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Optimization and sensitivity analysis of magneto-hydrodynamic natural convection nanofluid flow inside a square enclosure using response surface methodology

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Abstract

This article studies buoyancy-driven natural convection of a nanofluid affected by a magnetic field within a square enclosure with an individual conductive pin fin. The effects of electromagnetic forces, thermal conductivity, and inclination angle of pin fin were investigated using non-dimensional parameters. An extensive sensitivity analysis was conducted seeking an optimal heat transfer setting. The novelty of this work lies in including different contributing factors in heat transfer analysis, rigorous analysis of design parameters, and comprehensive mathematical analysis of solution domain for optimization. Results showed that magnetic strength diminished the heat transfer efficacy, while higher relative thermal conductivity of pin fin improved it. Based on the problem settings, we also obtained the relative conductivity value in which the heat transfer is optimal. Higher sensitivity of heat transfer was, though, noticed for both magnetic strength and fin thermal conductivity in comparison to fin inclination angle. Further studies, specifically with realistic geometrical configurations and heat transfer settings, are urged to translate current findings to industrial applications.

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Abbreviations

B 0 :

Magnetic field strength

C p :

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

d :

Nanoparticle diameter, \(\left[ {\text{nm}} \right]\)

g :

Gravitational acceleration, [m s−2]

h :

Convection heat transfer coefficient, \(\left[ {{\text{W}}\;{\text{m}}^{ - 2} \;{\text{K}}^{ - 1} } \right]\)

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

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

d :

Nanoparticle diameter, \(\left[ {\text{nm}} \right]\)

Ha :

Hartmann number

k :

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

\(K^{*}\) :

Fin relative thermal conductivity, \(\left( {k_{\text{s}} /k_{\text{f}} } \right)\)

l :

Enclosure length, \(\left[ {\text{nm}} \right]\)

L :

Enclosure non-dimension length

\(Nu\) :

Nusselt number

\(Nu_{\text{s}}\) :

Local Nusselt number

\(Nu_{\text{ave}}\) :

Average Nusselt number

\(p\) :

Pressure, \(\left[ {\text{Pa}} \right]\)

\(\bar{P}\) :

Modified pressure, \(\left[ {\text{Pa}} \right]\)

P :

Non-dimensional pressure,\(\left( {{{\bar{P}l^{2} } \mathord{\left/ {\vphantom {{\bar{P}l^{2} } {\rho_{\text{nf}} \alpha_{\text{f}}^{2} }}} \right. \kern-0pt} {\rho_{\text{nf}} \alpha_{\text{f}}^{2} }}} \right)\)

Pr :

Prandtl number \((\vartheta_{\text{f}} /\alpha_{\text{f}} )\)

Ra :

Rayleigh number \(\left( {{{g\beta_{\text{f}} l^{3} \left( {{\text{T}}_{\text{h}} - {\text{T}}_{\text{c}} } \right)} \mathord{\left/ {\vphantom {{g\beta_{\text{f}} l^{3} \left( {{\text{T}}_{\text{h}} - {\text{T}}_{\text{c}} } \right)} {\alpha_{\text{f}} \vartheta_{f} }}} \right. \kern-0pt} {\alpha_{\text{f}} \vartheta_{\rm f} }}} \right)\)

T :

Temperature, [K]

u, v :

Velocity components in x and y directions, \(\left[ {{\text{m}}\;{\text{s}}^{ - 1} } \right]\)

\(v_{\text{Br}}\) :

Brownian motion velocity, \(\left[ {{\text{m}}\;{\text{s}}^{ - 1} } \right]\)

U, V :

Non-dimensional velocity components in x and y directions \(\left( {U = {{ul} \mathord{\left/ {\vphantom {{ul} {\alpha_{\text{f}} }}} \right. \kern-0pt} {\alpha_{\text{f}} }},V = {{vl} \mathord{\left/ {\vphantom {{vl} {\alpha_{\text{f}} }}} \right. \kern-0pt} {\alpha_{\text{f}} }}} \right)\)

x, y :

Cartesian coordinates, \(\left[ {\text{m}} \right]\)

X, Y :

Non-dimensional coordinates \(\left( {X = x/l,Y = y/l} \right)\)

\(\alpha_{\text{m}}\) :

Magnetic field angle, [°]

\(\alpha\) :

Thermal diffusivity, \(\left[ {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right]\)

\(\phi\) :

Solid volume fraction

\(k_{\text{b}}\) :

Boltzmann constant, \(\left[ {{\text{m}}^{2} \;{\text{kg}}\;{\text{s}}^{2} \;{\text{K}}^{1} } \right]\)

\(\theta\) :

Non-dimensional temperature

\(\mu\) :

Dynamic viscosity, \(\left[ {{\text{W}}\;{\text{m}}^{ - 1} \;{\text{K}}^{ - 1} } \right]\)

\(\vartheta\) :

Kinematic viscosity, \(\left[ {{\text{m}}^{2} \;{\text{s}}^{ - 1} } \right]\)

\(\rho\) :

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

\(\sigma\) :

Electrical conductivity, \(\left[ {\varOmega \;{\text{m}}} \right]\)

\(\gamma\) :

Fin angle, [°]

\(\psi\) :

Stream function

c:

Cold

h:

Hot

f:

Pure fluid

max:

Maximum

ave:

Average

nf:

Nanofluid

s:

Fin properties

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Shahrekord University, Shahrekord, Iran

    Ahmad Hajatzadeh Pordanjani

  2. Department of Mechanical Engineering, Faculty of Engineering, Semnan University, P.O.B. 35131-19111, Semnan, Iran

    Seyed Masoud Vahedi

  3. Gas Refining Technology Group, Gas Research Division, Research Institute of Petroleum Industry (RIPI), P.O. Box 14665-137, Tehran, Iran

    Seyed Masoud Vahedi

  4. Institute for Medical Engineering and Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Farhad Rikhtegar

  5. Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok, Thailand

    Somchai Wongwises

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  1. Ahmad Hajatzadeh Pordanjani
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Correspondence to Seyed Masoud Vahedi.

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Pordanjani, A.H., Vahedi, S.M., Rikhtegar, F. et al. Optimization and sensitivity analysis of magneto-hydrodynamic natural convection nanofluid flow inside a square enclosure using response surface methodology. J Therm Anal Calorim 135, 1031–1045 (2019). https://doi.org/10.1007/s10973-018-7652-6

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