Rotating Cylinder Turbulator Effect on the Heat Transfer of a ‎Nanofluid Flow in a Wavy Divergent Channel‎

Document Type : Research Paper


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 Department of Mathematics, Faculty of Education, Kafkas University, Kars, Turkey

3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamilnadu, India


In this research study, the numerical Galerkin Finite Element Method (GFEM) is used for forced laminar convection heat transfer of Cu-water nanofluid in a divergent wavy channel including a rotating cylinder turbulator. The above boundary of the channel is in low temperatures and the bottom boundary is in hot temperatures as well as the cylinder wall temperature. It is assumed that the cylinder rotates in the cavity and makes vortexes to enhance heat transfers. The dimensionless governing equations including velocity, pressure, and temperature formulation are solved by the Galerkin finite element method. The results are discussed based on the governing factors such as nanoparticle volume fraction, Reynolds number, cylinder diameter and rotating velocity. As a main result, among the all studied parameters (Re, u, Φ and r), increasing the Re number has the most effect on heat transfer which has 4.8 and 1.6 Average Nu for the cylinder wall and wavy wall, respectively.


Main Subjects

[1] Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, 1995, 99–105.
[2] Nandy Putra, Y., Ferdiansyah, N.I., Application of nanofluids to a heat pipe liquid-block and the thermoelectric cooling of electronic equipment, Experimental Thermal and Fluid Science, 35, 2011, 1274-1281.
[3] Kumar, A., Subudhi, S., Preparation, characterization and heat transfer analysis of nanofluids used for engine cooling, Applied Thermal Engineering, 160, 2019, 114092.
[4] Wang, G., Song, B., Liu, Zh., Operation characteristics of cylindrical miniature grooved heat pipe using aqueous CuO nanofluids, Experimental Thermal and Fluid Science, 34, 2010, 1415-1421.
[5] Javadi, F.S., Saidur, R., Kamalisarvestani, M., Investigating performance improvement of solar collectors by using nanofluids, Renewable and Sustainable Energy Reviews, 28, 2013, 232-245.
[6] Liu, F., Zhang, D., Cai, Y., Qiu, Zh., Zhu, Q., Zhao, J., Wang, L., Tian, H., Multiplicity of forced convective heat transfer of nanofluids in curved ducts, International Journal of Heat and Mass Transfer, 129, 2019, 534-546.
[7] Nguyen, T.K., Saidizad, A., Jafaryar, M., Sheikholeslami, M., Barzegar Gerdroodbary, M., Moradi, R., Shafee, A., Li, Zh., Influence of various shapes of CuO nanomaterial on nanofluid forced convection within a sinusoidal channel with obstacles, Chemical Engineering Research and Design, 146, 2019, 478-485
[8] Andreozzi, A., Manca, O., Nardini, S., Ricci, D., Forced convection enhancement in channels with transversal ribs and nanofluids, Applied Thermal Engineering, 98, 2016, 1044-1053.
[9] Ho, C.J., Chang, C.Y., Wei-Mon, Y., Amani, P., A combined numerical and experimental study on the forced convection of Al2O3-water nanofluid in a circular tube, International Journal of Heat and Mass Transfer, 120, 2018, 66-75.
[10] Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D.D., Soleimani, S., Seyyedi, S.M., Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field, International Communications in Heat and Mass Transfer, 39, 2012, 1435-1443.
[11] Sheikholeslami, M., Influence of magnetic field on Al2O3-H2O nanofluid forced convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM, Journal of Molecular Liquids, 263, 2018, 472-488.
[12] Selimefendigil, F., Öztop, H. F., Magnetic field effects on the forced convection of CuO-water nanofluid flow in a channel with circular cylinders and thermal predictions using ANFIS, International Journal of Mechanical Sciences, 146-147, 2018, 9-24.
[13] Besanjideh, M., Hajabdollahi, M., Gandjalikhan Nassab, S.A., CFD Based Analysis of Laminar Forced Convection of Nanofluid Separated Flow Under the Presence of Magnetic Field, Journal of Mechanics, 32(6), 2016, 777-785.
[14] Uddin, M.J., Rahman, M.M., Finite element computational procedure for convective flow of nanofluids in an annulus, Thermal Science and Engineering Progress, 6, 2018, 251-267.
[15] Ranal, P., Bhargava1, R., Anwar Bég, O., Finite element modeling of conjugate mixed convection flow of Al2O3-water nanofluid from an inclined slender hollow cylinder, Physica Scripta, 87, 2013, 055005.
[16] Baheri Islami, S., Dastvareh, B., Gharraei, R., Numerical study of hydrodynamic and heat transfer of nanofluid flow in microchannels containing micromixer, International Communications in Heat and Mass Transfer, 43, 2013, 146–154.
[17] Hussain, S., Jamal, M., Ahmed, S.E., Hydrodynamic forces and heat transfer of nanofluid forced convection flow around a rotating cylinder using finite element method: The impact of nanoparticles, International Communications in Heat and Mass Transfer, 108, 2019, 104310.
[18] Nath, R., Krishnan, M., Numerical study of double diffusive mixed convection in a backward facing step channel filled with Cu-water nanofluid, International Journal of Mechanical Sciences, 153–154, 2019, 48–63.  
[19] Hussain, S., Ahmed, S.E., Akbar, T., Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle, International Journal of Heat and Mass Transfer, 114, 2017, 1054–1066.
[20] Ali, M. M., Alim, M.A., Ahmed, S.S., Oriented magnetic field effect on mixed convective flow of nanofluid in a grooved channel with internal rotating cylindrical heat source, International Journal of Mechanical Sciences, 151, 2019, 385–409.
[21] Rahimi-Esbo, M., Ranjbar, A.A., Ramiar, A., Arya, A., Rahgoshay, M., Numerical study of turbulent forced convection jet flow in a converging sinusoidal channel, International Journal of Thermal Sciences, 59, 2012, 176-185.
[22] Hatami, M., Ganji, D.D., Motion of a spherical particle in a fluid forced vortex by DQM and DTM, Particuology, 16, 2014, 206-212.
[23] Hatami, M., Ganji, D.D., Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy multi-step differential transformation method, Powder Technology, 258, 2014, 94-98.
[24] Dogonchi, A.S., Hatami, M., Domairry, G., Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow, Powder Technology, 274, 2015, 186-192.
[25] Hatami, M., Sheikholeslami, M., Domairry, G., High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by Multi-step Differential Transformation Method, Powder Technology, 260, 2014, 59-67.
[26] Ghadikolaei, S.S., Hosseinzadeh, Kh., Ganji, D.D., Hatami, M., Fe3O4–(CH2OH)2 nanofluid analysis in a porous medium under MHD radiative boundary layer and dusty fluid, Journal of Molecular Liquids, 258, 2018, 172-185.
[27] Hatami, M., Song, D., Jing, D., Optimization of a circular-wavy cavity filled by nanofluid under the natural convection heat transfer condition, International Journal of Heat and Mass Transfer, 98, 2016, 758-767.
[28] Hatami, M., Nanoparticles migration around the heated cylinder during the RSM optimization of a wavy-wall enclosure, Advanced Powder Technology, 28(3), 2017, 890-899.
[29] Wenhui, T., Hatami, M., Zhou, J., Jing, D., Natural convection heat transfer in a nanofluid-filled cavity with double sinusoidal wavy walls of various phase deviations, International Journal of Heat and Mass Transfer, 115, 2017, 430-440.
[30] Hatami, M., Jing, D., Optimization of wavy direct absorber solar collector (WDASC) using Al2O3-water nanofluid and RSM analysis, Applied Thermal Engineering, 121, 2017, 1040-1050.
[31] Hatami, M., Zhou, J., Geng, J., Song, D., Jing, D., Optimization of a lid-driven T-shaped porous cavity to improve the nanofluids mixed convection heat transfer, Journal of Molecular Liquids, 231, 2017, 620-631.
[32] Jiandong, Zh., Hatami, M., Song, D., Jing, D., Design of microchannel heat sink with wavy channel and its time-efficient optimization with combined RSM and FVM methods, International Journal of Heat and Mass Transfer, 103, 2016, 715-724.
[33] Ali, F.H., Hamzah, H.K., Abdulkadhim, A., Numerical study of mixed convection nanofluid in an annulus enclosure between outer rotating cylinder and inner corrugation cylinder, Heat Transfer, 48, 2019, 343-360.
[34] Alsabery, A.I., Sheremet, M.A., Chamkha, A.J., Hashim, I.J.S.R., MHD convective heat transfer in a discretely heated square cavity with conductive inner block using two-phase nanofluid model, Scientific Reports, 8(1), 2018, 1-23.
[35] Alsabery, A.I., Chamkha, A.J., Saleh, H., Hashim, I., Natural convection flow of a nanofluid in an inclined square enclosure partially filled with a porous medium, Scientific Reports, 7(1), 2017, 1-18.
[36] Dinarvand, S., Rostami, M.N., Pop, I., A novel hybridity model for TiO2-CuO/water hybrid nanofluid flow over a static/moving wedge or corner, Scientific Reports, 9(1), 2019, 1-11.
[37] Nouri-Borujerdi, A., Nakhchi, M.E., Prediction of local shear stress and heat transfer between internal rotating cylinder and longitudinal cavities on stationary cylinder with various shapes, International Journal of Thermal Sciences, 138, 2019, 512-520.
[38] Nakhchi, M. E., Esfahani, J. A., Numerical investigation of heat transfer enhancement inside heat exchanger tubes fitted with perforated hollow cylinders, International Journal of Thermal Sciences, 147, 2020, 106153.
[39] Nakhchi, M.E., Esfahani, J.A., Kim, K.C., Numerical study of turbulent flow inside heat exchangers using perforated louvered strip inserts, International Journal of Heat and Mass Transfer, 148, 2020, 119143.
[40] Nakhchi, M.E., Esfahani, J.A., CFD approach for two-phase CuO nanofluid flow through heat exchangers enhanced by double perforated louvered strip insert, Powder Technology, 367(1), 2020, 877-888.
[41] Nakhchi, M.E., Rahmati, M.T., Entropy generation of turbulent Cu–water nanofluid flows inside thermal systems equipped with transverse-cut twisted turbulators, Journal of Thermal Analysis and Calorimetry, 2020, 1-10 (in press).
[42] Ghalambaz, M., Doostani A., Izadpanahi, E., Chamkha, A.J., Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity, Journal of Thermal Analysis and Calorimetry, 139(3), 2020, 2321-2336.
[43] Tayebi, T., Chamkha, A.J., Entropy generation analysis during MHD natural convection flow of hybrid nanofluid in a square cavity containing a corrugated conducting block, International Journal of Numerical Methods for Heat & Fluid Flow, 30(3), 2019, 1115-1136.
[44] Alsabery, A. I., Ghalambaz, M., Armaghani, T., Chamkha, A., Hashim, I., Saffari Pour, M., Role of Rotating Cylinder toward Mixed Convection inside a Wavy Heated Cavity via Two-Phase Nanofluid Concept, Nanomaterials, 10(6), 2020, 1138.
[45] Alsabery, A.I., Hashim, I., Hajjar, A., Ghalambaz, M., Nadeem, S., Saffari Pour, M., Entropy Generation and Natural Convection Flow of Hybrid Nanofluids in a Partially Divided Wavy Cavity Including Solid Blocks, Energies, 13(11), 2020, 2942.
[46] Mehryan, S. A. M., Ghalambaz, M., Chamkha, A. J., Izadi M., Numerical study on natural convection of Ag–MgO hybrid/water nanofluid inside a porous enclosure: A local thermal non-equilibrium model, Powder Technology, 367, 2020, 443-455.
[47] Subharthi, S., Endalew, M.F., Makinde, O.D., Study of MHD Second Grade Flow through a Porous Microchannel under the Dual-Phase-Lag Heat and Mass Transfer Model, Journal of Applied and Computational Mechanics, 5(4), 2019, 763-778.
[48] Babu, D.D., Venkateswarlu, S., Reddy, E.K., Multivariate Jeffrey Fluid Flow past a Vertical Plate through Porous Medium, Journal of Applied and Computational Mechanics, 6(3), 2020, 605-616.
[49] Biswal, U., Chakraverty, S., Ojha, B.K., Application of homotopy perturbation method in inverse analysis of Jeffery–Hamel flow problem, European Journal of Mechanics-B/Fluids, 86, 2021, 107-112.
[50] Bildik, N., Deniz, S., Optimal iterative perturbation technique for solving Jeffery–Hamel flow with high magnetic field and nanoparticle, Journal of Applied Analysis & Computation, 10(6), 2020, 2476-2490.
[51] Usman, M., Zubair, T., Hamid, M., Haq, R.U., Novel modification in wavelets method to analyze unsteady flow of nanofluid between two infinitely parallel plates, Chinese Journal of Physics, 66, 2020, 222-236.
[52] Aly, A.M., Mixing between solid and fluid particles during natural convection flow of a nanofluid-filled H-shaped cavity with three center gates using ISPH method, International Journal of Heat and Mass Transfer, 157, 2020, 119803.
[53] Zhang, R., Aghakhani, S., Pordanjani, A.H., Vahedi, S.M., Shahsavar, A., Afrand, M., Investigation of the entropy generation during natural convection of Newtonian and non-Newtonian fluids inside the L-shaped cavity subjected to magnetic field: application of lattice Boltzmann method, The European Physical Journal Plus, 135(2), 2020, 184.
[54] Qi, C., Tao, L., Maoni, L., Fan, F., Yuying, Y., Experimental study on the flow and heat transfer characteristics of nanofluids in double-tube heat exchangers based on thermal efficiency assessment, Energy Conversion and Management, 197, 2019, 111877.
[55] Zhao, N., Cong, Q., Tiantian, C., Jinghua, T., Xin, C., Experimental study on influences of cylindrical grooves on thermal efficiency, exergy efficiency and entropy generation of CPU cooled by nanofluids, International Journal of Heat and Mass Transfer, 135, 2019, 16-32.
[56] Zhao, N., Leixin, G., Cong, Q., Tiantian, C., Xin, C., Experimental study on thermo-hydraulic performance of nanofluids in CPU heat sink with rectangular grooves and cylindrical bugles based on exergy efficiency, Energy Conversion and Management, 181, 2019, 235-246.
[57] Lu, G., Jun, Z., Lin, L., Xiao-Dong, W., Wei-Mon, Y., A new scheme for reducing pressure drop and thermal resistance simultaneously in microchannel heat sinks with wavy porous fins, International Journal of Heat and Mass Transfer, 111, 2017, 1071-1078.