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Unsteady MHD hybrid nanofluid mixed convection heat transfer in a wavy porous cavity with thermal radiation

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Abstract

In the current investigation, a (TiO2–Ag/water) hybrid nanofluid (NF), saturated porous medium filled wavy-walled enclosure, and an unstable magneto-mixed convective flow are examined. Heat radiation (Rd) is present with the constant magnetic field (B0), and the cavity, which is partially heated from its bottom wall and cooled from its wavy-left and right walls, contains a square solid block that is solidly surrounded on all sides. The governing PDEs, which are represented in terms of stream function, temperature, and nanoparticle volume percent, are numerically solved using a finite volume technique. It is discovered that as the dimensionless heat source length (B) rises, the streamlines' strength marginally changes while the isotherms in the wavy porous cavity grow increasingly obvious. The results show that increasing the number of undulations and hybrid NF generally produces a higher average Nusselt number when the wave amplitude parameter A = 0.3 and the volume fractions of (TiO2 − Ag/water) Hybrid NF = 0.05. Raising the volume percentage of Hybrid NF enhances the average Nusselt number while increasing the Hartmann number observed happened with decreases the average Nusselt number. One of the primary factors contributing to the production of entropy is the irreversibility of the magnetic force, which leads the isentropic lines to diffuse toward the interior of the enclosure as Ha rises. In comparison with previous case studies, the highest Nusselt number is at λ = 3, and it rises in every case as the wave amplitude parameter and the percentage of hybrid NF volume increase. It was discovered that increasing porosity greatly increased local Nusselt numbers due to improved heat transfer within the enclosure. The lowest local Nusselt number has been determined to be Q = − 2, which represents the heat generation/absorption factor.

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Abbreviations

A :

Wave amplitude parameter (m)

b :

Heat source length, (m)

B :

Dimensionless heat source length (T)

\(B_{0}\) :

Magnetic field strength, (T) (N/A m2)

\(C_{{\text{p}}}\) :

Specific heat at constant pressure, (\({\text{J}}\;{\text{kg}}^{ - 1} \;{\text{K}}^{ - 1}\))

D :

Heat source position (m)

D :

Dimensionless heat source position (−)

Da:

Darcy number

H :

Length of cavity, (m)

Ha:

Hartmann number, \(B_{0} H\sqrt {\sigma_{{\text{f}}} /\rho_{{\text{f}}} \nu_{{\text{f}}} }\)

Gr:

Grashof number, \(g\beta_{{\text{f}}} \,H^{3} \Delta T/\upsilon^{2}_{{\text{f}}}\)

G :

Acceleration due to gravity, m s−2)

\(k\) :

Thermal conductivity, (wm−1kk−1)

Nus :

Local Nusselt number (W m−2 K−1)

\({\text{Nu}}_{{\text{m}}}\) :

Average Nusselt number of heat source (W m−2 K−1)

\(p\) :

Fluid pressure, Pa

\(P\) :

Dimensionless pressure, \(p\,H/\rho_{{{\text{nf}}}} \,\alpha_{{\text{f}}}^{2}\)

\(\Pr\) :

Prandtl number, \(\upsilon_{{\text{f}}} /\alpha_{{\text{f}}}\)

Rd:

Thermal radiation parameter

Re:

Reynolds number, U0H/vf

Q 0 :

Dimensional heat generation/absorption parameter

Q :

Heat generation/absorption factor (Wm−2)

T :

Dimensional time, (s)

T :

Temperature, (K)

T c :

Cold wall temperature, (K)

T h :

Heated wall temperature, (K)

U 0 :

Constant speed (m s−1)

u, v :

Velocity components in x, y directions, (m s−1)

\(U,V\) :

Dimensionless velocity components, (u/U0, v/U0) (−)

\(x,y\) :

Cartesian coordinates, (m)

X, Y :

Dimensionless coordinates, (x/H, y/H) (−)

α :

The cavity inclination angle

\(\alpha_{{{\text{eff}}}}\) :

Effective thermal diffusion, \({\text{m}}^{{2}} \;{\text{s}}^{{ - {1}}}\), \(k/\rho \,c_{{\text{p}}}\)(m2 s−1)

\(\beta\) :

Thermal expansion coefficient, (k−1)

\(\phi\) :

Solid volume fraction

\(\Phi\) :

Inclination angle of magnetic field

Ε :

Porosity factor

\(\lambda\) :

Undulations number (m)

\(\sigma\) :

Effective electrical conductivity, μS/cm

\(\theta\) :

Dimensionless temperature, (T − Tc)/(Th − Tc)(−)

\(\mu\) :

Dynamic viscosity, (N s m−2)

\(\nu\) :

Kinematic viscosity, (\({\text{m}}^{2} \;{\text{s}}^{ - 1}\))

\(\rho\) :

Density, kg m−3

\(\tau\) :

Dimensionless of time (−)

Ag:

Silver nanoparticles

Bf:

Base fluid (m3)

\(c\) :

Cold

\(f\) :

Pure fluid

\(h\) :

Hot

\(m\) :

Average

\({\text{nf}}\) :

Nanofluid

\({\text{hnf}}\) :

Hybrid nanofluid

p :

Nanoparticle (nm)

TiOs :

Titanium dioxide

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    A. M. Rashad

  2. Department of Mechanical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq

    Hussein Togun

  3. Department of Mathematics, Faculty of Science, Assuit University, Assuit, 71515, Egypt

    M. A. Mansour

  4. Basic and Applied Sciences Department, College of Engineering and Technology, Aswan Branch, Arab Academy for Science & Technology and Maritime Transport (AASTMT), Aswan, Egypt

    T. Salah

  5. Department of Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran

    T. Armaghani

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Rashad, A.M., Togun, H., Mansour, M.A. et al. Unsteady MHD hybrid nanofluid mixed convection heat transfer in a wavy porous cavity with thermal radiation. J Therm Anal Calorim 149, 2425–2442 (2024). https://doi.org/10.1007/s10973-023-12690-4

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