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Hybrid Nanofluid Unsteady MHD Natural Convection in an Inclined Wavy Porous Enclosure with Radiation Effect, Partial Heater and Heat Generation/Absorption

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Abstract

In this study, the flow and heat transfer components of convection are numerically investigated in a hybrid nanofluid-filled, porous-medium enclosure with wavy walls. The flow is considered to be buoyancy-driven under a constant inclined magnetic field and heat radiation (Rd). The cavity is partially heated from its left wall and is cooled by its wave-like right wall while the other walls are adiabatic. To express the results, streamlines, isothermal, and the Nu are used. Analysis is done to determine how heat transfer is affected by thermal radiation (Rd), the Hartmann number Ha, the inclined magnetic field, the left heater’s dimensionless location (D), the heat source’s dimensionless length (B), and the hybrid nanofluid’s volume fraction. The average Nusselt number is increased when the volume friction of hybrid nanofluids increases. Additionally, as the dimensionless heat source length B rises, the rate of heat generation rises as well, enhancing the buoyancy force while reducing the impact of shear-driven force. The left heater’s dimensionless position, D = 0.7, exhibits the largest local Nu in contrast to other occurrences. It was found that the minimum Nu occurred at the heat generation/absorption coefficient Q = − 8 at the lowest wall of the enclosure because the intensity of the isothermal formed at the upper wall of the enclosure was greater than that at the bottom of the enclosure in comparison to other cases. The results also showed that, due to the irreversibility of magnetic force, which is one of the main processes for heat transmission, isentropic lines diffuse toward the interior of the enclosure as porosity decreases. On the surface of the enclosure’s vertical left wall (Y-axis at X = 0), the Nu shows as symmetrical profiles, and it can be seen that the Nu increases as the wave length of the wavy walls diminishes. The effects of the Hartmann number and Darcy number on streamlines and isothermal temperature are also investigated.

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Abbreviations

\(B_{0}\) :

Magnetic field strength (m)

b :

Heat source length (m)

B :

Dimensionless heat source length

Da:

Darcy number (= K/h2)

H :

Length of cavity (m)

Nus :

Local Nusselt number (W/m2/K)

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

Average Nusselt number of heat source (W/m2/K)

\(p\) :

Fluid pressure (Pa)

u, v :

Velocity components in x, y directions (ms−1)

\(P\) :

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

\(\Pr\) :

Prandtl number \(( = \upsilon_{f} /\alpha_{f} )\)

\(x,y\) :

Cartesian coordinates (m)

Rd:

Thermal radiation

Ha:

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

T :

Temperature (K)

T C :

Cold wall temperature (K)

\(U,V\) :

Dimensionless velocity components \(( = \left( {u,v} \right)H/\alpha_{f} )\)

X, Y :

Dimensionless coordinates (x/H, y/H)

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

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

T h :

Heated wall temperature (K)

Ra:

Rayleigh number \(( = g\beta_{f} \left( {T_{{\text{h}}} - T_{{\text{c}}} } \right)H^{3} /\alpha_{f} \nu_{f} )\)

g :

Acceleration due to gravity (m s−2)

\(k\) :

Thermal conductivity (Wm−1 K−1)

k*:

The mean absorption coefficient

K :

Permeability of porous medium

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\mu\) :

Dynamic viscosity (Ns m−2)

\(\theta\) :

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

\(\phi\) :

Solid volume fraction

\(\rho\) :

Density (kg m−3)

\(\alpha\) :

Thermal diffusivity (\(( = k/\rho \,c_{p} ),{\text{m}}^{2} \;{\text{s}}^{ - 1}\)

\(\sigma\) :

Effective electrical conductivity \((\upmu \,{\text{S}}/{\text{cm}})\)

\(\sigma *\) :

Stephan–Boltzman constant

\(\tau\) :

Dimensionless time parameter

\(\nu\) :

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

p :

Nanoparticle

\(m\) :

Average

\(f\) :

Pure fluid

\(h\) :

Hot

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

Hybrid Nanofluid

\(c\) :

Cold

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

Nanofluid

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Authors and Affiliations

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

    T. Armaghani

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

    A. M. Rashad

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

    Hussein Togun

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

    M. A. Mansour

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

    T. Salah

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  1. T. Armaghani
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Correspondence to T. Armaghani.

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Armaghani, T., Rashad, A.M., Togun, H. et al. Hybrid Nanofluid Unsteady MHD Natural Convection in an Inclined Wavy Porous Enclosure with Radiation Effect, Partial Heater and Heat Generation/Absorption. Iran J Sci Technol Trans Mech Eng (2024). https://doi.org/10.1007/s40997-023-00720-3

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