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MHD Mixed Convection of Nanofluid in a Lid-Driven Porous Trapezoidal Cavity with a Heated Obstacle

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Abstract

This study uses numerical simulation to model MHD mixed convection nanofluid flow within a permeable trapezoidal chamber with a heated obstacle. Considered are the volume fractions (1–5%) of copper (Cu), alumina (Al2O3), and silver (Ag) nano-sized particles when mixed with water (H2O). With a constant velocity, upper wall moves left to right while bottom wall steps from right to left. A lower temperature is kept on upper wall, while left, right, and bottom walls are kept at warmed. There are two types of obstacles inside the enclosure: a constant square heated obstacle (case-I) and a heat-generating square obstacle (case-II). To investigate how the liquid flow and heat transport properties within the chamber are impacted with the Darcy number (Da) and Richardson number (Ri), the governing PDEs are solved by Galerkin weighted residual based finite element technique. Results are compared to published papers to validate the computational process. The findings are displayed using streamlines, isotherms, temperature, and velocity profiles, and mean Nusselt numbers. The outcomes demonstrate that when Richardson number rises, heat transportation rate increases. It is shown that an effective control parameter for temperature transport is Darcy number. Moreover, it is found that when only 5% nanoparticles are used, heat transport rate augment by 17.12%. Richardson number is an effective control parameter for heat transport via a porous material enclosure. Mass and heat transport rates both rise with an increment in the thermal Darcy number. Furthermore, the flow strength rises as Richardson number rises. Moreover, the average Nu increases by 15.27% for 5% nanoparticles volume at \(Da=1{0}^{-2}\) in case I whereas it increases only 0.3% for same number of nanoparticles in case II.

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Since no data was generated or investigated for this article, there is no date sharing available.

Abbreviations

B 0 :

Magnetic induction [Wbm−2]

C p :

Specific heat at constant pressure [Jkg−1 K−1]

q :

Heat flux

∆T :

Dimensional temperature difference [K]

g :

Gravitational acceleration [ms−2]

h :

Convective heat transfer coefficient [Wm−2 K−1]

k :

Thermal conductivity of fluid [W/mK]

L :

Height or base of square cavity [m]

K :

Thermal conductivity ratio fluid

N :

Total number of nodes

Nu av :

Average Nusselt number

Nu l :

Local Nusselt number

P :

Non-dimensional pressure

p :

Pressure

Gr :

Grashof number

Ha :

Hartmann number

Pr :

Prandtl number

Ra :

Rayleigh number

Re :

Reynolds number

Da :

Darcy number

Ri :

Richardson number

T :

Dimensional fluid temperature [K]

T h :

Temperature of hot wall [K]

T c :

Temperature of cold wall [K]

U :

X component of dimensionless velocity

u :

X component of velocity [ms−1]

V :

Y component of dimensionless velocity

v :

Y component of velocity [ms−1]

U 0 :

X component of lid velocity [ms−1]

V 0 :

Y component of lid velocity [ms−1]

x, y :

Cartesian coordinates [m]

X, Y :

Dimensionless coordinates

∝:

Thermal diffusivity [ms−2]

β:

Coefficient of thermal expansion [K−1]

ρ:

Density of the fluid [kg/m3]

∆θ :

Dimensionless temperature difference

θ :

Dimensionless fluid temperature

θ αυ :

Average temperature

μ :

Dynamic viscosity of the fluid [m2s−1]

Ψ :

Stream function

ν :

Kinematic viscosity of the fluid [m2s−1]

σ :

Fluid electrical conductivity [Ω−1 m−1]

ϕ:

Nanoparticle volume fraction

b :

Bottom wall

l :

Left wall

r :

Right wall

c :

Cold

h :

Hot

f :

Base fluid

s :

Nanoparticle

nf :

Nanofluid

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Acknowledgements

The authors are grateful to the editors and reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Salim Uddin Chowdhuri Degree College, Narayongonj, Bangladesh

    Hamida Akter

  2. Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Hamida Akter & Nazma Parveen

  3. Department of Mathematics, Hamdard University Bangladesh, Munshigonj, Bangladesh

    M. Jahirul Haque Munshi

  4. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Gopalganj, Bangladesh

    Tarikul Islam

  5. CMUP, University of Porto, Porto, Portugal

    Tarikul Islam

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  1. Hamida Akter
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Akter, H., Parveen, N., Munshi, M.J.H. et al. MHD Mixed Convection of Nanofluid in a Lid-Driven Porous Trapezoidal Cavity with a Heated Obstacle. Multiscale Sci. Eng. (2024). https://doi.org/10.1007/s42493-024-00113-x

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