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Heat Transfer Characteristics of Low Reynolds Number Flow of Nanofluid Around a Heated Circular Cylinder
Available online at www.sciencedirect.com
ScienceDirect Procedia Technology 14 (2014) 348 – 356
2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014
Heat transfer characteristics of low Reynolds number flow of nanofluid around a heated circular cylinder Mitesh Vegada,*, Sagar Satadiab, Panara Pradipb, Patel Chiragb, Panchasara Bhargavb a
Assistant Professor, Department of Mechanical Engineering, G H Patel College of Engineering & Technology, V V Nagar, India-388120 b BE Mechanical, G H Patel College of Engineering & Technology, V V Nagar, India-388120
Abstract Numerical investigation of heat transfer phenomena over an isothermal cylinder, for low Reynolds number flow of nanofluid is presented. Conservation equation of mass, momentum and energy under steady state have been solved using finite volume method. Heat transfer characteristic and flow over the stationary cylinder has been studied for water based copper nano fluid with different solid fraction values. Local Nusselt number over the cylinder surface has been found to increase with increase in nano particle fraction as well as increase in flow strength, though, the physics behind the rise in two cases is entirely different. Local heat flux drops along the cylinder wall and increases with increase in nano particle fraction as well as Reynolds number. Neglecting buoyancy effect, flow separation angle is not affected by presence of nano particles in the base fluid. © © 2014 2014 The The Authors. Authors. Published Publishedby byElsevier ElsevierLtd. Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2014. Peer-review under responsibility of the Organizing Committee of ICIAME 2014. Keywords: Circular cylinder; Reynolds number; nano fluid ; heat transfer; Nusselt number
Nomenclature Cp g h k D Nu P
specific heat, J/kg K gravitational acceleration, m/s2 convection heat transfer coefficient, W/m2K thermal conductivity, W/mK cylinder diameter, m local Nusselt number on the cylinder surface fluid pressure, Pa
Greek symbols Į thermal diffusivity, m2/s I solid volume fraction M scalar parameter in Eq. (1)
*M
diffusion term in Eq. (1)
* Corresponding author. Tel.: +91-987-912-8555 E-mail address: [email protected]
2212-0173 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICIAME 2014. doi:10.1016/j.protcy.2014.08.045
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
· § Prandtl number ¨ X f ¸ ¨D ¸ © f ¹
Pr
sM
source term in Eq. (1)
T U,V X,Y
temperature, K velocity components in x, y directions, m/s x and y coordinates
1.
ȝ ȣ ȡ
349
dynamic viscosity, Ns/m2 kinematic viscosity, m2/s density, kg/m3
Subscripts f fluid (pure water) nf nanofluid p nanoparticle
Introduction
Classical flow configuration of flow around a circular cylinder has been an area of investigation over the decades. Flow over a heated circular cylinder and related transport phenomena over the surface are of vital importance in different technological equipments like heat exchangers, solar systems, electronic cooling systems etc. Furthermore the flow structure in the separated zone behind a circular cylinder also strongly influences the heat transfer characteristics in that zone. Low Reynolds number flow over a cylinder has been studies by many researchers over the decades [1-3]. Experiments on flow past circular cylinder at low Reynolds number have been done by D J Tritton [4]. Subhankar Sen et al. [5] have reported numerical investigated flow past a circular cylinder and have also developed empirical relation for separation angle as a function of Reynolds number. B Sharman et al. [6] have made numerical predictions of low Reynolds number flow over two tandem cylinders and have reported critical cylinder spacing where large jump in fluctuating forces and Stroutal number is observed. W A Khan et al. [7] have focused on analytical study of flow and heat transfer around a circular cylinder. D G Roychowdhury et al.[8] have shown that thermal boundary condition, fluid Prandtl number and geometry aspect ratio have a significant influence on flow pattern, thermal stratification and heat transfer rate for natural convection around a heated circular cylinder inside an enclosure. On the other hand Arnab Kumar De and Amaresh Dalal [9] have studied natural convection over a square heated cylinder for various geometry configuration characterized by different aspect ratio. The last decade has witnessed almost an exponential growth in nano fluid related to published literature, with stress on improvement of transport phenomena with use of different types of nano particles [10,11]. Nano fluids which are nano size particles having high thermal conductivity suspended in the base fluid and have been reported to be promising in improvement of thermal characteristic. In recent times Robert Taylor et al [12] have recently reviewed diverse application of nano fluids. Review of work related to heat transfer characteristic of nano fluid has been reported by Trisaksri and Wongwises [13]. Eiyad Abu Nada [14] has investigated application of nano fluid heat transfer enhancement of separated flow in backward facing step configuration. Outside the recirculation zone higher thermal conductivity nano particles have better enhancement of Nusselt number where as within the recirculation zone lower thermal conductivity particles are better. There is an increase in Nusselt number with increase in percentage of nano particle for whole range of Reynolds number. Rehana Nasirin [15] have carried out numerical investigation of water aluminum oxide nano fluid natural convection in a closed enclosure for various volume fraction, Prandtl number and aspect ratio. Md. Mahbubar Rahman et al. [16] have investigated two dimensional unsteady flow of nano fluid past a circular cylinder. A S Dalkilic [17] has reported critical information on theoretical, experimental and numerical work related to forced convection heat transfer of nano fluids. Summary of research on fluid flow and heat transfer characteristic of nano fluids in forced as well as free convection has been reported by Xiang Qi Wnag and Arun S Majumdar [18]. Sandip Sarkar et al. [19] have studied buoyancy driven mixed convection of nano fluid around a circular cylinder. They have shown that presence of nano fluid minimizes the effect of buoyancy force and stabilizes the flow regime. The present investigation had been motivated by increased interest and research in potential improvements in heat transfer characteristics using nano fluids, typically for flow characterized by low Reynolds number. Effort has been
350
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
made to study effect of nano particles on the transport phenomena around a circular cylinder maintained at constant temperature. The problem has been investigated numerically solving mass, momentum and energy equation under steady state. Heat transfer characteristic around the cylinder has been investigated for flow characterized by Reynolds number less than 40, using different volume fraction copper nano particles suspended in water. 2.
Problem description and mathematical model
The problem geometry under consideration is shown in Fig. 1. The base fluid is water and nano particles are in thermal equilibrium with the base fluid and there is no slip between them. Flow considered is two dimensional, steady, laminar and incompressible. Effect of buoyancy has not been taken into consideration as the stress is on investigating effect of nano particle concentration on heat transfer characteristic around the cylinder surface. The governing equation of mass, momentum and energy under steady state can be expressed in generalized dimensional form as:
w UM w VM wX wY
w § wM · w § wM · ¸ SM ¸ ¨J M ¨J M wX © wX ¹ wY © wY ¹
(1)
M is the unknown scalar, J M and SM are the diffusion and source term coefficient respectively. Values of
Where
these parameters are summarized in Table 1. The governing equations are subject to following boundary as mentioned in Table 2.Thermo physical properties of nano fluid used for simulation have been borrowed from work of A Kargar et al. [20]. Thermo-physical property of nanofluid had been calculated using Eqs. (2)-(6) and have been borrowed from classical model suggested by Y. Xuan et al [21]. Adiabatic Wall
Velocity Inlet, T=303.16K
Outlet, 32D
Adiabatic Wall Fig. 1. Problem geometry with boundary condition and mesh inside the solution domain
1 I ȡ f
ȡ nf
ȡ&
p nf
ȝ nf
I ȡp
1 I ȡ& p f
ȝ f 1 I
2.5
(2)
I ȡ& p f
(3) (4)
351
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
ª k p 2k f 2I k f k p º kf « » «¬ k p 2k f I k f k p »¼
k nf
k nf
Į nf
(5) (6)
ȡ&
p nf
Table 1 Summary of governing equations. Scalar
Equation
Diffusion coefficient
M
Mass conservation
1
X momentum
U (x velocity)
Y momentum
V (y velocity)
Energy
T (Temperature)
Source term
*M 0
SM
0
§ ȝ nf · ¨ ¸ ¨ȡ ¸ © nf ¹ § ȝ nf · ¨ ¸ ¨ȡ ¸ nf © ¹ Į nf
1 § wP · ¨ ¸ ȡ nf © wX ¹
1 § wP · ¨ ¸ ȡ nf © wY ¹
0
Table 2 Boundary conditions. Surface
Boundary Condition
Inlet
U=1, V=0, T=303.16K
Outlet
§ wU · ¨ ¸ © wX ¹
Top and horizontal walls Cylinder surface
bottom
U=0, V=0,
§ wT · wV 0, §¨ ·¸ 0, ¨ ¸ X w © wX ¹ ¹ © § wT · ¨ ¸ © wY ¹
0
U=0,V=0, T=373.16K
Table 3 Mesh independence test data for Re=40 Grid Size Angle of (cylinder x radial) separation 50 x 50 129.57 100 x 100 127.79 150 x 150 127.19 180 x 180 126.99
3.
0
Percentage change in angle of separation 1.37 0.47 0.15
Length Reattachment 1.49 1.78 1.81 1.83
of
Percentage change in length of reattachment 19.46 1.68 1.10
Numerical Methodology
Conservation equations of mass, momentum and energy subject to boundary condition specified in Table 2, have been by discritised using finite volume approach. Patankar’s SIMPLE algorithm has been employed for pressure velocity coupling issues. Momentum interpolation at the control volume face has been achieved using Rie Chow interpolation scheme. Convection term has been discritised using second order upwind scheme and diffusion term
352
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
has been handled using second order scheme. Structured grid with collocated arrangement of variable has been adopted for numerical simulation. The solution domain has been divided into smaller control volume ensuring that control volumes next to the cylinder surface and in the wake region are sufficiently small and gradually expand along radial direction away from the cylinder.The discritized algebraic finite volume equations have been solved iteratively and residuals have been reduced to value 10-10. The solution obtained solving the governing equation has been subsequently used to calculate derived parameter of interest. Local Nusselt number which is ratio of convection to conduction heat transfer over a given length (L), over the cylinder surface can be expressed as:
Nu
§ knf § wT · · ¨ ¨ ¸cy ln der ¸ Y k w © ¹ f ¨ surface ¸ ¨L T T ¸ wall basefluid ¸ ¨ ¨ ¸ © ¹
4.
(7)
Grid Testing and Code Validation
Extensive grid testing has been carried out to ensure that the solution is mesh independent. Gird of different size in region next to the cylinder and wake region has been used for simulating transport phenomena around the cylinder for flow characterized by Reynolds of 40, which is the largest value in the range of interest for current investigation. Flow separation angle and length of reattachment has been computed for different mesh size and are summarized in Table 3. Mesh having 180 control volumes along half the cylinder periphery and 180 control volumes along the radial direction away from the cylinder has been used for all simulations and is shown in Fig. 1. Expansion factor of 1.05 has been used along radial direction. The solution methodology has been validated by comparing angle of separation and length of reattachment for Re=40 which is the largest value in the range considered for simulation. Values obtained in current simulation are found to match closely with data published in literature [22]. 5.
Results and Discussion
Effect of variation of Reynolds number and nano particle concentration on temperature gradient normal to cylinder surface is shown in Fig. 2. For a fixed Reynolds number, higher concentration of nano particle leads to increased thermal conductivity of nanofluid, which in turn leads to reduction in normal direction temperature gradient at the cylinder wall. As the flow velocity increases, for a fixed nano particle fraction, there is an increase in temperature gradient normal to cylinder surface owing to decrease in thermal and momentum boundary layer thickness which can be seen in Fig. 3. Variation of temperature along the normal direction at three different planes L1, L2 and L3 at angles 45, 90 and 135 degree respectively is shown in Fig. 4. Point of stagnation on the inlet side of flow geometry has been taken to be reference with angle equal to zero degree. Temperature gradient normal to the cylinder surface drops towards the stagnation point in the wake behind the cylinder. There is sharp increase in normal direction temperature gradient at the cylinder wall with increase in flow velocity. Variation of heat transfer coefficient and Nusselt number along the top half of the cylinder for different values of Reynolds number and solid fraction is show in Fig. 5 and Fig. 6, respectively. It can be seen that heat transfer coefficient and Nusselt number increase with increase in solid fraction as well as increase in Reynolds number. However, the reason for increase in the two cases is entirely different. Increase in flow velocity characterized by higher Reynolds number results in increased temperature gradient normal to the cylinder wall (refer Fig. 2) which in turn results in higher value of Nusselt number, and heat transfer coefficient, for the same nano fluid fraction. On the
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
other hand, temperature gradient on the cylinder surface reduces towards the trailing part of the cylinder owing to growth of thermal boundary layer. This leads to drop in heat transfer coefficient. Inclusion of nano particle in base fluid leads to increase in thermal conductivity of the fluid, where as temperature gradient normal to the cylinder surface decreases as shown. However reduction in gradient is lower compared to increase in thermal conductivity thus leading to overall increase in heat transfer coefficient and Nusselt number value.
Fig. 2. Temperature gradient normal to the cylinder surface
Fig. 3. Temperature and velocity variation normal to cylinder surface at angle equal to 90 degree. (a) Re=10, (b) 2% nano particle
Variation of local heat flux along the cylinder surface is shown in Fig. 7 and is found to be increasing with higher fraction of nano particle as well as increase in Reynolds number. This can be accounted to higher heat transfer coefficient owing to increased fraction of nano particle and higher flow velocity respectively. For a fixed Reynolds number and nano particle concentration, the temperature gradient reduces towards the trailing part of cylinder leading to lower heat flux (refer Fig. 4). Angle of flow separation for Reynolds number equal to 40 is around 140 degrees and not found to change with change in nano particle fraction as the effect of buoyancy has not been taken into account.
353
354
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
6.
Conclusion
Flow of water based copper nano fluid around an isothermal cylinder has been investigated. It has been observed that: x There is increase in the heat transfer coefficient with increase in value of solid fraction. This can be attributed to improved thermal conductivity of nanofluid due to presence of nano particle. x Temperature gradient at the cylinder surface along normal direction drops with increase in nano particle concentration. However there is an increase in the thermal conductivity of nanofluid, thus leading to increase in Nusselt number. x Local heat flux drops along the cylinder surface towards the rear stagnation point. There is increase in heat flux with increase in nano particle fraction as well as flow velocity. x Presence of nano particle has no effect on point of flow separation for a fixed Reynolds number because the effect of buoyancy force has not been taken into consideration.
Fig. 4. Temperature variation normal to cylinder surface at three different planes. (a) Re=10, 2% nano fraction (b) Re=40, 2% nano fraction
Fig. 5. Heat transfer coefficient along the cylinder surface. (a) Re=10 (b) Re=40
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
Fig. 6. Nusselt number along the cylinder surface. (a) Re=10 (b) Re=40
Fig. 7. Local heat flux along the cylinder surface. (a) Re=10 (b) Re=40
References [1] S. Mittal and A. Raghuvanshi, Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers. Int. J. Numerical Methods in Fluids, 35 (2001) 421-447. [2] Bengt Fornberg, A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, part 4 (1980) 819-855. [3] Laszol Baranyi et al., Analysis of low Reynolds number flow around a heated circular cylinder. Journal ofMechanical Science and Technology, 23 (2009) 1829-1834. [4] D J Tritton, Experiments on the flow past a circular cylinder at low Reynolds number. Journal of Fluid Mechanics, 6 (1959) 547-567. [5] Subhankar Sen et al., Numerical simulation of steady flow past a circular cylinder. Proceedings of the 37th National & 4th International Conference on Fluid Mechanics and Fluid Power December 16-18 (2010) IIT Madras, Chennai, India. [6] B. Sharman etal., Numerical predictions of low Reynolds number flows over two tandem circular cylinders. Int. J. Numer. Meth. Fluids. 47 (2005) 423–447. [7] W A Khan et al., Fluid flow around and heat transfer from an infinite circular cylinder. Journal of Heat Transfer, 127 (2005) 785-790. [8] D. G. Roychowdhury et. al., Numerical simulation of natural convective heat transfer and fluid flow around a heated cylinder inside an enclosure. Heat and Mass Transfer, 38 (2002) 565-576. [9] Arnab Kumar De, Amaresh Dalal, A numerical study of natural convection around a square, horizontal, heated cylinder placed in an enclosure. Int. J. of Heat and Mass Transfer, 49 (2006) 4608–4623. [10] Kaufui V.Wong , Omar De Leon, Applications of Nanofluids: Current and Future. Advances in Mechanical Engineering, Volume 2010, Article ID 519659, 11 pages. [11] Robert Taylor et al., Small particles, bug impacts: A review of the diverse applications of nanofluids. Journal of Applied Physics, 113 (2013)
355
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011301-19. [12] Robert Taylori et al., Critical review of the novel applications and uses of nanofluids. Poceedings of the ASME 2012 3rd Micro/Nanoscale Heat & Mass Transfer International Conference MNHMT2012 March 3-6 (2012) Atlanta, Georgia, USA. [13] Trisaksri V, Wongwises S, Critical Review of Heat Transfer Characteristics of Nanofluids, Renewable Sustainable Energy Rev., 11 (2007) 512–523. [14] Eiyad Abu-Nada, Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat and Fluid Flow. 29 (2008) 242-249. [15] Rehena Nasrin , M.A. Alim , Ali J. Chamkha, Buoyancy-driven heat transfer of water–Al2O3 nanofluid in a closed chamber: Effects of solid volume fraction, Prandtl number and aspect ratio. Int. J. of Heat and Mass Transfer, 55 (2012) 7355–7365. [16] Md. Mahbubar Rahman et al., Numerical Investigation of unsteady flow past a circular cylinder using 2-D finite volume method. J. of Naval Architecture and Marine Engg. 4 (2007) 27-42. [17] A.S. Dalkilic et al., Forced Convective Heat Transfer of Nanofluids - A Review of the Recent Literature. Current Nanoscience, 8 (2012) 949-969. [18] Xiang-Qi Wang, Arun S. Mujumdar, Heat transfer characteristics of nanofluids: a review. Int. J. of Thermal Sciences, 46 (2007) 1-19. [19] Sandip Sarkar et.al., Mixed convective heat transfer of nanofluids past a circular cylinder in cross flow in unsteady regime, 55 (2012) 4783– 4799. [20] A. Kargar, B. Ghasemi, S. M. Aminossadati, An artificial neural network approach to cooling analysis of electronic components in enclosures filled with nanofluids. ASME Journal of Electronic Packaging. 133 (2011) 011010-1-011010-9. [21] Y. Xuan, W. Roetzel., Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer 43 (19) 2000, 3701-3707. [22] H. Ding et al, Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method. Comput. Methods Appl. Mech. Engrg. 193 (2004) 727–744.
ScienceDirect Procedia Technology 14 (2014) 348 – 356
2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014
Heat transfer characteristics of low Reynolds number flow of nanofluid around a heated circular cylinder Mitesh Vegada,*, Sagar Satadiab, Panara Pradipb, Patel Chiragb, Panchasara Bhargavb a
Assistant Professor, Department of Mechanical Engineering, G H Patel College of Engineering & Technology, V V Nagar, India-388120 b BE Mechanical, G H Patel College of Engineering & Technology, V V Nagar, India-388120
Abstract Numerical investigation of heat transfer phenomena over an isothermal cylinder, for low Reynolds number flow of nanofluid is presented. Conservation equation of mass, momentum and energy under steady state have been solved using finite volume method. Heat transfer characteristic and flow over the stationary cylinder has been studied for water based copper nano fluid with different solid fraction values. Local Nusselt number over the cylinder surface has been found to increase with increase in nano particle fraction as well as increase in flow strength, though, the physics behind the rise in two cases is entirely different. Local heat flux drops along the cylinder wall and increases with increase in nano particle fraction as well as Reynolds number. Neglecting buoyancy effect, flow separation angle is not affected by presence of nano particles in the base fluid. © © 2014 2014 The The Authors. Authors. Published Publishedby byElsevier ElsevierLtd. Ltd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2014. Peer-review under responsibility of the Organizing Committee of ICIAME 2014. Keywords: Circular cylinder; Reynolds number; nano fluid ; heat transfer; Nusselt number
Nomenclature Cp g h k D Nu P
specific heat, J/kg K gravitational acceleration, m/s2 convection heat transfer coefficient, W/m2K thermal conductivity, W/mK cylinder diameter, m local Nusselt number on the cylinder surface fluid pressure, Pa
Greek symbols Į thermal diffusivity, m2/s I solid volume fraction M scalar parameter in Eq. (1)
*M
diffusion term in Eq. (1)
* Corresponding author. Tel.: +91-987-912-8555 E-mail address: [email protected]
2212-0173 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICIAME 2014. doi:10.1016/j.protcy.2014.08.045
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
· § Prandtl number ¨ X f ¸ ¨D ¸ © f ¹
Pr
sM
source term in Eq. (1)
T U,V X,Y
temperature, K velocity components in x, y directions, m/s x and y coordinates
1.
ȝ ȣ ȡ
349
dynamic viscosity, Ns/m2 kinematic viscosity, m2/s density, kg/m3
Subscripts f fluid (pure water) nf nanofluid p nanoparticle
Introduction
Classical flow configuration of flow around a circular cylinder has been an area of investigation over the decades. Flow over a heated circular cylinder and related transport phenomena over the surface are of vital importance in different technological equipments like heat exchangers, solar systems, electronic cooling systems etc. Furthermore the flow structure in the separated zone behind a circular cylinder also strongly influences the heat transfer characteristics in that zone. Low Reynolds number flow over a cylinder has been studies by many researchers over the decades [1-3]. Experiments on flow past circular cylinder at low Reynolds number have been done by D J Tritton [4]. Subhankar Sen et al. [5] have reported numerical investigated flow past a circular cylinder and have also developed empirical relation for separation angle as a function of Reynolds number. B Sharman et al. [6] have made numerical predictions of low Reynolds number flow over two tandem cylinders and have reported critical cylinder spacing where large jump in fluctuating forces and Stroutal number is observed. W A Khan et al. [7] have focused on analytical study of flow and heat transfer around a circular cylinder. D G Roychowdhury et al.[8] have shown that thermal boundary condition, fluid Prandtl number and geometry aspect ratio have a significant influence on flow pattern, thermal stratification and heat transfer rate for natural convection around a heated circular cylinder inside an enclosure. On the other hand Arnab Kumar De and Amaresh Dalal [9] have studied natural convection over a square heated cylinder for various geometry configuration characterized by different aspect ratio. The last decade has witnessed almost an exponential growth in nano fluid related to published literature, with stress on improvement of transport phenomena with use of different types of nano particles [10,11]. Nano fluids which are nano size particles having high thermal conductivity suspended in the base fluid and have been reported to be promising in improvement of thermal characteristic. In recent times Robert Taylor et al [12] have recently reviewed diverse application of nano fluids. Review of work related to heat transfer characteristic of nano fluid has been reported by Trisaksri and Wongwises [13]. Eiyad Abu Nada [14] has investigated application of nano fluid heat transfer enhancement of separated flow in backward facing step configuration. Outside the recirculation zone higher thermal conductivity nano particles have better enhancement of Nusselt number where as within the recirculation zone lower thermal conductivity particles are better. There is an increase in Nusselt number with increase in percentage of nano particle for whole range of Reynolds number. Rehana Nasirin [15] have carried out numerical investigation of water aluminum oxide nano fluid natural convection in a closed enclosure for various volume fraction, Prandtl number and aspect ratio. Md. Mahbubar Rahman et al. [16] have investigated two dimensional unsteady flow of nano fluid past a circular cylinder. A S Dalkilic [17] has reported critical information on theoretical, experimental and numerical work related to forced convection heat transfer of nano fluids. Summary of research on fluid flow and heat transfer characteristic of nano fluids in forced as well as free convection has been reported by Xiang Qi Wnag and Arun S Majumdar [18]. Sandip Sarkar et al. [19] have studied buoyancy driven mixed convection of nano fluid around a circular cylinder. They have shown that presence of nano fluid minimizes the effect of buoyancy force and stabilizes the flow regime. The present investigation had been motivated by increased interest and research in potential improvements in heat transfer characteristics using nano fluids, typically for flow characterized by low Reynolds number. Effort has been
350
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
made to study effect of nano particles on the transport phenomena around a circular cylinder maintained at constant temperature. The problem has been investigated numerically solving mass, momentum and energy equation under steady state. Heat transfer characteristic around the cylinder has been investigated for flow characterized by Reynolds number less than 40, using different volume fraction copper nano particles suspended in water. 2.
Problem description and mathematical model
The problem geometry under consideration is shown in Fig. 1. The base fluid is water and nano particles are in thermal equilibrium with the base fluid and there is no slip between them. Flow considered is two dimensional, steady, laminar and incompressible. Effect of buoyancy has not been taken into consideration as the stress is on investigating effect of nano particle concentration on heat transfer characteristic around the cylinder surface. The governing equation of mass, momentum and energy under steady state can be expressed in generalized dimensional form as:
w UM w VM wX wY
w § wM · w § wM · ¸ SM ¸ ¨J M ¨J M wX © wX ¹ wY © wY ¹
(1)
M is the unknown scalar, J M and SM are the diffusion and source term coefficient respectively. Values of
Where
these parameters are summarized in Table 1. The governing equations are subject to following boundary as mentioned in Table 2.Thermo physical properties of nano fluid used for simulation have been borrowed from work of A Kargar et al. [20]. Thermo-physical property of nanofluid had been calculated using Eqs. (2)-(6) and have been borrowed from classical model suggested by Y. Xuan et al [21]. Adiabatic Wall
Velocity Inlet, T=303.16K
Outlet, 32D
Adiabatic Wall Fig. 1. Problem geometry with boundary condition and mesh inside the solution domain
1 I ȡ f
ȡ nf
ȡ&
p nf
ȝ nf
I ȡp
1 I ȡ& p f
ȝ f 1 I
2.5
(2)
I ȡ& p f
(3) (4)
351
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
ª k p 2k f 2I k f k p º kf « » «¬ k p 2k f I k f k p »¼
k nf
k nf
Į nf
(5) (6)
ȡ&
p nf
Table 1 Summary of governing equations. Scalar
Equation
Diffusion coefficient
M
Mass conservation
1
X momentum
U (x velocity)
Y momentum
V (y velocity)
Energy
T (Temperature)
Source term
*M 0
SM
0
§ ȝ nf · ¨ ¸ ¨ȡ ¸ © nf ¹ § ȝ nf · ¨ ¸ ¨ȡ ¸ nf © ¹ Į nf
1 § wP · ¨ ¸ ȡ nf © wX ¹
1 § wP · ¨ ¸ ȡ nf © wY ¹
0
Table 2 Boundary conditions. Surface
Boundary Condition
Inlet
U=1, V=0, T=303.16K
Outlet
§ wU · ¨ ¸ © wX ¹
Top and horizontal walls Cylinder surface
bottom
U=0, V=0,
§ wT · wV 0, §¨ ·¸ 0, ¨ ¸ X w © wX ¹ ¹ © § wT · ¨ ¸ © wY ¹
0
U=0,V=0, T=373.16K
Table 3 Mesh independence test data for Re=40 Grid Size Angle of (cylinder x radial) separation 50 x 50 129.57 100 x 100 127.79 150 x 150 127.19 180 x 180 126.99
3.
0
Percentage change in angle of separation 1.37 0.47 0.15
Length Reattachment 1.49 1.78 1.81 1.83
of
Percentage change in length of reattachment 19.46 1.68 1.10
Numerical Methodology
Conservation equations of mass, momentum and energy subject to boundary condition specified in Table 2, have been by discritised using finite volume approach. Patankar’s SIMPLE algorithm has been employed for pressure velocity coupling issues. Momentum interpolation at the control volume face has been achieved using Rie Chow interpolation scheme. Convection term has been discritised using second order upwind scheme and diffusion term
352
Mitesh Vegad et al. / Procedia Technology 14 (2014) 348 – 356
has been handled using second order scheme. Structured grid with collocated arrangement of variable has been adopted for numerical simulation. The solution domain has been divided into smaller control volume ensuring that control volumes next to the cylinder surface and in the wake region are sufficiently small and gradually expand along radial direction away from the cylinder.The discritized algebraic finite volume equations have been solved iteratively and residuals have been reduced to value 10-10. The solution obtained solving the governing equation has been subsequently used to calculate derived parameter of interest. Local Nusselt number which is ratio of convection to conduction heat transfer over a given length (L), over the cylinder surface can be expressed as:
Nu
§ knf § wT · · ¨ ¨ ¸cy ln der ¸ Y k w © ¹ f ¨ surface ¸ ¨L T T ¸ wall basefluid ¸ ¨ ¨ ¸ © ¹
4.
(7)
Grid Testing and Code Validation
Extensive grid testing has been carried out to ensure that the solution is mesh independent. Gird of different size in region next to the cylinder and wake region has been used for simulating transport phenomena around the cylinder for flow characterized by Reynolds of 40, which is the largest value in the range of interest for current investigation. Flow separation angle and length of reattachment has been computed for different mesh size and are summarized in Table 3. Mesh having 180 control volumes along half the cylinder periphery and 180 control volumes along the radial direction away from the cylinder has been used for all simulations and is shown in Fig. 1. Expansion factor of 1.05 has been used along radial direction. The solution methodology has been validated by comparing angle of separation and length of reattachment for Re=40 which is the largest value in the range considered for simulation. Values obtained in current simulation are found to match closely with data published in literature [22]. 5.
Results and Discussion
Effect of variation of Reynolds number and nano particle concentration on temperature gradient normal to cylinder surface is shown in Fig. 2. For a fixed Reynolds number, higher concentration of nano particle leads to increased thermal conductivity of nanofluid, which in turn leads to reduction in normal direction temperature gradient at the cylinder wall. As the flow velocity increases, for a fixed nano particle fraction, there is an increase in temperature gradient normal to cylinder surface owing to decrease in thermal and momentum boundary layer thickness which can be seen in Fig. 3. Variation of temperature along the normal direction at three different planes L1, L2 and L3 at angles 45, 90 and 135 degree respectively is shown in Fig. 4. Point of stagnation on the inlet side of flow geometry has been taken to be reference with angle equal to zero degree. Temperature gradient normal to the cylinder surface drops towards the stagnation point in the wake behind the cylinder. There is sharp increase in normal direction temperature gradient at the cylinder wall with increase in flow velocity. Variation of heat transfer coefficient and Nusselt number along the top half of the cylinder for different values of Reynolds number and solid fraction is show in Fig. 5 and Fig. 6, respectively. It can be seen that heat transfer coefficient and Nusselt number increase with increase in solid fraction as well as increase in Reynolds number. However, the reason for increase in the two cases is entirely different. Increase in flow velocity characterized by higher Reynolds number results in increased temperature gradient normal to the cylinder wall (refer Fig. 2) which in turn results in higher value of Nusselt number, and heat transfer coefficient, for the same nano fluid fraction. On the
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other hand, temperature gradient on the cylinder surface reduces towards the trailing part of the cylinder owing to growth of thermal boundary layer. This leads to drop in heat transfer coefficient. Inclusion of nano particle in base fluid leads to increase in thermal conductivity of the fluid, where as temperature gradient normal to the cylinder surface decreases as shown. However reduction in gradient is lower compared to increase in thermal conductivity thus leading to overall increase in heat transfer coefficient and Nusselt number value.
Fig. 2. Temperature gradient normal to the cylinder surface
Fig. 3. Temperature and velocity variation normal to cylinder surface at angle equal to 90 degree. (a) Re=10, (b) 2% nano particle
Variation of local heat flux along the cylinder surface is shown in Fig. 7 and is found to be increasing with higher fraction of nano particle as well as increase in Reynolds number. This can be accounted to higher heat transfer coefficient owing to increased fraction of nano particle and higher flow velocity respectively. For a fixed Reynolds number and nano particle concentration, the temperature gradient reduces towards the trailing part of cylinder leading to lower heat flux (refer Fig. 4). Angle of flow separation for Reynolds number equal to 40 is around 140 degrees and not found to change with change in nano particle fraction as the effect of buoyancy has not been taken into account.
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6.
Conclusion
Flow of water based copper nano fluid around an isothermal cylinder has been investigated. It has been observed that: x There is increase in the heat transfer coefficient with increase in value of solid fraction. This can be attributed to improved thermal conductivity of nanofluid due to presence of nano particle. x Temperature gradient at the cylinder surface along normal direction drops with increase in nano particle concentration. However there is an increase in the thermal conductivity of nanofluid, thus leading to increase in Nusselt number. x Local heat flux drops along the cylinder surface towards the rear stagnation point. There is increase in heat flux with increase in nano particle fraction as well as flow velocity. x Presence of nano particle has no effect on point of flow separation for a fixed Reynolds number because the effect of buoyancy force has not been taken into consideration.
Fig. 4. Temperature variation normal to cylinder surface at three different planes. (a) Re=10, 2% nano fraction (b) Re=40, 2% nano fraction
Fig. 5. Heat transfer coefficient along the cylinder surface. (a) Re=10 (b) Re=40
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Fig. 6. Nusselt number along the cylinder surface. (a) Re=10 (b) Re=40
Fig. 7. Local heat flux along the cylinder surface. (a) Re=10 (b) Re=40
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