Heat transfer and nanofluids flow through the circular concentric heat pipes: a comparative study using least square method (LSM)

Volume 17, Issue 2, pp 235-245

Publication Date: 2017-06-15



M. Hatami - International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xian Jiaotong University, Xian 710049, China.
S. Mosayebidorcheh - Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran.
J. Geng - International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xian Jiaotong University, Xian 710049, China.
D. Jing - International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xian Jiaotong University, Xian 710049, China.


In this paper, hydro-thermally performance of a circular concentric heat pipe is evaluated using the analytical least square method (LSM) and the accuracy of results is examined by fourth order Runge-kutta numerical method. In described problem, the pipe walls are permitted to carry different and opposite slip velocities of nanouids and they are either preserved at constant heat flux of outer wall with the inner wall insulated or vice versa. For this study, five distinct types of nanoparticles: \(Ag, Cu, Cuo, Al_2O_3\) and \(TiO_2\) are considered in the water base fluid and the results of velocity profiles and Nusselt numbers in different slip conditions were presented and discussed. As a main result, by decreasing the distance between the pipes, more heat will transfer to nanofluids from the wall under the heat flux, so it makes larger Nusselt number.


Heat pipe, nanofluid, Nusselt number, LSM.


[1] A. R. Ahmadi, A. Zahmatkesh, M. Hatami, D. D. Ganji, A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate, Powder Technol., 258 (2014), 125–133.
[2] N. S. Akbar, M. Raza, R. Ellahi, Copper oxide nanoparticles analysis with water as base fluid for peristaltic flow in permeable tube with heat transfer, Compu. Methods Programs Biomed., 130 (2016), 22–30.
[3] M. Akbarzadeh, S. Rashidi, M. Bovand, R. Ellahi, A sensitivity analysis on thermal and pumping power for the flow of nanofluid inside a wavy channel, J. Mol. Liq., 220 (2016), 1–13.
[4] M. M. Bhatti, T. Abbas, M. M. Rashidi, Effects of thermal radiation and electromagnetohydrodynamic on viscous nanofluid through a riga plate, Multidiscip. Model. Mater. Struct., 12 (2016), 605–618.
[5] M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. S. Ali, Numerical simulation of entropy generation with thermal radiation on MHD Carreau nanofluid towards a shrinking sheet, Entropy, 18 (2016), 14 pages.
[6] M. M. Bhatti, M. M. Rashidi, Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet, J. Mol. Liq., 221 (2016), 567–573.
[7] M. Bovand, S. Rashidi, G. Ahmadi, J. A. Esfahani, Effects of trap and reflect particle boundary conditions on particle transport and convective heat transfer for duct flow-A two-way coupling of Eulerian-Lagrangian model, Appl. Therm. Eng., 108 (2016), 368–377.
[8] A. S. Dogonchi, M. Hatami, G. Domairry, Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow, Powder Technol., 274 (2015), 186–192.
[9] G. Domairry, A. Aziz, Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method, Math. Probl. Eng., 2009 (2009), 19 pages.
[10] G. Domairry, M. Hatami, Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM-Pad´e Method, J. Mol. Liq., 193 (2014), 37–44.
[11] R. Ellahi, M. Hassan, A. Zeeshan, Shape effects of nanosize particles in Cu–H2O nanofluid on entropy generation, Int. J. Heat Mass Transf., 81 (2015), 449–456.
[12] R. Ellahi, M. Hassan, A. Zeeshan, Aggregation effects on water base nano fluid over permeable wedge in mixed convection, Asia Pac. J. Chem. Eng., 11 (2016), 179–186.
[13] M. Fakour, A. Vahabzadeh, D. D. Ganji, M. Hatami, Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls, J. Mol. Liq., 204 (2015), 198–204.
[14] S.-Q. Gao, H.-Y. Duan, Negative norm least-squares methods for the incompressible magnetohydrodynamic equations, Acta Math. Sci. Ser. B Engl. Ed., 28 (2008), 675–684.
[15] S. E. Ghasemi, M. Hatami, G. R. M. Ahangar, D. D. Ganji, Electrohydrodynamic flow analysis in a circular cylindrical conduit using least square method, J. Electrostat., 72 (2014), 47–52.
[16] S. E. Ghasemi, M. Hatami, D. D. Ganji, Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation, Case Stud. Therm. Eng., 4 (2014), 1–8.
[17] S. E. Ghasemi, M. Hatami, A. K. Sarokolaie, D. D. Ganji, Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods, Phys. E Low Dimens. Syst. Nanostruct., 70 (2015), 146–156.
[18] S. E. Ghasemi, P. Valipour, M. Hatami, D. D. Ganji, Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method, J. Cent. South Univ., 21 (2014), 4592–4598.
[19] S. G¨oktepe, K. Atalık, H. Ert ¨ urk, Comparison of single and two-phase models for nanofluid convection at the entrance of a uniformly heated tube, Int. J. Thermal Sci., 80 (2014), 83–92.
[20] M. Haghshenas Fard, M. Nasr Esfahany, M. R. Talaie, Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model, Int. Commun. Heat Mass Transf., 37 (2010), 91–97.
[21] M. Hatami, G. R. M. Ahangar, D. D. Ganji, K. Boubaker, Refrigeration efficiency analysis for fully wet semi-spherical porous fins, Energy Convers. Manage., 84 (2014), 533–540.
[22] M. Hatami, G. Domairry, Transient vertically motion of a soluble particle in a Newtonian fluid media, Powder Technol., 253 (2014), 481-485.
[23] M. Hatami, D. D. Ganji, Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis, Int. J. Refrig., 40 (2014), 140–151.
[24] M. Hatami, D. D. Ganji, Motion of a spherical particle in a fluid forced vortex by DQM and DTM, Particuology, 16 (2014), 206–212.
[25] M. Hatami, D. D. Ganji, Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy multistep differential transformation method, Powder Technol., 258 (2014), 94–98.
[26] M. Hatami, D. D. Ganji, Natural convection of sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates by analytical and numerical methods, Case Stud. Therm. Eng., 2 (2014), 14–22.
[27] M. Hatami, D. D. Ganji, Thermal behavior of longitudinal convectiveradiative porous fins with different section shapes and ceramic materials (\(SiC\) and \(Si_3N_4\)), Ceram. Int., 40 (2014), 6765–6775.
[28] M. Hatami, H. Safari, Effect of inside heated cylinder on the natural convection heat transfer of nanofluids in a wavy-wall enclosure, Int. J. Heat Mass Transf., 103 (2016), 1053–1057.
[29] T. Hayat, M. Imtiaz, A. Alsaedi, M. A. Kutbi, MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation, J. Magn. Magn. Mater., 396 (2015), 31–37.
[30] J. A. Khan, M. Mustafa, T. Hayat, A. Alsaedi, Three-dimensional flow of nanofluid over a non-linearly stretching sheet: an application to solar energy, Int. J. Heat. Mass. Transf., 86 (2015), 158–164.
[31] P. Krajnik, F. Pusavec, A. Rashid, Nanofluids: Properties, applications and sustainability aspects in materials processing technologies, Advances in Sustainable Manufacturing, Springer, Berlin, (2011), 107–113.
[32] R. P. Laein, S. Rashidi, J. A. Esfahani, Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV, Adv. Powder Technol., 27 (2016), 312–322.
[33] S. T. Mohyud-Din, Z. A. Zaidi, U. Khan, N. Ahmed, On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates, Aerosp. Sci. Technol., 46 (2015), 514–522.
[34] M. N. O¨ zis¸ik, Heat conduction, second edition, John Wiley & Sons Inc., New York, (1993).
[35] P. Rana, R. Bhargava, Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 212–226.
[36] M. M. Rashidi, N. Freidoonimehr, A. Hosseini, O. A. B´eg, T.-K. Hung, Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration, Meccanica, 49 (2014), 469–482.
[37] R. H. Stern, H. Rasmussen, Left ventricular ejection: model solution by collocation, an approximate analytical method, Comput. Biol. Med., 26 (1996), 255–261.
[38] M. Turkyilmazoglu, Analytical solutions of single and multi-phase models for the condensation of nanofluid film flow and heat transfer, Eur. J. Mech. B/Fluid., 53 (2015), 272–277.
[39] M. Turkyilmazoglu, Anomalous heat transfer enhancement by slip due to nanofluids in circular concentric pipes, Int. J. Heat Mass Transf., 85 (2015), 609–614.
[40] B. Vaferi, V. Salimi, D. D. Baniani, A. Jahanmiri, S. Khedri, Prediction of transient pressure response in the petroleum reservoirs using orthogonal collocation, J. Petrol. Sci. Eng., 98 (2012), 156–163.


XML export