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Optimum constituents for MHD heat transfer of nanofluids within porous cavities

A Taguchi analysis in natural and mixed convection configurations

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Abstract

In this paper, the Taguchi experimental design method is utilized to determine optimum combination of constituents for MHD heat transfer of nanofluids in porous cavities in natural and mixed convection configurations. The tested constituents include ethylene glycol and water for the base fluid, silver, aluminum oxide, carbon nanotubes, cobalt, copper, copper oxide, ferroferric oxide, and titanium oxide for the nanoparticles, and aluminum foam and glass balls for the solid matrix. The governing equations are those presented by Buongiorno that include Brownian diffusion and thermophoresis effect which are solved numerically. In the Taguchi experimental design method, the mean Nusselt number is considered as the performance parameter and an L16 orthogonal array is used as the experimental plan for the control factors. Analysis is undertaken for several Hartmann numbers (i.e., \(Ha = 0, \,1,\, 30\)). The optimum design in all of the circumstances is achieved for CuO–water nanofluid within glass balls. In the mixed convection configuration, the most important factor affecting the heat transfer is found to be the solid matrix material. But, in the natural convection configuration, with an increase in the strength of the magnetic field, the highest contribution shifts from the nanoparticles type to the solid matrix material. The outcomes of this contribution provide insight into design of thermal systems.

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Abbreviations

\(a_{\text{i}}\) :

Defined in Eq. (17)

\(B_{0}\) :

Externally applied horizontal magnetic field \(\left( {\text{T}} \right)\)

\(C\) :

Specific heat \(\left( {{\text{J}}\,{\text{kg}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

dB:

Decibel

D B :

Brownian diffusion coefficient \(({\text{m}}^{2} \,{\text{s}}^{ - 1} )\)

D T :

Thermophoretic diffusion coefficient \(({\text{m}}^{2} \,{\text{s}}^{ - 1} )\)

g :

Gravitational acceleration \(\left( {{\text{m}}\,{\text{s}}^{ - 2} } \right)\)

Ha :

Hartmann number

k :

Thermal conductivity \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

K :

Permeability \(\left( {{\text{m}}^{2} } \right)\)

L :

Size of the cavity \(\left( {\text{m}} \right)\)

Le :

Lewis number

N TB :

Ratio between thermophoresis and Brownian coefficients

Nu :

Local Nusselt number

\(\overline{Nu}\) :

Mean Nusselt number

P :

Pressure \(\left( {\text{Pa}} \right)\)

Pe :

Peclet number

Ra :

Rayleigh number

\({\text{SNR}}\) :

Signal-to-noise ratio \(\left( {\text{dB}} \right)\)

t :

Time \(\left( {\text{s}} \right)\)

T :

Temperature \(\left( {\text{K}} \right)\)

u, v :

Velocity components \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)

\(u_{\text{in}}\) :

Inlet velocity \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)

V :

Velocity vector \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)

\(x, y\) :

Cartesian coordinates \(\left( {\text{m}} \right)\)

\(X, Y\) :

Dimensionless Cartesian coordinates

\(\alpha\) :

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

\(\beta\) :

Volumetric thermal expansion coefficient \(\left( {{\text{K}}^{ - 1} } \right)\)

\(\varepsilon\) :

Porosity

\(\bar{\varPhi }\) :

Nanoparticles fraction

\(\varPhi\) :

Dimensionless nanoparticles fraction

\(\mu\) :

Dynamic viscosity \(\left( {{\text{N}}\,{\text{s}}\,{\text{m}}^{ - 2} } \right)\)

\(\xi\) :

Stream function temperature, or nanoparticles fraction in Eq. (25)

\(\varTheta\) :

Dimensionless temperature

\(\rho\) :

Density \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)

\(\sigma\) :

Electrical conductivity \(\left( {\varOmega^{ - 1} \,{\text{m}}^{ - 1} } \right)\)

\(\tau\) :

Dimensionless time

\(\psi\) :

Stream function \(({\text{m}}^{2} \,{\text{s}}^{ - 1} )\)

Ψ:

Dimensionless stream function

\(\omega\) :

Defined by \(\left( {\rho c} \right)_{\text{mf}} /\left( {\rho c} \right)_{\text{f}}\)

Ω:

Control volume

0:

Reference value

c:

Cold

f:

Base fluid

h:

Hot

mf:

Clear fluid-saturated porous medium

mnf:

Nanofluid-saturated porous medium

nf:

Nanofluid

p:

Nanoparticle

s:

Solid matrix

AF:

Aluminum foam

ANOVA:

Analysis of variance

EG:

Ethylene glycol

GB:

Glass balls

MHD:

Magnetohydrodynamics

W:

Water

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Authors and Affiliations

  1. Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Iman Zahmatkesh & Mohammad Reza Habibi Shandiz

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  1. Iman Zahmatkesh
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  2. Mohammad Reza Habibi Shandiz
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Correspondence to Iman Zahmatkesh.

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Zahmatkesh, I., Shandiz, M.R.H. Optimum constituents for MHD heat transfer of nanofluids within porous cavities. J Therm Anal Calorim 138, 1669–1681 (2019). https://doi.org/10.1007/s10973-019-08191-y

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