Mesoscopic Simulation of Forced Convective Heat Transfer of Carreau-Yasuda Fluid Flow over an Inclined Square: Temperature-dependent Viscosity

Document Type : Research Paper


1 Department of Mechanical Engineering, Payame Noor University (PNU), P.O. BOX 19395-3697, Tehran, Iran

2 Department of Mechanical Engineering, University of Bojnord, Bojnord, Iran

3 Department of Mechanical Engineering, Payam Noor University, Mashhad, Iran

4 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran


In the current study, non-Newtonian flow pattern and heat transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and heat transfer have been successfully verified with the previous studies. Several parameters such as Nusselt number, Drag coefficient, and Carreau number are investigated in details. Considering the temperature-dependent viscosity, it is seen that with increasing thetemperature-thinning index, the drag coefficient increases, but the Nusselt number decreases. By rotating the square obstacle, the results display that increasing the angle of inclination from zero to 45 degrees, increases both the drag coefficient and the Nusselt number. Also, the highest rate of heat transfer occur at the angle of 45 degrees (diamond); however it has a negative impact on the Drag coefficient.


Main Subjects

[1] M. Izadi, R. Mohebbi, H. Sajjadi, and A. A. Delouei, LTNE modeling of Magneto-Ferro natural convection inside a porous enclosure exposed to nonuniform magnetic field, Physica A: Statistical Mechanics and its Applications, 535, 2019, 122394.
[2] M. Bhatti, A. Zeeshan, and N. Ijaz, Slip effects and endoscopy analysis on blood flow of particle-fluid suspension induced by peristaltic wave, Journal of Molecular Liquids, 218, 2016, 240-245.
[3] P. Mellin, E. Kantarelis, and W. Yang, Computational fluid dynamics modeling of biomass fast pyrolysis in a fluidized bed reactor, using a comprehensive chemistry scheme, Fuel, 117, 2014, 704-715.
[4] H. Huang, K. Wang, and H. Zhao, Numerical study of pressure drop and diffusional collection efficiency of several typical noncircular fibers in filtration, Powder Technology, 292, 2016, 232-241.
[5] M. A. Dandan, S. Samion, M. N. Musa, and F. M. Zawawi, Evaluation of Lift and Drag Force of Outward Dimple Cylinder Using Wind Tunnel, CFD Letters, 11(3), 2019, 145-153.
[6] A. A. R. Alkumait, M. H. Zaidan, and T. K. Ibrahim, Numerical Investigation of Forced Convection Flow over Backward Facing Step Affected By A Baffle Position, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 52(1), 2018, 33-45.
[7] K. Prasad, H. Vaidya, K. Vajravelu, and U. Vishwanatha, Influence of Variable Liquid Properties on Mixed Convective MHD Flow over a Slippery Slender Elastic Sheet with Convective Boundary Condition, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 56(1), 2019, 100-123.
[8] S. Succi, The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford university press, 2001.
[9] C. K. Aidun and J. R. Clausen, Lattice-Boltzmann method for complex flows, Annual Review of Fluid Mechanics, 42, 2010, 439-472.
[10] H. Xu, Z. Xing, and K. Vafai, Analytical considerations of flow/thermal coupling of nanofluids in foam metals with local thermal non-equilibrium (LTNE) phenomena and inhomogeneous nanoparticle distribution, International Journal of Heat and Fluid Flow, 77, 2019, 242-255.
[11] A. Mohamad, Lattice Boltzmann Method. Springer, 2011.
[12] S. Ubertini and S. Succi, Recent advances of lattice Boltzmann techniques on unstructured grids, Progress in Computational Fluid Dynamics, an International Journal, 5(1-2), 2004, 85-96.
[13] H. Xu and Z. Xing, The lattice Boltzmann modeling on the nanofluid natural convective transport in a cavity filled with a porous foam, International Communications in Heat and Mass Transfer, 89, 2017, 73-82.
[14] S. Karimnejad, A. A. Delouei, M. Nazari, M. Shahmardan, and A. Mohamad, Sedimentation of elliptical particles using Immersed Boundary–Lattice Boltzmann Method: A complementary repulsive force model, Journal of Molecular Liquids, 262, 2018, 180-193.
[15] S. Karimnejad, A. A. Delouei, M. Nazari, M. Shahmardan, M. Rashidi, and S. Wongwises, Immersed boundary—thermal lattice Boltzmann method for the moving simulation of non-isothermal elliptical particles, Journal of Thermal Analysis and Calorimetry, 2019, DOI: 10.1007/s10973-019-08329-y.
[16] T. N. Phillips and G. W. Roberts, Lattice Boltzmann models for non-Newtonian flows, IMA Journal of Applied Mathematics, 76(5), 2011, 790-816.
[17] R. P. Chhabra, Bubbles, drops, and particles in non-Newtonian fluids. CRC press, 2006.
[18] A. De Rosis, Harmonic oscillations of laminae in non-Newtonian fluids: a lattice Boltzmann-immersed boundary approach, Advances in Water Resources, 73, 2014, 97-107.
[19] A. E. F. Monfared, A. Sarrafi, S. Jafari, and M. Schaffie, Thermal flux simulations by lattice Boltzmann method; investigation of high Richardson number cross flows over tandem square cylinders, International Journal of Heat and Mass Transfer, 86, 2015, 563-580.
[20] A. A. Delouei, M. Nazari, M. Kayhani, S. Kang, and S. Succi, Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary–lattice Boltzmann approach, Physica A: Statistical Mechanics and its Applications, 447, 2016, 1-20.
[21] E. Aharonov and D. H. Rothman, Non‐Newtonian flow (through porous media): A lattice‐Boltzmann method, Geophysical Research Letters, 20(8), 1993, 679-682.
[22] A. A. Delouei, M. Nazari, M. Kayhani, and S. Succi, Non-Newtonian unconfined flow and heat transfer over a heated cylinder using the direct-forcing immersed boundary–thermal lattice Boltzmann method, Physical Review E, 89(5), 2014, 053312.
[23] A. A. Delouei, M. Nazari, M. Kayhani, and S. Succi, Immersed boundary–thermal lattice Boltzmann methods for non-Newtonian flows over a heated cylinder: a comparative study, Communications in Computational Physics, 18(2), 2015, 489-515.
[24] S. Gabbanelli, G. Drazer, and J. Koplik, Lattice Boltzmann method for non-Newtonian (power-law) fluids, Physical Review E, 72(4), 2005, 046312.
[25] C. Sasmal and R. Chhabra, Effect of aspect ratio on natural convection in power-law liquids from a heated horizontal elliptic cylinder, International Journal of Heat and Mass Transfer, 55(17-18), 2012, 4886-4899.
[26] A. K. Tiwari and R. Chhabra, Laminar natural convection in power-law liquids from a heated semi-circular cylinder with its flat side oriented downward, International Journal of Heat and Mass Transfer, 58(1-2), 2013, 553-567.
[27] M. Ashrafizaadeh and H. Bakhshaei, A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations, Computers & Mathematics with Applications, 58(5), 2009, 1045-1054.
[28] D. Wang and J. Bernsdorf, Lattice Boltzmann simulation of steady non-Newtonian blood flow in a 3D generic stenosis case, Computers & Mathematics with Applications, 58(5), 2009, 1030-1034.
[29] Z.-G. Feng and E. E. Michaelides, Inclusion of heat transfer computations for particle laden flows, Physics of Fluids, 20(4), 2008, 040604.
[30] M. Sheikholeslami, H. Ashorynejad, and P. Rana, Lattice Boltzmann simulation of nanofluid heat transfer enhancement and entropy generation, Journal of Molecular Liquids, 214, 2016, 86-95.
[31] H. Xu, Z. Xing, F. Wang, and Z. Cheng, Review on heat conduction, heat convection, thermal radiation and phase change heat transfer of nanofluids in porous media: Fundamentals and applications, Chemical Engineering Science, 195, 2019, 462-483.
[32] H. Xu, L. Gong, S. Huang, and M. Xu, Flow and heat transfer characteristics of nanofluid flowing through metal foams, International Journal of Heat and Mass Transfer, 83, 2015, 399-407.
[33] G. Barrios, R. Rechtman, J. Rojas, and R. Tovar, The lattice Boltzmann equation for natural convection in a two-dimensional cavity with a partially heated wall, Journal of Fluid Mechanics, 522, 2005, 91-100.
[34] A. Dhiman, R. Chhabra, and V. Eswaran, Flow and heat transfer across a confined square cylinder in the steady flow regime: effect of Peclet number, International Journal of Heat and Mass Transfer, 48(21-22), 2005, 4598-4614.
[35] A. Korichi and L. Oufer, Numerical heat transfer in a rectangular channel with mounted obstacles on upper and lower walls, International Journal of Thermal Sciences, 44(7), 2005, 644-655.
[36] A. A. Delouei, M. Nazari, M. Kayhani, and G. Ahmadi, Direct-forcing immersed boundary–non-Newtonian lattice Boltzmann method for transient non-isothermal sedimentation, Journal of Aerosol Science, 104, 2017, 106-122.
[37] A. Soares, J. Ferreira, L. Caramelo, J. Anacleto, and R. Chhabra, Effect of temperature-dependent viscosity on forced convection heat transfer from a cylinder in crossflow of power-law fluids, International Journal of Heat and Mass Transfer, 53(21-22), 2010, 4728-4740.
[38] R. Mohebbi, M. Izadi, H. Sajjadi, A. A. Delouei, and M. A. Sheremet, Examining of nanofluid natural convection heat transfer in a Γ-shaped enclosure including a rectangular hot obstacle using the lattice Boltzmann method, Physica A: Statistical Mechanics and its Applications, 526, 2019, 120831.
[39] M. Breuer, J. Bernsdorf, T. Zeiser, and F. Durst, Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume, International Journal of Heat and Fluid Flow, 21(2), 2000, 186-196.
[40] Q. Zou and X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, 9(6), 1997, 1591-1598.
[41] Mei R., Yu D., Shyy W., and Luo L.-S., Force evaluation in the lattice Boltzmann method involving curved geometry, Physical Review E, 65, 2002, 041203.