Numerical study of a confined slot impinging jet with nanofluids
© Manca et al; licensee Springer. 2011
Received: 14 December 2010
Accepted: 1 March 2011
Published: 1 March 2011
Heat transfer enhancement technology concerns with the aim of developing more efficient systems to satisfy the increasing demands of many applications in the fields of automotive, aerospace, electronic and process industry. A solution for obtaining efficient cooling systems is represented by the use of confined or unconfined impinging jets. Moreover, the possibility of increasing the thermal performances of the working fluids can be taken into account, and the introduction of nanoparticles in a base fluid can be considered.
In this article, a numerical investigation on confined impinging slot jet working with a mixture of water and Al2O3 nanoparticles is described. The flow is turbulent and a constant temperature is applied on the impinging. A single-phase model approach has been adopted. Different geometric ratios, particle volume concentrations and Reynolds number have been considered to study the behavior of the system in terms of average and local Nusselt number, convective heat transfer coefficient and required pumping power profiles, temperature fields and stream function contours.
The dimensionless stream function contours show that the intensity and size of the vortex structures depend on the confining effects, given by H/ W ratio, Reynolds number and particle concentrations. Furthermore, for increasing concentrations, nanofluids realize increasing fluid bulk temperature, as a result of the elevated thermal conductivity of mixtures. The local Nusselt number profiles show the highest values at the stagnation point, and the lowest at the end of the heated plate. The average Nusselt number increases for increasing particle concentrations and Reynolds numbers; moreover, the highest values are observed for H/W = 10, and a maximum increase of 18% is detected at a concentration equal to 6%. The required pumping power as well as Reynolds number increases and particle concentrations grow, which is almost 4.8 times greater than the values calculated in the case of base fluid.
List of symbols
Heat transfer enhancement is very important in the industry, and several techniques are employed to realize this aim. Impinging jets, whether confined or unconfined, have been widely used for efficient cooling in industrial applications as a means of providing highly localized heat transfer coefficients, representing a possible solution. Depending on the application, flow conditions can range from laminar to highly turbulent ones. Applications of impinging jets include drying of textiles, film and paper, cooling of gas turbine components and the outer walls of combustors, freezing of tissue in cryosurgery and manufacturing, material processing and electronic cooling. There are numerous articles dealing with this problem both numerically and experimentally as reported in the literature reviews on the subject [1–6].
Several studies have been developed on impinging air jets [1, 2]. Recently, a greater attention has been dedicated to the impinging liquid jet since orders of magnitude of the heat transfer rates are several times those of gas jets. Liquid jets have possible application to the cooling of heat engines [5, 7], thermal control in electronic devices [8–10] and in the thermal treatment of metals and material processing [11–14].
In the application of jet impingements, circular or slot jets are the main jet configurations. For these two configurations, flow and heat transfer mechanics are significantly different. It seems that greater research activity on heat and mass transfer with circular impinging jets has been predominantly published [1–3, 15, 16]. However, investigations on heat and mass transfer with slot jet impingement have attracted more attention recently. In fact, slot jet impingements offer many more beneficial features, such as higher cooling effectiveness, greater uniformity and more controllability, as underlined in . For example, these factors allow for fulfillment of the increasing heat flux and decreasing dimensions in electronics packages [17–24]. The common types of impinging jets are with or without confinement. Confined impinging jets have the advantages of smaller space design, while unconfined impinging jets have an advantage of simple design and easy fabrication. The two types of impinging jets have their own merits, and they are both commonly used as the cooling solutions, and the literature reviews on the subject have been provided in [2, 3, 6]. The effects of confinement on impinging jet heat transfer have been considered in [25–27]. Moreover, several studies show the importance of the subject and different cases have been investigated, such as confined slot-jet impingement on a moving plate , impinging jet on obliquely a flat surface , impinging jet on a porous medium  and slot jet impingement cooling on a semi-circular concave .
In order to obtain a heat transfer enhancement in jet impingement, different techniques have been employed, such as the insert of foams or fins . These techniques determine a modification of the cooling system whereas the use of nanofluids in a coolant seems to be simpler in realizing a heat transfer enhancement . However, nanofluids are to this day controversial in many areas such as inconsistencies in published data and disagreements on the heat transfer mechanisms, as observed by Gherasim et al. . Various aspects of nanofluids have been covered in several reviews and some of these are given in [35–47].
The employment of nanofluids in impinging jets has been investigated recently by some researchers and, to the best of our knowledge, their investigations have been reported in [34, 48–60]. The numerical investigation on hydrodynamic and thermal fields of Al2O3/water nanofluid in a radial laminar flow cooling system carried out by Roy et al.  can be can be considered as the first article on an impinging jet. Those authors found that considerable heat transfer enhancement was observed up to 200% in the case of a nanofluid with 10% in nanoparticle volume concentration at a Reynolds number equal to 1200. However, a significant increase in wall shear stress was noticed increasing the nanoparticle volume concentration. The laminar-forced convection flow of nanofluids between two coaxial and parallel disks with central axial injection was investigated numerically considering temperature-dependent properties by Palm et al. . Results indicated a heat transfer benefit by adopting Al2O3/water nanofluid with a volume fraction of nanoparticles of 4%. An increase of 25% was evaluated in terms of average wall heat transfer coefficient, when referred to the water. Moreover, the use of temperature-dependent properties determined for greater heat transfer predictions with corresponding decreases in wall shear stresses when compared to evaluations employing constant properties. A numerical study on steady, laminar radial flow of a nanofluid in a simplified axi-symmetric configuration with axial coolant injection was performed by Roy et al.  for electronic cooling applications. Also in this investigation increases in heat removal capabilities were detected with the use of nanofluids.
An experimental investigation in a confined and submerged impinging jet on a flat, horizontal and circular heated surface with nanofluid (Al2O3 dispersed in water) was carried out by Nguyen et al. . Experimental results were obtained for both laminar and turbulent flow regimes and they showed that, depending on the combination of nozzle-to-heated surface distance and particle volume fraction, the use of a nanofluid can determine a heat transfer enhancement in some cases, but an adverse effect on the convective heat transfer coefficient may occur in other cases. A circular confined and submerged jet impinging on a horizontal hot plate was numerically simulated by Vaziei and Abouali . Water and 36-nm Al2O3-water nanofluid with various particle volume fractions were considered as a working fluid for cooling the hot plate. Both laminar and turbulent impinging jets in various nozzle-to-plate distances and Reynolds numbers were simulated. The results showed that the use of Al2O3 nanoparticles in laminar jets enhanced the heat transfer but for the turbulent jets Al2O3-water nanofluid had a lower performance for heat removal compared with the base fluid. The heat transfer enhancement capabilities of Al2O3/water inside a confined impinging jet cooling device was numerically studied by Gherasim et al. . Results highlighted those limitations in the use of this nanofluid type in a radial flow configuration, due to the significant increase in the associated pumping power. Steady laminar incompressible thermal alumina-water flow between parallel disks was simulated by Feng and Kleinstreuer . The results indicated that the Nusselt number increases with higher nanoparticle volume fraction, smaller nanoparticle diameter, reduced disk-spacing and larger inlet Reynolds number. The laminar forced convective heat transfer features of Al2O3/water nanofluid in the confined radial flow were numerically investigated by Yang and Lai [59, 60] with constant  and temperature-dependent properties . Results showed the same trend given in the previous published works: the Nusselt number increases with the increases in Reynolds number and nanoparticle volume fraction, though the increase in pressure drop is more significant with the increase of particle concentration. Furthermore, temperature-dependent thermo-physical properties of nanofluids were found to have a marked bearing on the simulation results.
It seems that a slot-confined and submerged impinging jet on a flat surface with nanofluids has not been investigated in both laminar and turbulent flow regimes in spite of its importance in engineering applications such as electronic cooling and material processing.
In this article, a numerical investigation on turbulent flow on a slot-confined and submerged impinging jet on an isothermal flat surface is carried out. The results are given to evaluate the fluid dynamic and thermal features of the considered geometry with Al2O3/water as the working nanofluid adopting the single phase model.
Physical properties of nanofluids
Material properties at a temperature of 293 K
c p (J/kg K)
998 × 10-6
Properties of nanofluids, single-phase model.
c p (J/kg K)
998 × 10-6
1083 × 10-6
1486 × 10-6
1877 × 10-6
However, it is well known that the evaluation of these properties by various research groups differs from each other because of the numerical and experimental approaches and processes adopted [64, 65].
Mathematical description and governing equations
where C μ is a constant. The model constant values are the following:
C1ε= 1.44, C2ε= 1.92, C μ = 0.09, σk = 1.0 and σ ε = 1.3.
Inlet jet section: uniform velocity and temperature profile;
Outlet section: pressure outlet;
Bottom wall: velocity components equal to zero and constant temperature;
Upper wall: velocity components equal to zero and adiabatic condition.
where u j is the jet velocity, W is the jet width, is the impingement surface heat flux, TH and TJ represent the temperature of the impingement surface and the jet temperature, respectively.
Inlet velocities (m/s).
The core region, for Re y > 200, is solved by means of the standard k-ε model, while in the other region the Wolfstein model is applied .
Along the solid walls, no slip condition is employed, whereas a velocity inlet is given for the jet orifice and pressure conditions are set for the outlet sections.
Four different grid distributions are tested on the model with H/W ratio equal to 6 at Re = 5000, with water (ϕ = 0%) as working fluid, to ensure that the calculated results are grid independent. The four grids have 4950 (90 × 55), 19800 (180 × 110), 79200 (360 × 220), and 316800 (720 × 440) nodes, respectively. The grid mesh is structured in each case with grid adoption for y+ = 1 at adjacent wall region and a sketch is shown in Figure 1b. For the adiabatic wall and the bottom surface, nodes are distributed by means of an exponential relation (n = 0.9), to have a fine mesh near the impingement region, where an equi-spatial distribution is chosen. On the vertical ones, a bi-exponential (n = 0.8) distribution is considered.
Results and discussion
A computational thermo-fluid dynamic analysis of a two-dimensional model, regarding a confined impinging jet on a heated wall with nanofluids, is considered to evaluate the thermal and fluid-dynamic performances and study the velocity and temperature fields. Different inlet velocities are considered to ensure a turbulent regime, and the working fluids are water and mixtures of water and γ-Al2O3 at different volume fractions, treated by a single-phase model approach. The range of Reynolds numbers, geometric ratio and volume fractions are given below:
Reynolds number, Re: 5000, 10000, 15000 and 20000;
H/W ratio: 4, 6, 8, 10, 15 and 20;
particle concentrations, ϕ: 0, 1, 4 and 6%.
Results are presented in terms of average and local Nusselt number profiles, as a function of Reynolds number, H/W ratio and particle concentrations; moreover, dimensionless temperature fields and stream function contours are provided.
The temperature fields, depicted in Figure 5, follow the stream line patterns. For increasing concentrations, nanoparticles produce an increase of fluid bulk temperature, because of the elevated thermal conductivity of mixtures. Near the impingement surface, temperature grows and tends to decrease for increasing x/W values. For larger Reynolds numbers, the efficiency of heat transfer increases.
List of symbols
Heat transfer coefficient
Turbulent kinetic energy
Required pumping power
Pr = ν/a Prandtl number
Impingement surface heat flux W/m 2
Volume flow rate
Kronecher delta function
Rate of dissipated turbulent
Turbulent Prandtl number
Wall shear stress
This study was supported by SUN Grant Initiative of 2008 grant and by MIUR with Articolo D.M. 593/2000 Grandi Laboratori "EliosLab".
- Martin H: Heat and mass transfer between impinging gas jets and solid surface. Adv Heat Transfer 1977, 13: 1–60. full_textView Article
- Downs SJ, James EH: Jet impingement heat transfer-a literature survey. Tech. Rep. 1987-HT-35, ASME
- Jambunathan K, Lai E, Moss M, Button B: A review of heat transfer data for single circular jet impingement. Int J Heat Fluid Flow 1992, 13: 106–115. 10.1016/0142-727X(92)90017-4View Article
- Viskanta R: Heat transfer to impinging isothermal gas and flame jets. Exp Thermal Fluid Sci 1993, 6: 111–134. 10.1016/0894-1777(93)90022-BView Article
- Webb B, Ma CF: Single-phase liquid jet impingement heat transfer. Adv Heat Transfer 1995, 26: 105–117. full_textView Article
- Tesar V, Travnicek Z: Increasing heat and/or mass transfer rates in impinging jets. J Vis 2005, 8: 91–98. 10.1007/BF03181651View Article
- Ma CF, Bergles AE: Convective heat transfer on a small vertical heated surface in an impingement circular liquid jet. In Heat Transfer Science and Technology. Edited by: Wang BX. New York: Hemisphere; 1990:193–200.
- Ma CF: Fundamental research on extremely small size liquid jet impingement heat transfer. Proceedings of the 3rd International Thermal Energy Congress: 28 June-1 August 1997; Kitakyushu, Japan 1997, 195–202.
- Jiji LM, Dagan Z: Experiment investigation of single phase multi-jet impingement cooling of an array of microelectronic heat sources. In Cooling Technology for Electronic Equipment. Edited by: Aung W. New York: Hemisphere; 1988:332–352.
- Punch J, Walsh E, Grimes R, Jeffers N, Kearney D: Jets and rotary flows for single-phase liquid cooling: an overview of some recent experimental findings. Proceedings of the 11th International Conference on Thermal, Mechanical and Multi-Physics Simulation, and Experiments in Microelectronics and Microsystems, EuroSimE 2010: 26–28 April 2010; Bordeaux 2010, 5464505.
- Kohing FC: Waterwall: water cooling system. Iron-Steel Eng 1985, 62: 30–36.
- Ma CF, Yu J, Lei DH, Gan YP, Tsou FK, Auracher H: Transient jet impingement boiling heat transfer on hot surfaces. In Multiphase Flow and Heat Transfer-Second International Symposium. Edited by: Chen XJ et al. New York: Hemisphere; 1990:349–357.
- Viskanta R: Heat transfer in material processing. In Handbook of Heat Transfer. 3rd edition. Edited by: Rohsenow WM, Hartnett JP, Cho YI. New York: McGraw-Hill; 1998.
- Schuettenberg S, Krause F, Hunkel M, Zoch HW, Fritsching U: Quenching with fluid jets. Mater Werkst 2010, 40: 408–413. 10.1002/mawe.200900468View Article
- Liu Z, Lienhard VJH, Lombara JS: Convective heat transfer by impingement of circular liquid jets. J Heat Transfer 1991, 113: 571–582. 10.1115/1.2910604View Article
- Ma CF, Zhao YH, Masuoka T, Gomi T: Analytical study on impingement heat transfer with single-phase free-surface circular liquid jets. J Thermal Sci 1996, 5: 271–277. 10.1007/BF02653234View Article
- Chen YC, Ma CF, Qin M, Li YX: Theoretical study on impingement heat transfer with single-phase free-surface slot jets. Int J Heat Mass Transfer 2005, 48: 3381–3386. 10.1016/j.ijheatmasstransfer.2005.02.027View Article
- Zhuang Y, Ma CF, Qin M: Experimental study on local heat transfer with liquid impingement flow in two-dimensional micro-channels. Int J Heat Mass Transfer 1997, 40: 4055–4059. 10.1016/S0017-9310(97)00039-2View Article
- Lin ZH, Chou YJ, Hung YH: Heat transfer behaviors of a confined slot jet impingement. Int J Heat Mass Transfer 1997, 40: 1095–1107. 10.1016/0017-9310(96)00135-4View Article
- Chiriac VA, Ortega A: A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface. Int J Heat Mass Transfer 2002, 45: 1237–1248. 10.1016/S0017-9310(01)00224-1View Article
- Park TH, Choi HG, Yoo JY, Kim SJ: Streamline upwind numerical simulation of two-dimensional confined impinging slot jets. Int J Heat Mass Transfer 2003, 46: 251–262. 10.1016/S0017-9310(02)00270-3View Article
- Sahoo D, Sharif MAR: Numerical modeling of slot-jet impingement cooling of a constant heat flux surface confined by a parallel wall. Int J Thermal Sci 2004, 43: 877–887. 10.1016/j.ijthermalsci.2004.01.004View Article
- Lee HG, Yoon HS, Ha MY: A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights. Int J Heat Mass Transfer 2008, 51: 4055–4059. 10.1016/j.ijheatmasstransfer.2008.01.015View Article
- Sivasamy A, Selladurai V, Kanna PR: Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: mixed convection regime. Int J Heat Mass Transfer 2010, 53: 5847–5855. 10.1016/j.ijheatmasstransfer.2010.07.063View Article
- Lytle D, Webb B: Air jet impingement heat transfer at low nozzle-plate spacings. Int J Heat Mass Transfer 1994, 37: 1687–1697. 10.1016/0017-9310(94)90059-0View Article
- Behnia M, Parneix S, Shabany Y, Durbin PA: Numerical study of turbulent heat transfer in confined and unconfined impinging jets. Int J Heat Mass Transfer 1999, 20: 1–9.
- Choo KS, Kim SJ: Comparison of thermal characteristics of confined and unconfined impinging jets. Int J Heat Mass Transfer 2010, 53: 3366–3371. 10.1016/j.ijheatmasstransfer.2010.02.023View Article
- Sharif MAR, Banerjee A: Numerical analysis of heat transfer due to confined slot-jet impingement on a moving plate. Appl Thermal Eng 2009, 29: 532–540. 10.1016/j.applthermaleng.2008.03.011View Article
- Ibuki K, Umeda T, Fujimoto H, Takuda H: Heat transfer characteristics of a planar water jet impinging normally or obliquely on a flat surface at relatively low Reynolds numbers. Exp Thermal Fluid Sci 2009, 33: 1226–1234. 10.1016/j.expthermflusci.2009.08.003View Article
- Dórea FT, de Lemos MJS: Simulation of laminar impinging jet on a porous medium with a thermal non-equilibrium model. Int J Heat Mass Transfer 2010, 53: 5089–5101.View Article
- Yang YT, Wei TC, Wang YH: Numerical study of turbulent slot jet impingement cooling on a semi-circular concave. Int J Heat Mass Transfer 2011, 54: 482–489. 10.1016/j.ijheatmasstransfer.2010.09.021View Article
- Naphon P, Wongwises S: Investigation on the jet liquid impingement heat transfer for the central processing unit of personal computers. Int Commun Heat Mass Transfer 2010, 37: 822–826. 10.1016/j.icheatmasstransfer.2010.05.004View Article
- Choi SUS: Enhancing thermal conductivity of fluids with nanoparticles, developments and applications of non-Newtonian flows. ASME FED 1995, 231: 99–105.
- Gherasim I, Roy G, Nguyen CT, Vo-Ngoc D: Heat transfer enhancement and pumping power in confined radial flows using nanoparticle suspensions (nanofluids). Int J Thermal Sci 2011, 50: 369–377. 10.1016/j.ijthermalsci.2010.04.008View Article
- Das SK, Choi SUS, Patel HE: Heat transfer in nanofluids-a review. Heat Transfer Eng 2006, 27: 3–19. 10.1080/01457630600904593View Article
- Buongiorno J: Convective transport in nanofluids. J Heat Transfer 2006, 128: 240–250. 10.1115/1.2150834View Article
- Daungthongsuk W, Wongwises S: A critical review of convective heat transfer of nanofluids. Renew Sustain Energy Rev 2007, 11: 797–817. 10.1016/j.rser.2005.06.005View Article
- Trisaksri V, Wongwises S: Critical review of heat transfer characteristics of nanofluids. Renew Sustain Energy Rev 2007, 11: 512–523. 10.1016/j.rser.2005.01.010View Article
- Yu W, France DM, Routbort JL, Choi SUS: Review and comparison of nanofluid thermal conductivity and heat Transfer enhancements. Heat Transfer Eng 2008, 29: 432–460. 10.1080/01457630701850851View Article
- Keblinski P, Prasher R, Eapen J: Thermal conductance of nanofluids: is the controversy over? J Nanoparticle Res 2008, 10: 1089–1097. 10.1007/s11051-007-9352-1View Article
- Kakaç S, Pramuanjaroenkij A: Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transfer 2009, 52: 3187–3196.View Article
- Choi SUS: Nanofluids: from vision to reality through research. J Heat Transfer 2009, 131: 1–9. 10.1115/1.3056479View Article
- Buongiorno J, et al.: A benchmark study on the thermal conductivity of nanofluids. J Appl Phys 2009, 106: 1–9. 10.1063/1.3245330View Article
- Özerinç S, Kakaç S, Yazıcıoğlu AG: Enhanced thermal conductivity of nanofluids: a state-of-the-art review. Microfluid Nanofluid 2010, 8: 145–170.View Article
- Wang L, Fan J: Nanofluids research: key issues. Nanoscale Res Lett 2010, 5: 1241–1252. 10.1007/s11671-010-9638-6View Article
- Godson L, Raja B, Lal DM, Wongwises S: Enhancement of heat transfer using nanofluids-an overview. Renew Sustain Energy Rev 2010, 14: 629–641. 10.1016/j.rser.2009.10.004View Article
- Venerus D, et al.: Viscosity measurements on colloidal dispersions (nanofluids) for heat transfer applications. Appl Rheol 2010, 20: 445–462.
- Roy G, Nguyen CT, Lajoie P: Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids. Superlattices Microstruct 2004, 35: 497–511. 10.1016/j.spmi.2003.09.011View Article
- Maiga S, Palm SJ, Nguyen CT, Roy G, Galanis N: Heat transfer enhancement by using nanofluids in forced convection flows. Int J Heat Fluid Flow 2005, 26: 530–546. 10.1016/j.ijheatfluidflow.2005.02.004View Article
- Roy G, Palm SJ, Nguyen CT: Heat transfer and fluid flow of nanofluids in laminar radial flow cooling systems. J Thermal Sci 2005, 14: 362–367. 10.1007/s11630-005-0059-2View Article
- Palm SJ, Roy G, Nguyen CT: Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties. Appl Thermal Eng 2006, 26: 2209–2218. 10.1016/j.applthermaleng.2006.03.014View Article
- Roy G, Nguyen CT, Comeau M: Numerical investigation of electronic component cooling enhancement using nanofluids in a radial flow cooling system. J Enhanc Heat Transfer 2006, 13: 101–115. 10.1615/JEnhHeatTransf.v13.i2.20View Article
- Schoeppler M: Correspondence address diverging ink-jet technologies and applications. Proceedings of the International Conference on Digital Printing Technologies: 16–17 September 2006; Denver 2006, 1–2.
- Liu ZH, Qiu YH: Boiling heat transfer characteristics of nanofluids jet impingement on a plate surface. Heat Mass Transfer 2007, 43: 699–706. 10.1007/s00231-006-0159-xView Article
- Liu ZH, Qiu YH: The boiling heat transfer of water based nanofluid jet impingement on a plate surface. J Shanghai Jiaotong Univ 2007, 41: 1658–1661.
- Nguyen CT, Galanis N, Polidori G, Fohanno S, Popa CV, Le Bechec A: An experimental study of a confined and submerged impinging jet heat transfer using Al2O3-water nanofluid. Int J Thermal Sci 2009, 48: 401–411. 10.1016/j.ijthermalsci.2008.10.007View Article
- Vaziei P, Abouali O: Numerical study of fluid flow and heat transfer for Al2O3-water nanofluid impinging jet. Proceedings of the 7th International Conference on Nanochannels, Microchannels and Minichannels 2009: 22–24 June 2009; Pohang 2009, 977–984.View Article
- Feng Y, Kleinstreuer C: Nanofluid convective heat transfer in a parallel-disk system. Int J Heat Mass Transfer 2010, 53: 4619–4628. 10.1016/j.ijheatmasstransfer.2010.06.031View Article
- Yang YT, Lai FH: Numerical study of heat transfer enhancement with the use of nanofluids in radial flow cooling system. Int J Heat Mass Transfer 2010, 53: 5895–5904. 10.1016/j.ijheatmasstransfer.2010.07.045View Article
- Yang YT, Lai FH: Numerical investigation of cooling performance with the use of Al2O3/water nanofluids in a radial flow system. Int J Thermal Sci 2011, 50: 61–72. 10.1016/j.ijthermalsci.2010.08.017View Article
- Rohsenow WM, Hartnett JP, Cho YI: Handbook of Heat Transfer. 3rd edition. New York: McGraw-Hill; 1998.
- Pak BC, Cho YI: Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transfer 1998, 11: 151–170. 10.1080/08916159808946559View Article
- Maiga SEB, Nguyen CT, Galanis N, Roy G: Heat transfer behaviours of nanofluids in a uniformly heated tube. Superlattices Microstruct 2004, 35: 543–557. 10.1016/j.spmi.2003.09.012View Article
- Maiga SEB, Cong Tam N, Galanis N, Roy G, Mare T, Coqueux M: Heat transfer enhancement in turbulent tube flow using Al2O3nanoparticle suspension. Int J Numer Methods Heat Fluid Flow 2006, 16: 275–292. 10.1108/09615530610649717View Article
- Palm SJ, Roy G, Nguyen CT: Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature dependent properties. Appl Thermal Eng 2006, 26: 2209–2218. 10.1016/j.applthermaleng.2006.03.014View Article
- Launder BE, Spalding DB: The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 1974, 3: 269–289. 10.1016/0045-7825(74)90029-2View Article
- FLUENT Computational Fluid Dynamic Code Version 6.3 User Guide, Fluent, Inc[http://www.fluent.com]
- Wolfstein M: The velocity and temperature distribution of one-dimensional flow with turbulence augmentation and pressure gradient. Int J Heat Mass Transfer 1969, 12: 301–318. 10.1016/0017-9310(69)90012-XView Article
- Cadek FFA: Fundamental investigation of jet Impingement heat transfer. In Ph.D Thesis. University of Cincinnati; 1968.
- Gordon R, Akfirat JC: Heat transfer characteristics of impinging two-dimensional air jets. J Heat Transfer 1966, 88: 101–108.View Article
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.