Nanofluid Condensation and MHD Flow Modeling over Rotating Plates Using Least Square Method (LSM)

Document Type : Research Article


1 International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, CHINA

2 Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, I.R. IRAN


In this study, nanofluid condensation and MHD flow analysis over an inclined and rotating plate are investigated respectively using Least Square Method (LSM) and numerical method. After presenting the governing equations and solving them by LSM, the accuracy of results is examined by the fourth order Runge-Kutta numerical method. For condensation, modeling results show that the condensate film thickness is reduced and in turn, the rate of heat transfer is enhanced by the addition of nanoparticles to the regular fluid. Effect of normalized thickness on velocity and temperature profiles reveals that increasing normalized thickness leads to an increase in f, f’ and a decrease in g, q. Effect of normalized thickness on k and s are similar to those of f’ and g, respectively.


Main Subjects

[1] Stefan M.J., Versuch Über Die Scheinbare Adhesion, Akad Wissensch Wien Math Natur, 69: 713–721 (1874).
[2] Mahmood M, Asghar S, Hossain MA, Squeezed Flow and Heat Transfer over a Porous Surface for Viscous Fluid, Heat Mass Transf, 44: 165–173 (2007).
[5] Mustafa M., Hayat T., Obaidat S., On Heat and Mass Transfer in the Unsteady Squeezing Flow between Parallel Plates, Meccanica, 47: 1581-1589 (2012).
       DOI 10.1007/s11012-012-9536-3.
[6] Turkyilmazoglu M., Analytical Solutions of Single and Multi-Phase Models for the Condensation of Nanofluid Film Flow and Heat Transfer, European Journal of Mechanics B/Fluids, 53: 272–277 (2015).
[7] Hatami M., Domairry G., Transient Vertically Motion of a Soluble Particle in a Newtonian Fluid Media, Powder Technology, 253: 481-485 (2014).
[9] Hatami M., Ganji D.D., Motion of a Spherical Particle in a Fluid Forced Vortex by DQM and DTM, Particuology, 16: 206-212 (2014).
[10] Dogonchi A.S., Hatami M., Domairry G., Motion Analysis of a Spherical Solid Particle in Plane Couette Newtonian Fluid Flow, Powder Technology, 274: 186-192 (2015).
[11] Haghshenas Fard M., Nasr Esfahany M., Talaie M.R., Numerical Study of Convective Heat Transfer of Nanofluids in a Circular Tube Two-Phase Model Versus Single-Phase Model, International Communications in Heat and Mass Transfer, 37: 91–97 (2010).
[12] GöktepeS., Atalık K., Ertürk H., Comparison of Single and Two-Phase Models for Nanofluid Convection at the Entrance of a Uniformly Heated Tube, International Journal of Thermal Sciences, 80: 83-92 (2014).
[13] Syed Tauseef Mohyud-Din, Zulfiqar Ali Zaidi,
Umar Khan, Naveed Ahmed, On Heat and Mass Transfer Analysis for the Flow of a Nanofluid between Rotating Parallel Plates, Aerosp. Sci. Technol. (2015),
[14] HayatT., Imtiaz M., Alsaedi A., KutbiM.A., MHD Three-Dimensional Flow of Nanofluid with Velocity Slip and Nonlinear Thermal Radiation, Journal of Magnetism and Magnetic Materials, 396: 31–37 (2015).
[15] Khan J.A., Mustafa M., Hayat T., Alsaedi A., Three-Dimensional Flow of Nanofluid over a Non-Linearly Stretching Sheet: An Application to Solar Energy, Int. J. Heat. Mass. Trans., 86: 158-164(2015).
[17] Fakour M., Vahabzadeh A., Ganji D.D., Hatami M., Analytical Study of Micropolar Fluid Flow and Heat Transfer in a Channel with Permeable Walls, Journal of Molecular Liquids, 204: 198-204 (2015).
[18] Ghasemi S.E., Hatami M., Kalani Sarokolaie A., Ganji D.D., Study on Blood Flow Containing Nanoparticles through Porous Arteries in Presence of Magnetic Field Using Analytical Methods, Physica E: Low-dimensional Systems and Nanostructures, 70: 146-156 (2015)
[19] Ghasemi S.E., Hatami M., Mehdizadeh Ahangar Gh.R., Ganji D.D., Electrohydrodynamic Flow Analysis 
in a Circular Cylindrical Conduit Using Least Square Method, Journal of Electrostatics, 72(1): 47-52 (2014).
[20] Rahimi-Gorji M., Pourmehran O., Hatami M.,
Ganji D.D., Statistical Optimization of Microchannel Heat Sink (MCHS) Geometry Cooled by Different Nanofluids Using RSM Analysis, The European Physical Journal Plus, 130: 22-      (2015).
[21] Domairry G., Hatami M., Squeezing Cu–Water Nanofluid Flow Analysis between Parallel Plates
by DTM-Padé Method
, Journal of Molecular Liquids, 193: 37-44 (2014).
[22] Ahmadi A.R., Zahmatkesh A., Hatami M., Ganji D.D., A Comprehensive Analysis of the Flow and Heat Transfer for a Nanofluid over an Unsteady Stretching Flat Plate, Powder Technology, 258: 125-133 (2014).
[23] Ozisik M.N., “Heat Conduction”, 2nd ed., John Wiley & Sons Inc. USA, (1993).
[24] Stern R. H., Rasmussen H., Left Ventricular Ejection: Model Solution by Collocation, an Approximate Analytical Method, Comput. Boil. Med., 26: 255-261 ((1996)).
[25] Vaferi B., Salimi V., Dehghan Baniani D., Jahanmiri A., Khedri S., Prediction of Transient Pressure
Response in the Petroleum Reservoirs Using Orthogonal Collocation
, J. of Petrol. Sci. and Eng. (2012).
[28] Hatami M., Mehdizadeh Ahangar GH.R., Ganji D.D., Boubaker K., Refrigeration Efficiency Analysis for Fully Wet Semi-Spherical Porous Fins, Energy Conversion and Management, 84: 533-540 (2014).
[29] Ghasemi S.E., Valipour P., Hatami M., Ganji D.D., Heat Transfer Study on Solid and Porous Convective Fins with Temperature-Dependent Heat Generation Using Efficient Analytical Method, Journal of Central South University, 21(12): 4592-4598 (2014).
[30] Shaoqin G., Huoyuan D., Negative Norm Least-Squares Methods for the Incompressible Magneto-Hydrodynamic Equations, Act. Math. Sci., 28B(3): 675–684 (2008).
[31] Ghasemi S.E., Hatami M., Ganji D.D., Thermal Analysis of Convective Fin with Temperature-Dependent Thermal Conductivity and Heat Generation, Case Studies in Thermal Engineering, 4: 1-8 (2014).
[32] Aziz A., “Heat Conduction with Maple”, Philadelphia (PA), R.T. Edwards, (2006).
[33] Hatami M., Cuijpers M.C.M., Boot M.D., Experimental Optimization of the Vanes Geometry for a Variable Geometry Turbocharger (VGT) Using a Design of Experiment (DoE) Approach, Energy Conversion and Management, 106: 1057-1070 (2015).
[34] Hayat T., Abbas Z., Javed T., Sajid M., Three-Dimensional Rotating Flow Induced by a Shrinking Sheet for Suction, Chaos, Solitons and Fractals, 39: 1615–1626 (2009).