The cavity with lid-driven is greatly used in mixing, coating, and drying applications and is a substantial issue in the study of thermal performance rate and fluid field. A numerical approach is presented to study the thermal distribution and passage of fluid in a lid-driven cavity with an upper oscillating surface and an attached baffle. The walls of a cavity at the left and right were maintained at 350 and 293 K, respectively. The upper oscillating surface was equipped with a variable height to baffle to increase the convection of the three kinds of TiO_{2}, Al_{2}O_{3}, and CuO nanofluids with various of 0.4, 0.8, and 0.4, 0.8, and 1.2 vol. % in volume fractions. It was found that using a baffle attached to the oscillating upper surface of the cavity will lead to improving the distribution of vorticity in the cavity and increase the stream in the cavity. Also, increasing the baffle height, oscillating velocity, and volume fraction of nanoparticles contributes to enhancing the Nusselt number values by 50% for increasing baffle height from h^{*} = 0.1 to 0.1. Also, the Nu improved by 20% for increasing oscillating velocity from w = 05 to 20 rad/s and by 12% for using Al_{2}O_{3} nanofluid instead of TiO_{3} at

Since it is relevant to industrial flows and the effectiveness of heat transfer, flow within a cavity where the lid is in motion, oscillating back and forth, has been researched throughout time by Zhu et al. [

The possibility of using a cavity with a viscometer utilizing oscillating lid-driven flow, which was explored in a preliminary study [_{2}O_{3} particles dispersed in water within a square cavity. Pourmahmoud et al. [_{2}O_{3}/water nanofluid’s natural convection in the cavity with sinusoidal of the distribution of wall temperature and isothermal barriers at Ri = 0.001. The findings demonstrated that the Nu increased in proportion to the nanoparticles volume fraction of 6% nanoparticles, the Nu jumped by 9.04% over the base fluid. Zheng et al. [_{2}O_{3} nanofluid in a titled cavity. The left wall of the cage has a circular quadrant at a hot temperature of Th. According to the statistics, there is a 160% and 40% increase in Nu when Ra is increased and Ha is decreased. Befalls as a result of raising Ra and lowering Ha. The maximal generation of entropy rises by 288% and 39%, respectively, when the Ra and Ha are increased. The largest average Nu and total entropy generation happen at a 30° inclination angle. Berrahil et al. [_{2}O_{3} nanofluid’s in a vertical annulus that is differentially heated and subjected to a uniform magnetic field is done by. They established an internal Nu rises once more after falling until it reaches a volume fraction of 0.05. The impact of nanopowder shape on irreversibilities and natural convection in water/alumina nanofluids was examined by Yan et al. [_{3}O_{4}) hybrid nanofluid MHD nano liquid convective flow in an oddly shaped cavity was designated by the Al-Kouz et al. [_{3}O_{4} nanofluid in a square enclosure were explored by Mehryan et al. [_{2}O_{3}-water nanofluid flow and heat transfer performance was examined numerically by Jehhef et al. [_{2}O_{3}-water nanofluid at 0.1–1.0 vol. % volume fraction upon the thin plate. Finally, In the presence of a triangular rib, Jehhef et al. [

All the above literature works concentrated on the heat transfer in lid-driven without moving baffle, but the current simulation study absorbed on outcome of attached baffle of moving wall on enhancement of the heat transfer and fluid flow in lid-driven. Thus, goal of this study is to evaluate the impacts of attaching baffles with various heights to the upper cavity with lid-driven for three types of nanofluids. A numerical simulation was created to characterize the hydrodynamics and heat transfer behavior in a 2D cavity. The influences of baffle height, oscillating velocity, and volume fraction of nanoparticle concentration have been investigated to achieve high thermal efficiency as compared to the cavity without an attached baffle. This particular study is important due to adding the effect of the baffle attached to the oscillation upper wall on the mixed convection inside the cavity.

After conducting a thorough review of the literature, Minea et al. [

1) Conservation equations of 2D form.

2) Incompressible Steady state fluid flow.

3) Nanofluids flow in the cavity have been considered turbulent.

4) Nanofluids thermos-physical properties are assessed at an average fluid temperature.

5) Heat transfer by conduction is neglected.

6) Radiation heat transfer in the model is neglected.

In the present work, it is presumed that the thermophysical characteristics of the nanofluid remain unchanged, except for density fluctuations that are estimated using the Boussinesq model. ANSYS-Fluent is employed to develop a two-dimensional model for heat and fluid flow within the enclosure, taking into account forced convective laminar heat transfer and steady-state incompressible fluid flow boundary. The equations that govern this particular type of flow are the time-independent equations of Navier-Stokes, which describe steady viscous, incompressible laminar flow in two dimensions. The given equations that are suitable can be expressed as:

The equation that describes the conservation of mass is:

x-direction momentum conservation formula:

y-direction momentum conservation formula:

Energy conservation formula:

The thermal diffusivity (α_{nf}), representing the measure of thermal inertia, is determined by the following calculation:

The formula for calculating α_{nf} involves the fluid thermal conductivity (k_{nf}) measured in W/m K, the density (ρ_{nf}) expressed in kg/m^{3}, and the (Cp_{nf}) of the nanofluid in J/kg.K. A greater magnitude of α_{nf} signifies efficient heat transfer and a nanofluid with enhanced thermal conductivity. The temperature variable is represented as T. While using the Boussinesq Approximation, density variations are a function of reference density, temperature, and a coefficient of thermal expansion.

where appears in the x-momentum equation and links it by incorporating the equation of energy. In this context, ∆T = Th − Tc represents the difference temperature between the hot and cold walls.

In the numerical work, the enclosed cavity is simulated in 2-dimensional modeling. The main goal is to investigate the rate of heat transfer and fluid flow profile of various volume fractions of Al_{2}O_{3}-water nanofluid. A constant temperature of 350 K is maintained for the hot temperature, while the cold wall is fixed at 293 K. To replicate the impact of nanoparticles, the Tiwari-Das model [

The viscosity that effectively characterizes the dynamic behavior of a nanofluid can be expressed using Brinkman’s formula [

The estimation of the nanofluid effective density can also be derived using Pak et al. [

The determination of the coefficient of thermal expansion for the nanofluid can be achieved by:

The nanofluid specific heat was given by Xuan et al. [

To ascertain the nanofluid’s effective thermal conductivity by employing the Maxwell-Garnet relation, specifically for spherical nanoparticles [

One possible approach for defining the local Rayleigh number involves the comparison between thermal buoyancy and viscous hydrodynamic force, and can be expressed as follows:

The Nusselt number is given by:

In the provided equation, the symbol ‘g’ corresponds to the acceleration due to gravity, ‘y’ represents the coordinate, ‘h’ signifies the convective heat transfer coefficient, H denotes the height of the enclosure, and ‘

Properties | Water | Al_{2}O_{3}-water nanofluid |
CuO-water nanofluid | TiO_{2}-water nanofluid |
||||||
---|---|---|---|---|---|---|---|---|---|---|

0.4 | 0.8 | 1.0 | 0.4 | 0.8 | 1.0 | 0.4 | 0.8 | 1.0 | ||

ρ (kg/m^{3}) |
998.2 | 1010.1 | 1021.9 | 1027.9 | 1020.207 | 1042.214 | 1053.218 | 1011.207 | 1024.214 | 1030.718 |

Cp (J/kg.K) | 4182 | 4128.2 | 4075.8 | 4050.1 | 4089.005 | 3999.937 | 3956.799 | 4123.23 | 4065.952 | 4037.856 |

k (W/mk) | 0.6 | 0.606 | 0.613 | 0.617 | 0.606548 | 0.613145 | 0.61646 | 0.605942 | 0.611924 | 0.614930 |

μ (Ns/m^{2}) |
0.001 | 0.00098 | 0.0012 | 0.0011 | 0.000987 | 0.001020 | 0.00103 | 0.000978 | 0.001002 | 0.001014 |

β (1/K) | 0.00021 | 0.00021 | 0.00021 | 0.00021 | 0.000204 | 0.000199 | 0.00019 | 0.000206 | 0.000203 | 0.000201 |

The thermal boundary conditions depicted in

The left wall: stationary with constant of temperature, T = 350 K.

The right wall remains stationary and maintains a constant temperature of 293 K.

The bottom walls are adiabatic and remain stationary.

The upper wall: oscillating moving wall with Adiabatic.

_{o}. In the third case, the upper lid without the baffle oscillates solely with a velocity of U = U_{o} cos (ωt), as depicted in _{o} cos (ωt), as shown in _{nf} denotes the viscosity of the nanofluid. The value of U is associated with the Mach number and should be sufficiently low to ensure the incompressibility of the fluid. As U influences the Reynolds number (Re), an increase in Re indicates a larger oscillation amplitude. This study aims to examine the variations in flow modes under antiparallel and parallel oscillating wall motions by systematically adjusting the parameters (Re and ω) across a wide range of values (see ^{–} has been normalized following the approach of Iwatsu et al. [

Parameters | Values |
---|---|

Re | 520, 1040, 1560 |

2π/5, 2π/10, 2π/15, 2π/20 | |

T | 5, 10, 15, 20 |

St | 160, 220, 330, 650 |

The highest and lowest values of St are determined as follows:

The oscillation period T, presented in

In the numerical simulation, the sum is not expected to be zero, but it should gradually decrease with each iteration. The residual serves as an indicator of the extent of deviation in the solution of a specific transport equation. Monitoring the average residual associated with each transport equation helps determine the convergence of the solution. In this simulation, approximately 500 iterations are required to achieve a final solution, with the residuals often decreasing by several orders of magnitude as listed in

Mesh type | Nodes number | Heat transfer coefficient (W/m^{2}.K) |
---|---|---|

Coarse | 22500 | 1533.337 |

Medium | 40000 | 1840.004 |

Fine | 62500 | 2208.005 |

Finer | 90000 | 2220.125 |

Convergence can face obstacles due to several factors, including a high volume of computational cells, excessively cautious under-relaxation factors, and intricate flow physics. Determining if a solution has truly converged can also pose challenges. The upcoming sections will delve into various numerical controls and modeling techniques that can be employed to improve convergence and uphold stability, as illustrated in ^{−6}) while the tolerance for energy was set to (1 × 10^{−8}).

To validate the accurateness of the ANSYS-Fluent model in simulating mixed convection within a cavity containing Al_{2}O_{3}-water nanofluid at a Rayleigh number of 104, a comparison was conducted with a study conducted by Minea et al. [

Present numerical results work regarding effect of the oscillating upper wall of the enclosed cavity filled with nanofluid are presented with the aid of plots for streamlining and isothermal lines. In this study, the following parameter is investigated numerically as three values of upper wall velocity u = 0.5, 1.0, and 1.5 without oscillating, four baffle height to cavity height ratios of h* = hb/H = 0.1, 0.15, 0.2 and 0.25, and five oscillating velocities π/2.5, π/5, π/7.5 and π/10.

To study the effect of upper wall velocity without baffle,

The results in numerical form regarding the influence of the ratio of the height of the baffle to the height of the cavity on the isothermal and streamlines function are depicted in ^{*} = 0) case. As a result, the increasing baffle height from h^{*} = 0.1 to 0.15 leads to increasing the heated zones that are oriented towards the cold side and this increases the heating process along the cold surface. In the top zone, due to pushing the heated zone towered the cold wall. However, the results showed the intensity of the vorticity of the center streamlines the function and it will separate into two strong vorticities caused by the baffle.

The impact of increasing the upper wall velocity is illustrated in ^{*} = 0.15. The results showed that increasing the oscillating velocity from ω = 5 to 15 caused to increase in the heated and cold fluids inside the enclosing cavity due to increasing velocity of the nanofluid neighboring the upper oscillation wall. Furthermore, elevating oscillating velocity leads to increasing the streamline function in the upper zone of the cavity due to the oscillating motion of the fluids in this region.

Nanofluids are a mixture of water and metal particles that are used to enhance the water’s thermal properties. In the present study, three categories of fluid suspensions containing nanoparticles were employed (Al_{2}O_{3}, TiO_{2}, and CuO-water nanofluids) with three nanoparticle concentrations of (0.4, 0.8, and 1.0 vol. %). Isotherms (left) and Streamlines (right) for Al_{2}O_{3}, CuO, and TiO_{2}-water in a cavity with a rectangular baffle along the moving top wall plotted in

In general, the figures demonstrated that the effect of using different nanofluids will lead to creating a small vorticity within the area situated between the baffle and the heated wall and lead to increasing the rate of thermal exchange between the heated and cold wall. Using CuO–water nanofluid instead of Al_{2}O_{3} will lead to increasing the maximum stream function from 2.05e–02 to 2.07e–02 because of the low viscosity of the fluid used later. Furthermore, for volume fraction increasing from 0.4 to 1.2 vol. %, the temperature isothermal profile will be changed and the heated plume will increase toward the cold surfaces. The stream function increased from 2.05 × 10^{−2} to 2.10 × 10^{−2} when increasing the fraction of volume from 0.4 to 0.8 vol. %. ^{*} = 0.25 due to increasing the baffle height led to reaching the central axis of the enclosed cavity. Moreover, the impact of increasing the oscillating velocity (w) on the centerline y-velocity is plotted in

The chief of present study focus is to examine the effects of the attached baffle upon the upper oscillating wall in the enclosed cavity on the improvement in convective heat transfer by utilizing three types of nanofluids. _{2}O_{3}, CuO and TiO_{2}-water) at volume fraction of (Ø = 1.2 vol. %) instead of using water at nanoparticles concentration of (Ø = 0.0 vol. %). The highest value of Nusselt number is obtain in Al_{2}O_{3}–water nanofluids outstanding for increasing the nanofluids thermal conductivity.

The study of thermal behavior and nanofluid flow by forced convection in a square cavity with an oscillating upper surface with an attached baffle at a variable height ratio (h^{*}) was presented numerically. Different concentrations of nanoparticles (Al_{2}O_{3}, CuO, and TiO_{2}) are used to fill the cavity with nanofluids. The numerical method is employed for numerical simulation. The current study describes the dependence of the thermal behavior and nanofluids flow field performance in an upper-sided oscillating lid-driven cavity concerning the parameters (h^{*}, Re, ^{*}, Re, and ^{*} exerts significant influence over the magnitude and dimensions of corner vortices primary that created by the movement of the upper lid. The results showed that the using attached baffle to the oscillating upper surface will expand the distribution of vorticity in the enclosure region and increase fluid movement in it. Also, increasing the baffle height will contribute to enhancing the Nusselt number values by 50% for increasing baffle height from h^{*} = 0.1 to 0.1. The future research directions can be achieved by using more baffles attached to the upper wall.

Nanofluids specific heat (J.kg^{−1}.K^{−1})

Channel height (m)

Height of the cavity (m)

Width of the cavity (m)

Baffle height, m

Angular velocity of moving wall (rad/s)

Nanofluids thermal conductivity (W/m.K)

Pressure (Pa)

Applied heat flux (W/m^{2})

Temperature (K)

Axial velocity (m/s)

Transverse velocity (m/s)

Cartesian coordinates

Nusselt number

Nanofluids Temperature (K)

Velocity components Dimensionless in x, y directions

Dimensionless Cartesian coordinates

Components of Velocity in x, y directions (m/s)

_{pa}

Nanoparticle volume

_{nf}

Nanofluid volume

Dynamic viscosity (Pa s)

Dimensionless temperature

Density (kg/m^{2})

Kinematics viscosity (m^{2}/s)

Difference

Nanoparticle volume fraction

_{f}

Nanofluid

Fluid

Solid nanoparticle

The authors gratefully acknowledge the Middle Technical University and University of Technology-Iraq for supporting this work.

The authors received no specific funding for this work.

The authors confirm contribution to the paper as follows: study conception and design: Kadhum Audaa Jehhef, Ali J. Ali, Akram H. Abed; analysis and interpretation of results: Kadhum Audaa Jehhef, Salah H. Abid Aun, Ali J. Ali; draft manuscript preparation: Kadhum Audaa Jehhef, Salah H. Abid Aun, Akram H. Abed; revising the manuscript critically for important intellectual content: Ali J. Ali, Salah H. Abid Aun; approval of the version of the manuscript to be published: Ali J. Ali, Akram H. Abed.

The data supporting the findings of this study are available from the corresponding author (Akram H. Abed) on request.

The authors declare that they have no conflicts of interest to report regarding the present study.

_{2}O

_{3}/water nanofluid with variable properties in an annular enclosure under magnetic field

_{3}O

_{4}/water) using galerkin finite element analysis