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Numerical simulation of thermal management during natural convection in a porous triangular cavity containing air and hot obstacles

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Abstract

A numerical study is presented of laminar viscous magnetohydrodynamic natural convection flow in a triangular-shaped porous enclosure filled with electrically conducting air and containing two hot obstacles. The mathematical model is formulated in terms of dimensional partial differential equations. The pressure gradient term is eliminated by using the vorticity–stream (\(\omega - \psi\)) function approach. The emerging dimensionless governing equations are employed by the regular finite difference scheme along with thermofluidic boundary conditions. The efficiency of the obtained computed results for isotherms and streamlines is validated via comparison with previously published work. The impact of physical parameters on streamlines and temperature contours for an extensive range of Rayleigh number (Ra = 103–105), Hartmann magnetohydrodynamic number (Ha = 5–30), Darcy parameter (Da = 0.0001–0.1) for fixed Prandtl number (Pr = 0.71) is considered. Numerical results are also presented for local and average Nusselt numbers along the hot base wall. Interesting features of the thermofluid behaviour are revealed. At lower Rayleigh number, the isotherms are generally parallel to the inclined wall and only distorted substantially near the obstacles at the left vertical adiabatic wall; however, with increasing Rayleigh number, this distortion is magnified in the core zone and simultaneously warmer zones expand towards the inclined cold wall. The simulations are relevant to magnetic materials processing and hybrid magnetic fuel cells.

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Abbreviations

x :

Coordinate parallel to base of enclosure (m)

y :

Coordinate perpendicular to base of enclosure (m)

g :

Acceleration due to gravity (m/s2)

L :

Length of base and vertical walls of triangular enclosure (m)

u :

X-direction velocity (m/s)

y :

Y-direction velocity (m/s)

B o :

Magnitude of applied magnetic field (Tesla)

K :

Permeability of the porous medium (m2)

p :

Hydrodynamic pressure (Pa)

K :

Effective thermal conductivity of fluid-saturated porous medium (W/mK)

t :

Time (s)

T :

Temperature (K)

C p :

Isobaric specific heat (J/kgK)

σ :

Electrical conductivity of fluid (Siemens/m)

β :

Thermal expansion coefficient of fluid (/K)

μ :

Dynamic viscosity of fluid (kg/ms)

ν :

Kinematic viscosity of fluid (m2/s)

ρ :

Fluid density at reference temperature (kg/m3)

α :

Thermal diffusivity of fluid-saturated porous medium (m2/s)

q :

Heat flux (W/m2)

τ :

Dimensionless time

Ha :

Hartmann hydromagnetic number

Da:

Darcy number

Pr:

Prandtl number

Nu:

Nusselt number

Ra:

Rayleigh number

X :

Dimensionless x coordinate

Y :

Dimensionless y coordinate

U :

Dimensionless u velocity

V :

Dimensionless v velocity

θ :

Dimensionless temperature

ψ:

Stream function

ω :

Vorticity function

()h :

Hot wall (base)

()c :

Cold wall (inclined)

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Authors and Affiliations

  1. Department of Applied Mathematics, Sri Padmavathi Mahila Visvavidyalayam, Tirupati, 517502, India

    Veena chandanam & C. Venkata lakshmi

  2. Department of Mathematics, Sreenivasa Institute of Technology and Management Studies, Chittoor, 517127, India

    K. Venkatadri

  3. Multi-Physical Engineering Sciences Group, Aeronautical/Mechanical Engineering, Salford University, School of Science, Engineering and Environment (SEE), Manchester, M54WT, UK

    O. Anwar Bég

  4. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 6322014, India

    V. Ramachandra Prasad

Authors
  1. Veena chandanam
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  2. C. Venkata lakshmi
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  3. K. Venkatadri
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  5. V. Ramachandra Prasad
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Correspondence to K. Venkatadri.

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chandanam, V., lakshmi, C.V., Venkatadri, K. et al. Numerical simulation of thermal management during natural convection in a porous triangular cavity containing air and hot obstacles. Eur. Phys. J. Plus 136, 885 (2021). https://doi.org/10.1140/epjp/s13360-021-01881-3

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01881-3

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