
density, and 
is the
viscosity of fluids.
Energy Equation: Energy can be transferred by heat, work, and mass only. The energy balance for a steady-flow control volume can be expressed as,
(4)
Here, 
is the
specific heat at constant pressure, 
is the
thermal conductivity, and 
is the fluid
temperature.
For evaluating the efficacy of two passive techniques, the overall performance of primary conditions and enhanced conditions have been compared.
Table 1: Thermofluidic properties of nanoparticles
|
Fluid |
𝐶p (J.mol-1 K-1) |
𝜌 (kgm-3) |
𝜇 (kgm−1s−1) |
K(Wm-1 K-1) |
|
H2O |
4178 |
998.23 |
0.001002 |
0.6 |
|
SWCNT |
425 |
2600 |
1.129 |
6600 |
The equation for Reynolds number for the flow of nanofluid is expressed as,
(5)
Here, 
is the
average fluid velocity, and 
is the
hydraulic diameter of the pipe.
The equation for the heat transfer rate of nanofluid,
(6)
Here, 
is the mass
flow rate, and 
is the
temperature difference.
The average heat transfer
coefficient 
is given by,
(7)
Here, 
is the
surface area of the pipe
The temperature difference between the wall and the pipe is calculated as,
(8)
The average Nusselt number is defined as follows,
(9)
Friction factor Darcy–Weisbach equation,
(10)
The pumping power per unit length,
(11)
Here, differential pressure difference,
(12)
D. Thermo Physical Properties of Nanofluid
Dynamic Viscosity: There are several equations for dynamic viscosity; among them, we utilized Batchelor (1977) equation for SWCNT-water nanofluid. The equation can be expressed as:
Batchelor equation:
(13)
Thermal Conductivity: There are several thermal conductivity equations; among them, we utilized Maxwell (1873) mode equation for nanofluid, which is given by:
(14)
Density: For calculating the density of nanofluid, Xuan and Roetzel (2000) equation has been used, which is given by:
(15)
Specific Heat: For calculating specific heat of nanofluid, Pak and Cho (2013) equation has been used, which is given by:
(16)
E. Validation Test
For model validation purposes, water has been moved through the
plain pipe at constant heat flux and uniform speed. Reynolds number within the
range of 100-1000
Figure 2: Comparison of Local Nusselt number of the present study and Shah and London (1978) theoretical equation.
Figure 3: Variation of Nusselt Number for different grid sizes.
Figure 4: Enhancement in Nusselt number due to the corrugation for water at different Reynolds numbers.
has been considered to determine the Nusselt number and friction factor. A comparison was made in a fully developed zone among the local Nusselt number obtained from Shah and London (1978) theoretical equation, which is shown in Fig. 2. The result indicated a good agreement with only a 2% error for the Nusselt number. The correlation developed by Shah and London (1978) theoretical equation for the laminar pipe can be expressed as follows:
,
,
where
.
F. Grid Refinement Test
For grid independence investigation, the working substance has been
taken as water, and the simulation was run at Reynolds number 600 for the plain
pipe. A grid independence test was carried out to discover the opti-
Figure 5: Enhancement in heat transfer coefficient due to the corrugation for water at different Reynolds numbers.
Figure 6: Enhancement in pumping power requirement due to the corrugation for water at different Reynolds numbers.
mum grid size for the present study. Five diffident nodes,
10000, 20000, 27000, 35000, and 48000, were tested to determine the effect on the Nusselt number calculated at a distance of 750 mm, which is shown in Fig. 3.
From Fig. 3, it was found that there was no significant change in Nusselt Number beyond the grid size of 1000×35, and at this grid, the Nusselt number was very close to 4.36. Therefore, for the present study, a grid size of 35000 was used to perform all the simulations.
III. RESULTS
A. Effect of corrugation on Nusselt Number and heat transfer coefficient
The corrugation effect on Nusselt number and the heat transfer coefficient has been evaluated for water taken as base fluid by considering plain and corrugated pipes. Figure 4 demonstrates the enhancement in Nusselt number due to corrugation at different Reynolds numbers, whereas Fig. 5 represents the increment of heat transfer coefficient due to corrugation at various Reynolds numbers. It has been found that the Nusselt number and heat transfer coefficient increased with the increment of Reynolds number and due to corrugation. With the rise of Reynolds number, the enhancement went up to 56.52% for Nusselt number and heat transfer coefficient.
B. Effect of corrugation on pumping power
Figure 6 shows the variations in the pumping power requirement of water due to corrugation at different Reynolds numbers. It has been identified that the pumping power requirement increased with the increment of Reynolds number and due to corrugation. With the rise of Reynolds number, the enhancement went up to 20.61%. Moreover, pressure decreases and losses due to friction in the corrugated pipe because of corrugation. Therefore, the pumping power needed in the corrugated pipe rather than the flat pipe is expected to be increased.
Figure 7: Variation of Nusselt Number with Reynolds Number for SWCNT-water nanofluid.
Figure 8: Variation of Heat Transfer Coefficient with Reynolds Number for SWCNT-water nanofluid.
Figure 9: Variation of Pumping power requirement with Reynolds number for SWCNT-water nanofluid.
C. Effect of using nanofluid in heat transfer performance
The analysis considered SWCNT-water nanofluid as the operating fluid across the semicircular domain with a 1%-5% volume fraction. With the increasing volume of nanofluid, the nanofluid's thermal conductivity was improving, which increased the Nusselt number and the heat transfer rate for nanofluid. Figure 7 demonstrates a variation of Nusselt number for SWCNT-water nanofluid, while Fig. 8 exhibits performances in terms of heat transfer coefficient for the same nanofluid. The change also occurred with the Reynolds number for a fixed volume fraction of the nanofluid. At a Reynolds number of 500, the maximum growth of Nusselt number and heat transfer coefficient were 13.88% for 5% SWCNT-water nanofluid.
D. Effect on pumping power using nanofluid
When the volume fraction of nanofluid increases, the pumping power requirement rises due to the higher viscosity of the working fluid. Figure 9 represents the variation of pumping power requirement with Reynolds number for SWCNT-water nanofluid. At a Reynolds number of 1200, the enhancement of pumping power requirement was 92% for 5% volume fraction of SWCNT-water nanofluid.
Figure 10: Comparison of SWCNT-water nanofluid’s Nusselt number between developed correlation and current numerical results for Re = 500.
Figure 11: Comparison of SWCNT-water nanofluid’s Nusselt number between developed correlation and current numerical results for Re = 1200.
E. Correlation of nanofluid’s Nusselt number for corrugated pipe
To calculate the Nusselt number of nanofluid, a correlation was developed and presented in Eq. (18) using numerical results for the corrugated pipe from Ansys shown in Figs. 10 and 11. The developed correlation of nanofluid’s Nusselt number is a function of Nusselt number of base fluid water, volume fraction of nanoparticles, and Reynolds number. The calculated Nusselt number of nanofluid from the developed correlation was compared with the Nusselt number of nanofluid from current numerical results to validate the developed correlation with numerical results. The comparison between the Nusselt number of nanofluid for developed correlation and current numerical results was presented in Fig. 10 and 11 for Reynolds numbers 500 and 1200, respectively. The figures showed that results from correlation showed good agreement only maximum 1.84% deviation with current numerical results which refers that currently developed correlation has potential to calculate Nusselt number for different nanofluid under steady-state laminar convective heat transfer condition for corrugated pipe and other assumptions mentioned in the numerical method section.
(17)
(18)
F. Correlation of nanofluid’s heat transfer coefficient for corrugated pipe
To
calculate the heat transfer coefficient of nanofluid, a correlation was
developed and presented in Eq. (20) using numerical results for the corrugated
pipe from Ansys shown in Figs. 12 and 13. The developed correlation of
Figure 12: Comparison of SWCNT-water nanofluid’s heat transfer coefficient between developed correlation and current numerical results for Re = 500.
Figure 13: Comparison of SWCNT-water nanofluid’s heat transfer coefficient between developed correlation and current numerical results for Re = 1200.
nanofluid’s heat transfer coefficient is a function of heat transfer coefficient of base fluid water, volume fraction of nanoparticles, and Reynolds number. The calculated heat transfer coefficient of nanofluid from the developed correlation was compared with the heat transfer coefficient of nanofluid from current numerical results to validate the developed correlation with numerical results. The comparison between the heat transfer coefficient of nanofluid for developed correlation and current numerical results was presented in Fig. 12 and 13 for Reynolds numbers 500 and 1200, respectively. The figures showed that results from correlation showed good agreement only maximum 7.12% deviation with current numerical results which refers that currently developed correlation has potential to calculate heat transfer coefficient for different nanofluid under steady-state laminar convective heat transfer condition for corrugated pipe and other assumptions mentioned in the numerical method section.
(19)
. (20)
In this study, up to 5% volume concentration of nanofluid was used only, and after checking the thermal properties of SWCNT, no visible sedimentation was noticed, which proved the stability of nanofluid. Moreover, the fluid density was kept constant during this whole study, and the fluid near the tube walls had a higher temperature owing to heat flux throughout the wall.
IV. CONCLUSIONS
This study considered corrugated pipe with nanofluid as the working fluid to improve heat transfer performance. Owing to the increased viscosity of a fluid through it, corrugation in the pipe provides more pumping capacity. In optimal comparability with water, nanofluid compensates for increased pumping capacity. Hence, from 1% to 5% volume fraction of SWCNT was used to improve the heat transfer rate and identify the pumping power for the corrugated pipe. The key findings of this study were:
1. Presented corrugated pipe provides more heat transfer rate in terms of Nusselt number and heat transfer coefficient than the plain pipe due to the heat transfer area's extension. Hence, utilization of corrugated pipe, the Nusselt number, and heat transfer coefficient increased up to 56.52% compared to the plain pipe.
2. SWCNT-water nanofluid showed a better heat transfer coefficient than water during flowing through corrugated pipe due to the higher thermofluidic properties of nanofluid. At the Reynolds number 500, the maximum increment of Nusselt number and heat transfer coefficient was 13.88% for 5% SWCNT-water nanofluid.
3. The results from this study also showed that SWCNT-water nanofluid required more pumping power than water at constant Reynolds Number due to the pressure loss and friction factor of nanofluid. At Reynolds number 1200, the increment of pumping power requirement was 92% for 5% volume fraction of SWCNT-water nanofluid.
4. A correlation to calculate the Nusselt number of nanofluid was also developed using numerical results from Ansys simulation, which showed good agreement, maximum 1.84% deviation only from the numerical result of Nusselt number for nanofluid. Additionally, another correlation was also developed for the heat transfer coefficient of nanofluid utilizing numerical results from Ansys simulation, where a maximum 7.12% deviation was recorded from the numerical result of heat transfer coefficient for nanofluid.
Therefore, it can be concluded that the use of corrugated pipe with nanofluid as working fluid provides better heat transfer performances and pumping power advantage compared to plain pipe with water as working fluid. Additionally, the developed correlations are also capable of calculating the Nusselt number and heat transfer coefficient of nanofluid.
NOMENCLATURE
|
𝜌 |
Density (kgm-3) |
|
|
𝑇 |
Temperature (°C or K) |
|
|
W |
Pumping power (KW) |
|
|
𝑈𝑎𝑣 |
Average inlet velocity (m/s) |
|
|
𝐶p |
Specific heat at constant pressure (J.mol-1.K-1) |
|
|
𝐷ℎ |
Hydraulic diameter (m) |
|
|
𝑚 |
Mass flow rate (kg/s) |
|
|
𝐾 |
Thermal conductivity (W.m-1.K-1) |
|
|
Q |
Heat transfer rate (J/s) |
|
|
∆𝑇 |
Temperature difference (°C or K) |
|
|
ℎc |
Average heat transfer coefficient (W.m-2.K-1) |
|
|
𝜇 |
Dynamic Viscosity (kg·m−1·s−1) |
|
|
∅ |
Volume concentration |
|
|
f |
Friction factor |
|
|
Nu |
Nusselt number |
|
|
Re |
Reynolds number |
|
|
∆P |
Pressure difference (Pa or N/m2) |
|
|
Subscript |
|
|
|
𝑖 |
Inlet |
|
|
𝑜 |
Outlet |
|
|
𝑤 |
Wall |
|
|
𝑛𝑓 |
Nanofluid |
|
|
𝑏𝑓 |
Basefluid |
|
|
𝑝 |
Particle size |
|
REFERENCES
Abbas, A.K. and Dhaidan, N.S. (2018) Turbulent forced convection of nanofluids flow in corrugated tubes. IOP Conf. Ser. Mater. Sci. Eng. 433, 012054.
Ahmed, S., Hussein, A.K., Mohammed, H. and Sivasankaran, S. (2014) Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids. Appl. Math. Comput. 238:149-162.
Ahmed, M.A., Yusoff, M.Z., Ng, K.C. and Shuaib, N.H. (2015) Numerical and experimental investigations on the heat transfer enhancement in corrugated channels using SiO2–water nanofluid. Case Stud. Therm. Eng. 6, 77-92.
Ajeel, R.K., Salim, W.I. and Hasnan, K. (2019) Thermal performance comparison of various corrugated channels using nanofluid: Numerical study. Alex. Eng. J. 58, 75-87.
Ali, H.M. (2020) In tube convection heat transfer enhancement: SiO2 aqua based nanofluids. J. Mol. Liq. 308, 113031.
Andrade, F., Moita, A.S., Nikulin, A., Moreira, A.L. and Santos, H. (2019) Experimental investigation on heat transfer and pressure drop of internal flow in corrugated tubes. Int. J. Heat Mass Transf. 140, 940-955.
Batchelor, G.K. (1977) The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J. Fluid Mech. 83, 97-117.
Chand, R., Rana, G. and Hussein, A.K. (2015a) On the onset of thermal instability in a low Prandtl number nanofluid layer in a porous medium. J. Appl. Fluid Mech. 8, 265-272.
Chand, R., Rana, G. and Hussein, A.K. (2015b) Effect of suspended particles on the onset of thermal convection in a nanofluid layer for more realistic boundary conditions. Int. J. Fluid Mech. Res. 42, 375-390.
Choi, S.B. (1991) Fluid flow and heat transfer in microtubes. Micromech Sens. Actuators Syst. ASME, 123-134.
Choi, T.J., Park, M.S., Kim, S.H. and Jang, S.P. (2021) Experimental study on the effect of nanoparticle migration on the convective heat transfer coefficient of EG/water-based Al2O3 nanofluids. Int. J. Heat Mass Transf. 169, 120903.
Ehsan, M.M., Noor, S., Salehin, S. and Islam, A.S. (2016) Study of turbulent convective heat transfer enhancement by Al2O3-water nanofluid through a rough circular tube. Appl. Mech. Mater. 819, 341-345.
Gao, D., Bai, M., Hu, C., Lv, J., Wang, C. and Zhang, X. (2020) Investigating control of convective heat transfer and flow resistance of Fe3O4/deionized water nanofluid in magnetic field in laminar flow. Nanotechnology. 31, 495402.
Hassanzadeh, R. and Tokgoz, N. (2017) Thermal-hydraulic characteristics of nanofluid flow in corrugated ducts. J. Eng. Phys. Thermophys. 26, 498-513.
Kamel, M., Lezsovits, F. and Hussein, A.K. (2019) Experimental studies of flow boiling heat transfer by using nanofluids: a critical recent review. J. Therm. Anal. Calorim. 138, 4019-4043.
Kamel, M.S., Al-Oran, O. and Lezsovits, F. (2021) Thermal conductivity of Al2O3 and CeO2 nanoparticles and their hybrid based water nanofluids: An experi-mental study. Period Polytech Chem. Eng. 65, 50-60.
Karimzadehkhouei, M., Sadaghiani, A.K., Motezakker, A.R., Akgönül, S., Ozbey, A., Şendur, K., Mengüç, M.P. and Koşar, A. (2019) Experimental and numerical investigation of inlet temperature effect on convective heat transfer of γ-Al2O3/Water nanofluid flows in microtubes. Heat Transfer Eng. 40, 738-752.
Kasmani, R.M., Sivasankaran, S., Bhuvaneswari, M. and Hussein, A.K. (2017) Analytical and numerical study on convection of nanofluid past a moving wedge with Soret and Dufour effects. Int. J. Numer. Method H., 27, 2333-2354.
Maxwell, J.C. (1873) A treatise on electricity and magnetism. Clarendon press, Oxford.
Mohammed, H., Al-Aswadi, A., Abu-Mulaweh, H., Hussein, A.K. and Kanna, P. (2014) Mixed convection over a backward-facing step in a vertical duct using nanofluids-buoyancy opposing case. J. Comput. Theor. Nanosci. 11, 860-872.
Navaei, A.S., Mohammed, H.A., Munisamy, K.M., Yarmand, H. and Gharehkhani, S. (2015) Heat transfer enhancement of turbulent nanofluid flow over various types of internally corrugated channels. Powder Technol. 286, 332-341.
Navickaitė, K., Cattani, L., Bahl, C.R. and Engelbrecht, K. (2019) Elliptical double corrugated tubes for enhanced heat transfer. Int. J. Heat Mass Tran. 128, 363-377.
Omer, E.A. and Alkhodari, S.B. (2018) Heat Transfer Enhancement in Turbulent Flows Utilizing Nanofluids. J. Eng. Res. 25, 55-68.
Pak, B.C. and Cho, Y. (2013) Hydrodynamic and heat transfer study of dispersed fluid with submicron based Al2O3 and CuO nanofluids in a triangular duct. J. Disper. Sci. Technol. 34, 1368-1375.
Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, New York.
Rabby, M.I., Hossain, F., Amin, S.S., Mumu, T.A., Bhuiyan, M.A. and Sadrul-Islam, A.K. (2020) Convective Heat Transfer and Power Saving Application of Si Based Nanoparticles in a Circular Pipe. Lat. Am. Appl. Res. 50, 321-327.
Rabby, M.I., Hossain, F., Amin, S.S. and Islam, A.S. (2021) Numerical simulation on performance evaluation among metal and oxide based nanofluids for power savings application of a circular tube. J. Therm. Eng. 7, 1150-1162.
Sajid, M.U. and Ali, H.M. (2019) Recent advances in application of nanofluids in heat transfer devices: a critical review. Renew. Sust. Energ. Rev. 103, 556-92.
Shah, R.K. and London, A.L. (1978) Laminar flow forced convection in ducts. Supplement 1. Advances in Heat Transfer. Academic Press, New York.
Smaisim, G.F. (2018) Augmentation of Heat Transfer in Corrugated Tube using Four-Start Spiral Wall. Al-Qadisiyah J. Eng. Sci. 10, 451-467.
Takabi, B. and Salehi, S. (2014) Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Adv. Mech. Eng. 6, 147059.
Tuckerman, D.B. and Pease, R.F. (1981) High-performance heat sinking for VLSI. IEEE Electron. Device Lett. 2, 126-129.
Xuan, Y. and Roetzel, W. (2000) Conceptions for heat transfer correlation of nanofluids. Int. J. Heat Mass Transf. 43, 3701-3707.
Yang, X., Mao, Z., Wu, Y., Liang, L. and Bi, Y. (2011) Numerical simulation on convection heat transfer of pulsating flow in corrugated tube. International Conference on Materials for Renewable Energy & Environment. 2, 1882-1884.
Received: July 18, 2021
Sent to Subject Editor: September 16, 2021
Accepted: December 7, 2021
Recommended by Subject Editor Gianfranco Caruso