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On the role of enclosure side walls thickness and heater geometry in heat transfer enhancement of water–Al2O3 nanofluid in presence of a magnetic field

Sensitivity analysis and optimization
  • Seyed Masoud VahediEmail author
  • Ahmad Hajatzadeh Pordanjani
  • Somchai Wongwises
  • Masoud Afrand
Article
  • 39 Downloads

Abstract

The natural heat convection within a square enclosure filled with water–Al2O3 nanofluid has been studied numerically in the presence of a magnetic field. The effect of heat source geometry attached to the bottom wall on the Nusselt number was investigated by changing its nondimensional width and height, and side walls thickness of the enclosure ranging from 0.1 to 0.5, 0.1 to 0.8 and 0.05 to 0.2, respectively. A regression model has been obtained along with conducting a sensitivity analysis seeking an optimal heat transfer. Results, reveal that Nusselt number increases by enlarging the fin, and reaching a peak point before it declines. Thus, interestingly, the ever-increasing heat transfer by means of fin size does not retain and there is an optimal point wherein the maximum heat transfer occurs. Moreover, the thermal performance of the system largely depends on the fin size rather than the relative side walls thickness. However, its effect intensifies as the fin width increases. Results of optimization show that the maximum heat transfer occurs at \(W = 0.4615\), \(H = 0.6467\) and \(L_{\text{b}} = 0.2\).

Keywords

Water–Al2O3 nanofluid Square enclosure Brownian motion MHD flow Response surface methodology 

List of symbols

B0

Magnetic intensity

Cp

Specific heat \(\left( {{\text{j}}{\kern 1pt} \,{\text{kg}}^{ - 1} .{\text{k}}^{ - 1} } \right)\)

d

Nanoparticles diameter \(({\text{m}})\)

h

Convection heat transfer coefficient \(({\text{wm}}^{ - 2} \,{\text{k}}^{ - 1} )\)

H

Heater nondimensional height (-)

Ha

Hartmann number

k

Thermal conductivity \(\left( {{\text{wm}}^{ - 1} {\text{k}}^{ - 1} } \right)\)

\(K^{*}\)

Conductivity ratio (\(k_{\text{s}} /k_{\text{f}}\))

Lb

Side walls nondimensional thickness (-)

\(Nu\)

Nusselt number (\({\text{hl}}/k_{\text{f}}\))

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

Local Nusselt number \(\left( {{\text{hl}}/k_{\text{f}} } \right)\)

\(Nu_{\text{m}}\)

Averaged Nusselt number \(\left( {{\text{hl}}/k_{\text{f}} } \right)\)

\(\bar{p}\)

Modified pressure (\(p + \rho gy\))

P

Pressure \(\left( {\bar{P}l^{2} /\rho_{\text{nf}} \alpha_{\text{f}}^{2} } \right)\)

Pr

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

Ra

Rayleigh number \(\left( {g\beta_{\text{f}} l^{3} (T_{\text{h}} - T_{{{\text{c}})}} /\alpha_{\text{f}} \vartheta_{f} } \right)\)

T

Temperature (K)

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

Brownian motion velocity \(\left( {{\text{ms}}^{ - 1} } \right)\)

U,V

Interstitial velocity components \(\left( {U = ul/\alpha_{\text{f}} ,\;V = \nu l/\alpha_{\text{f}} } \right)\)

W

Heater nondimensional width (-)

X, Y

Coordinates (x/l, y/l) \(\left( {X = x/l, \,Y = y/l} \right)\)

Greek symbols

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

Magnetic field angle (°)

α

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

ϕ

Nanofluid concentration (-)

kb

Boltzmann constant

θ

Nondimensional temperature(-)

μ

Dynamic viscosity \(({\text{wm}}^{ - 1} \,{\text{k}}^{ - 1} )\)

υ

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

ρ

Density (\({\text{kgm}}^{ - 3} )\)

σ

Electrical conductivity \(\left( {\varOmega .{\text{m}}} \right)\)

\(\gamma\)

Inclination angle (°)

Subscripts

ave

Average

c

Cold

f

Pure fluid

h

Hot

max

Maximum

nf

Nanofluid

s

Nanoparticles

Notes

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringSemnan UniversitySemnanIran
  2. 2.Gas Refining Technology Group, Gas Research DivisionResearch Institute of Petroleum Industry (RIPI)TehranIran
  3. 3.Department of Mechanical EngineeringShahrekord UniversityShahrekordIran
  4. 4.Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of EngineeringKing Mongkut’s University of Technology ThonburiBangkokThailand
  5. 5.Department of Mechanical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran

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