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Thermal performance in transient MHD thermogravitational convection of nanofluid with various heating effects

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Abstract

This work presents numerical simulation of two-dimensional thermogravitational energy transport in a chamber filled with copper–water (\({\hbox {Cu-H}}_\mathrm{2} \hbox {O}\)) nanoliquid under the uniform magnetic impact. In this study, our aim is to analyze the characteristic role of nanoliquid thermal conductivity under the influence of various thermal boundary conditions with constant magnetic effect. The mathematical model of the flow physics consists of the Navier–Stokes (N–S) equations written using streamfunction–vorticity (\(\psi\)--\(\zeta\)) variables including the energy transport equation. The governing equations are solved by using a higher-order compact scheme based on finite difference method. The impact of key characteristics including nanoliquid volume fraction (\(0\le \phi \le 0.04\)), Rayleigh number (\(10^{4}\le {\hbox {Ra}}\le 10^{6}\)), Hartmann number (\(0\le {\hbox {Ha}}\le 60\)) and amplitude of heating (\(0\le I \le 1\)) is analyzed in detail. It is found that the energy transport augmentation occurs with nonuniform heating over uniform heating and the rate of thermal transmission rises with a growth of \({\hbox {Ra}}\) and \(\phi\) but it decreases with the growth of \({\hbox {Ha}}\) number. In addition, the transient structures are very useful for understanding the thermo- and magnetohydrodynamic problems.

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Abbreviations

\(B_0\) :

Magnetic field strength (\({\hbox {Amp m}}^{-1}\))

\(C_\mathrm{p}\) :

Specific heat (\({\hbox {J kg}}^{-1} {\hbox {K}}^{-1}\))

g :

Gravitational acceleration (\({\hbox {m s}}^{-2}\))

\({\hbox {Ha}}\) :

Hartmann number (\(B_0L\sqrt{\sigma _\mathrm{nf}/\rho _\mathrm{nf}\nu _{\rm f}}\))

I :

Dimensionless amplitude of heating

k :

Thermal conductivity (\({\hbox {W m}}^{-1} {\hbox {K}}^{-1}\))

L :

Length of the side of a square cavity (m)

\({\hbox {Nu}}\) :

Nusselt number

p :

Dimensional pressure (\({\hbox {N m}}^{-2}\))

P :

Dimensionless pressure

\({\hbox {Pr}}\) :

Prandtl number

\({\hbox {Ra}}\) :

Rayleigh number

t :

Dimensional time

\(T_\mathrm{h}\) :

Temperature of hot bottom wall (K)

\(T_\mathrm{c}\) :

Temperature of cold vertical wall (K)

U, V :

Dimensionless velocities in X, Y directions, respectively

X, Y :

Dimensionless Cartesian coordinates

\(\xi\), \(\eta\) :

Dimensionless coordinate in computational plane

\(\nu\) :

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

\(\rho\) :

Density (kg \({\hbox {m}}^{-3}\))

\(\mu\) :

Dynamic viscosity (Pa s)

\(\alpha\) :

Thermal diffusivity (\({\hbox {m}}^{2}\,{\hbox {s}}^{-1})\)

\(\beta\) :

Thermal expansion coefficient (\({\hbox {K}}^{-1}\))

\(\gamma\) :

Frequency of the temperature oscillation

\(\sigma\) :

Electrical conductivity (\(\upmu {\hbox {S cm}}^{-1}\))

\(\iota\) :

Dimensionless time

\(\phi\) :

Solid volume fraction

\(\varphi\) :

Phase deviation angle

\(\theta\) :

Dimensionless temperature

\(\lambda\) :

Stretching parameter

i, j:

Cell faces

nf:

Nanofluid

f:

Fluid

s:

Solid

b:

Bottom wall

m:

Average

c:

Cold wall

h:

Hot wall

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Authors and Affiliations

  1. Department of Mathematics, Government General Degree College, Ranibandh, Bankura, West Bengal, 722 135, India

    Anirban Chattopadhyay

  2. Integrated Science Education and Research Centre (ISERC), Visva-Bharati, Santiniketan, West Bengal, 731 235, India

    Krishno D. Goswami & Swapan K. Pandit

  3. Laboratory on Convective Heat and Mass Transfer, Tomsk State University, Tomsk, Russia, 634050

    Mikhail A. Sheremet

Authors
  1. Anirban Chattopadhyay
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  2. Krishno D. Goswami
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  3. Swapan K. Pandit
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  4. Mikhail A. Sheremet
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Correspondence to Krishno D. Goswami.

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Chattopadhyay, A., Goswami, K.D., Pandit, S.K. et al. Thermal performance in transient MHD thermogravitational convection of nanofluid with various heating effects. J Therm Anal Calorim 146, 1255–1281 (2021). https://doi.org/10.1007/s10973-020-10077-3

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