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Numerical investigation on the effect of magnetic field on natural convection heat transfer from a pair of embedded cylinders within a porous enclosure

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Abstract

The present work examines the influence of magnetohydrodynamic field on natural convection phenomena inside a porous square enclosure with a pair of embedded hot circular cylinders. Numerical investigations are performed to understand the effects of interspacing distance between the embedded cylinders, Hartmann number, Rayleigh number and Darcy number on the thermal transport process and the total irreversibility generation. It is observed that the isotherm distribution is strongly affected by the presence of magnetic field although the distribution of streamlines remains independent of the strength of magnetic field. This underlines the fact that magnetic field strongly influences the heat transfer process and entropy generation characteristics. It reveals that the natural convection is suppressed in the presence of a higher magnetic field as evident from the reduction in Nusselt number. It is observed that an increase in the spacing between the cylinders increases the heat transfer rate, and moreover, the effect of the magnetic field on heat transfer is more pronounced at higher interspacing distance between the embedded cylinders. The heat transfer rate increases significantly with the increase in the permeability of the medium. The entropy generation rate is independent of the strength of applied magnetic field. Further, the contribution of the entropy generation owing to friction is found to be negligible in total irreversibility obtained at lower values of Rayleigh number irrespective of Darcy number. However, the contribution of irreversibility owing to heat transfer is found to be minimal at higher values of Rayleigh number.

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Abbreviations

B 0 :

Applied magnetic field (N m−1 A−1)

Be :

Bejan number

c p :

Specific heat capacity at constant pressure (J K−1)

d :

Diameter of the embedded cylinder (m)

D :

Dimensionless diameter of the embedded cylinder (dL−1)

Da :

Darcy number \((\kappa /L^{2} )\)

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2 K−2)

Ha :

Hartmann number \(\left({{\text{B}_{0}\text{L}}\sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma \mu }} \right. \kern-0pt} \mu }} } \right)\)

k :

Thermal conductivity (W m−1 K−1)

L :

Side length of the square enclosure (m)

Nu φ :

Local Nusselt number

\(\overline{\text{Nu}}\) :

Surface average Nusselt number

\(\overline{\text{Nu}_{\text{t}} }\) :

Time average Nusselt number

N θ,T :

Dimensionless volumetric thermal entropy generation

N Ψ,T :

Dimensionless volumetric viscous entropy generation

N mf,T :

Dimensionless volumetric magnetic field entropy generation

p :

Pressure (Pa)

P * :

Dimensionless pressure \(\left( {{{pL^{2} } \mathord{\left/ {\vphantom {{pL^{2} } {\rho \alpha^{2} }}} \right. \kern-0pt} {\rho \alpha^{2} }}} \right)\)

Pr :

Prandtl number, \(\left( {{{\mu c_{\text{p}} } \mathord{\left/ {\vphantom {{\mu c_{\text{p}} } k}} \right. \kern-0pt} k}} \right)\)

Ra :

Rayleigh number, \(\left( {{{g\beta \left( {T_{\text{h}} - T_{\text{c}} } \right)L^{3} \Pr } \mathord{\left/ {\vphantom {{g\beta \left( {T_{\text{h}} - T_{\text{c}} } \right)L^{3} \Pr } {\upsilon^{2} }}} \right. \kern-0pt} {\upsilon^{2} }}} \right)\)

s :

Distance between cylinders, (m)

S :

Dimensionless distance between cylinders, (s/L)

T c :

Minimum temperature, (K)

T h :

Maximum temperature, (K)

u, v :

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

U*, V* :

Dimensionless velocity components in X and Y directions, \(\left( {{{uL} \mathord{\left/ {\vphantom {{uL} \alpha }} \right. \kern-0pt} \alpha },{{vL} \mathord{\left/ {\vphantom {{vL} \alpha }} \right. \kern-0pt} \alpha }} \right)\)

x, y :

Cartesian coordinates, (m)

X*, Y* :

Cartesian coordinates in dimensionless form, \(\left( {{x \mathord{\left/ {\vphantom {x L}} \right. \kern-0pt} L},{y \mathord{\left/ {\vphantom {y L}} \right. \kern-0pt} L}} \right)\)

\(\alpha\) :

Thermal diffusivity, (m2 s−1)

\(\beta\) :

Coefficient of thermal expansion, (K−1)

θ :

Dimensionless temperature, \(\left( {{{T - T_{\text{c}} } \mathord{\left/ {\vphantom {{T - T_{\text{c}} } {T_{\text{h}} - T_{\text{c}} }}} \right. \kern-0pt} {T_{\text{h}} - T_{\text{c}} }}} \right)\)

κ :

Permeability, (m2)

µ :

Dynamic viscosity, (N s m−2)

ν :

Kinematic viscosity, (m2 s−1)

σ :

Electrical conductivity, (S m−1)

ρ :

Fluid density, (kg m−3)

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Acknowledgements

The authors acknowledge the financial support from TEQIP-III, NIT Silchar.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar, 788010, India

    Debayan Bhowmick, Subhasis Chakravarthy, Pitambar R. Randive & Sukumar Pati

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  1. Debayan Bhowmick
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Correspondence to Pitambar R. Randive.

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Bhowmick, D., Chakravarthy, S., Randive, P.R. et al. Numerical investigation on the effect of magnetic field on natural convection heat transfer from a pair of embedded cylinders within a porous enclosure. J Therm Anal Calorim 141, 2405–2427 (2020). https://doi.org/10.1007/s10973-020-09411-6

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