Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

2021;
: pp. 807–820
https://doi.org/10.23939/mmc2021.04.807
Received: May 23, 2021
Accepted: June 07, 2021
1
Laboratory of Mechanics, Faculty of Sciences Ain Chock, Hassan II University
2
Laboratory of Mechanics, Faculty of Sciences Ain-Chock, University Hassan II Casablanca, Morocco
3
Laboratory of Mechanics, Faculty of Sciences Ain Chock, Hassan II University
4
Laboratory of Mechanics, Faculty of Sciences Ain-Chock, University Hassan II Casablanca, Morocco

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity.  By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature.  Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function.  The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations.  A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations.  The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM).  After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters.  Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

  1. Aly A. M., Raizah Z. A. S., Sheikholeslami M.  Analysis of mixed convection in a sloshing porous cavity filled with a nanofluid using ISPH method.  Journal of Thermal Analysis and Calorimetry. 139, 1977–1991 (2020).
  2. Muhammad N., Nadeem S., Issakhov A.  Finite volume method for mixed convection flow of Ag-ethylene glycol nanofluid flow in a cavity having thin central heater.  Physica A: Statistical Mechanics and its Applications. 537, 122738 (2020).
  3. Jamesahar E., Sabour M., Shahabadi M., Mehryan S. A. M., Ghalambaz M.  Mixed convection heat transfer by nanofluids in a cavity with two oscillating flexible fins: A fluid-structure interaction approach.  Applied Mathematical Modelling. 82, 72–90 (2020).
  4. Alsabery A. I., Armaghani T., Chamkha A. J., Hashim I.  Two-phase nanofluid model and magnetic field effects on mixed convection in a lid-driven cavity containing heated triangular wall.  Alexandria Engineering Journal. 59, 129–148 (2020).
  5. Qasim M., Ali Z., Wakif A., Boulahia Z.  Numerical simulation of MHD peristaltic flow with variable electrical conductivity and Joule dissipation using generalized differential quadrature method.  Communications in Theoretical Physics. 71, 509–518 (2019).
  6. Afridi I. M., Qasim M., Wakif A., Hussanan A.  Second Law Analysis of Dissipative Nanofluid Flow over a Curved Surface in the Presence of Lorentz Force: Utilization of the Chebyshev–Gauss–Lobatto Spectral Method.  Nanomaterials. 9 (2), 195 (2019).
  7. Amanulla C. H., Wakif A., Boulahia Z., Fazuruddin S., Mohammed S. N.  A Study on Non-Newtonian Transport Phenomena in MHD Fluid Flow From a Vertical Cone With Navier Slip and Convective Heating.  Nonlinear Engineering. 8 (1), 534–545 (2019).
  8. Qasim M.,  Afridi M. I., Wakif A., Saleem S.  Influence of Variable Transport Properties on Nonlinear Radioactive Jeffrey Fluid Flow Over a Disk: Utilization of Generalized Differential Quadrature Method.  Arabian Journal for Science and Engineering. 44, 5987–5996 (2019).
  9. Qasim M.,  Afridi M. I., Wakif A., Thoi T. N., Hussanan A.  Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method.  Entropy. 21 (3), 240 (2019).
  10. Amanulla C. H., Saleem S., Wakif A., AlQarni M. M.  MHD Prandtl fluid flow past an isothermal permeable sphere with slip effects.  Case Studies in Thermal Engineering. 14, 100447 (2019).
  11. Wakif A., Qasim M., Afridi M. I., Saleem S., Al-Qarni M. M.  Numerical Examination of the Entropic Energy Harvesting in a Magnetohydrodynamic Dissipative Flow of Stokes’ Second Problem: Utilization of the Gear-Generalized Differential Quadrature Method.  Journal of Non-Equilibrium Thermodynamics. 44 (4), 385–403 (2019).
  12. Wakif A.  A novel numerical procedure for simulating steady MHD convective flows of radiative Casson fluids over a horizontal stretching sheet with irregular geometry under the combined influence of temperature-dependent viscosity and thermal conductivity.  Math. Probl. Eng. 2020, Article ID: 1675350  (2020).
  13. Diouf M., Sene N.  Analysis of the financial chaotic model with the fractional derivative operator.  Complexity. 2020, Article ID: 9845031 (2020).
  14. Sene N.  Second-grade fluid model with Caputo-Liouville generalized fractional derivative.  Chaos, Solitons & Fractals. 133, 109631 (2020).
  15. Haq R. U., Usman M., Algehyne E. A.  Natural convection of CuO-water nanofluid filled in a partially heated corrugated cavity: KKL model approach.  Communications in Theoretical Physics. 72, 85003 (2020).
  16. Seyyedi S. M., Dogonchi A. S., Hashemi-Tilehnoee M., Waqas M., Ganji D. D.  Investigation of entropy generation in a square inclined cavity using control volume finite element method with aided quadratic Lagrange interpolation functions.  International Communications in Heat and Mass Transfer. 110, 104398 (2020).
  17. Syrakos A., Dimakopoulos Y., Tsamopoulos J.  A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case.  Journal of Non-Newtonian Fluid Mechanics. 275, 104216 (2020).
  18. Sajjadi H., Mohammadifar H., Amiri Delouei A.  Investigation of the effect of the internal heating system position on heat transfer rate utilizing Cu/water nanofluid.  Journal of Thermal Analysis and Calorimetry. 139, 2035–2054 (2020).
  19. Buongiorno J. et al.  A benchmark study on the thermal conductivity of nanofluids.  Journal of Applied Physics. 106, 094312 (2009).
  20. Nayak M. K. Wakif A., Animasaun I. L., Alaoui M. S. H.  Numerical Differential Quadrature Examination of Steady Mixed Convection Nanofluid Flows Over an Isothermal Thin Needle Conveying Metallic and Metallic Oxide Nanomaterials: A Comparative Investigation.  Arabian Journal for Science and Engineering. 45, 5331–5346 (2020).
  21. Tiwari R. K., Das M. K.  Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids.  International Journal of Heat and Mass Transfer. 50 (9–10), 2002–2018 (2007).
  22. Eid M. R., Mahny K. L., Dar A., Muhammad T.  Numerical study for Carreau nanofluid flow over a convectively heated nonlinear stretching surface with chemically reactive species.  Physica A: Statistical Mechanics and its Applications. 540, 123063 (2020).
  23. Rasool G., Chamkha A. J., Muhammad T., Shafiq A., Khan I.  Darcy–Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface.  Propulsion and Power Research. 9 (2), 159–168 (2020).
  24. Ahmad M., Muhammad T., Ahmad I., Aly S.  Time-dependent 3D flow of viscoelastic nanofluid over an unsteady stretching surface.  Physica A: Statistical Mechanics and its Applications. 551, 124004 (2020).
  25. Hayat T., Haider F., Muhammad T., Alsaedi A.  Darcy–Forchheimer flow of carbon nanotubes subject to heat flux boundary condition.  Physica A: Statistical Mechanics and its Applications. 554, 124002 (2020).
  26. Naqvi S. M. R. S., Muhammad T., Saleem S., Kim H. M.  Significance of non-uniform heat generation/absorption in hydromagnetic flow of nanofluid due to stretching/shrinking disk.  Physica A: Statistical Mechanics and its Applications. 553, 123970 (2020).
  27. Rana P., Bhargava R.  Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids.  Communications in Nonlinear Science and Numerical Simulation. 16 (11), 4318–4334 (2011).
  28. Zaraki A., Ghalambaz M., Chamkha A. J., Ghalambaz M., De Rossi D.  Theoretical analysis of natural convection boundary layer heat and mass transfer of nanofluids: Effects of size, shape and type of nanoparticles, type of base fluid and working temperature.  Advanced Powder Technology. 26 (3), 935–946 (2015).
  29. Buongiorno J.  Convective Transport in Nanofluids.  Journal Heat Transfer. 128 (3), 240–250 (2006).
  30. Mebarek-Oudina F.  Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source.  Heat Transfer-Asian Res. 48, 135–147 (2019).
  31. Wakif A., Boulahia Z., Sehaqui R.  Numerical analysis of the onset of longitudinal convective rolls in a porous medium saturated by an electrically conducting nanofluid in the presence of an external magnetic field.  Results in Physics. 7, 2134–2152 (2017).
  32. Wakif A., Boulahia Z., Sehaqui R.  A Semi-Analytical Analysis of Electro-Thermo-Hydrodynamic Stability in Dielectric Nanofluids Using Buongiorno’s Mathematical Model Together with More Realistic Boundary Conditions.  Results in Physics. 9, 1438–1454 (2018).
  33. Wakif A., Boulahia Z., Mishra S. R., Mehdi Rashidi M., Sehaqui R.  Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model.  The European Physical Journal Plus. 133, Article number: 181 (2018).
  34. Wakif A., Animasaun I. L., Satya Narayana P. V., Sarojamma G.  Meta-analysis on thermo-migration of tiny/nano-sized particles in the motion of various fluids.  Chinese Journal of Physics. 68, 293–307 (2020).
  35. Khanafer K. M., Chamkha A. J.  Mixed convection flow in a lid-driven enclosure filled with a fluid-saturated porous medium.  International Journal of Heat and Mass Transfer. 42 (13), 2465–2481 (1999).
  36. Waheed M. A.  Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate.  International Journal of Heat and Mass Transfer. 52 (21–22), 5055–5063 (2009).
  37. Ghaffari A., Mustafa I., Javed T.  Influence of nonlinear radiation on natural convection flow of carbon nanotubes suspended in water-based fluid along a vertical wavy surface.  Physica Scripta. 94, 115214 (2019).
  38. Mustafa I., Ghaffari A., Javed T., Abbasi J. N.  Numerical Examination of Thermophysical Properties of Cobalt Ferroparticles over a Wavy Surface Saturated in Non-Darcian Porous Medium.  J. Non-Equilibrium Thermodyn. 45 (2), 109–120 (2020).
  39. Wakif A., Boulahia Z., Amine A., Animasaun I. L., Afridi M. I., Qasim M., Sehaqui R.  Magneto-convection of alumina - water nanofluid within thin horizontal layers using the revised generalized Buongiorno’s model.  Frontiers in Heat and Mass Transfer. 12, 3 (2019).
  40. Wakif A., Chamkha A., Thumma T., Animasaun I. L., Sehaqui R.  Thermal radiation and surface roughness effects on the thermo-magneto-hydrodynamic stability of alumina-copper oxide hybrid nanofluids utilizing the generalized Buongiorno’s nanofluid model.  Journal of Thermal Analysis and Calorimetry. 143, 1201–1220 (2020).
  41. Corcione M.  Empirical Correlating Equations for Predicting the Effective Thermal Conductivity and Dynamic Viscosity of Nanofluids.  Energy Conversion and Management. 52 (1), 789–793 (2011).
  42. Shah N. A., Animasaun I. L., Wakif A., Koriko O. K., Sivaraj R., Adegbie K. S., Abdelmalek Z., Vaidyaa H., Ijirimoye A. F., Prasad K. V.  Significance of suction and dual stretching on the dynamics of various hybrid nanofluids: Comparative analysis between type I and type II models.  Physica Scripta. 95 (9), 95205 (2020).
  43. Iqbal M. S., Mustafa I., Riaz I., Ghaffari A., Khan W. A.  Influence of carbon nanotubes on heat transfer in MHD nanofluid flow over a stretchable rotating disk: A numerical study.  Heat Transfer. 50, 619–637 (2020).
  44. Wakif A., Boulahia Z., Ali F., Eid M. R., Sehaqui R.  Numerical Analysis of the Unsteady Natural Convection MHD Couette Nanofluid Flow in the Presence of Thermal Radiation Using Single and Two-Phase Nanofluid Models for Cu-Water Nanofluids.  International Journal of Applied and Computational Mathematics. 4, Article number: 81 (2018).
  45. Erturk E.  Numerical performance of compact fourth-order formulation of the Navier–Stokes equations.  Communications in Numerical Methods in Engineering. 24, 2003–2019 (2008).
  46. Peaceman D. W., Rachford J. H. H.  The Numerical Solution of Parabolic and Elliptic Differential Equations.  Journal of the Society for Industrial and Applied Mathematics. 3 (1), 28–41 (1955).
  47. Erturk E., Gökcötol C.  Fourth-order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers.  International Journal for Numerical Methods in Fluids. 50 (4), 421–436 (2006).
  48. Störtkuhl T., Zenger C., Zimmer S.  An asymptotic solution for the singularity at the angular point of the lid driven cavity.  International Journal of Numerical Methods for Heat & Fluid Flow. 4 (1), 47–59 (1994).
  49. De Vahl Davis G.  Natural convection of air in a square cavity: A benchmark numerical solution.  International Journal for Numerical Methods in Fluids. 3, 249–264 (1983).
  50. Barakos G., Mitsoulis E., Assimacopoulos D.  Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions.  International Journal for Numerical Methods in Fluids. 18, 695–719 (1994).
  51. Khanafer K., Vafai K., Lightstone M.  Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids.  International Journal of Heat and Mass Transfer. 46 (19), 3639–3653 (2003).
Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 807–820 (2021)