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An investigation of Marangoni-Benard convection in water based nanofluids

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Abstract

The impact of copper nanoparticles on Marangoni-Benard convection in water-based nanofluids was investigated numerically by examining the effect of variations in the Rayleigh and Marangoni numbers for different values of the Biot number. The aspect ratio of the cavity, and the interaction of the buoyant forces and forces due to surface tension inhomogeneity were also investigated. The relationship between these parameters and the heat transfer behavior was then determined by examining the average Nusselt number. This allowed the development of a methodology by which the critical values of the Rayleigh number and the Marangoni number could be identified. The results indicated that the average Nusselt number increased with increases in the Biot number. In addition, the presence of the copper nanoparticles enhanced the heat transfer rate significantly, with the positive enhancement increasing with increased Biot number.

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Abbreviations

C :

Gladstone-Dale constant

c p :

Specific heat

g :

Gravitational acceleration

H :

Height

h :

Surface heat transfer coefficient

k :

Thermal conductivity

L :

Width

L b :

Length of the model in the beam direction

n :

Refractive index

P :

Non-dimensional pressure

p :

Pressure

q :

Heat flux

S :

Fringe number

T :

Temperature

T r :

Reference temperature

u, v :

Velocity components in x and y direction

U, V :

Non-Dimensional velocity components in X and Y direction

x, y :

Cartesian coordinates

X, Y :

Non-dimensional Cartesian coordinates

α :

Thermal diffusivity

β :

Coefficient of thermal expansion

λ :

Wavelength

ϕ :

Concentration of nanoparticles

ρ :

Density

σ :

Surface tension

θ :

Non-dimensional temperature

μ :

Viscosity

ν :

Kinematic viscosity

AR:

Aspect Ratio L/H

Bi :

Biot number

Ma :

Marangoni Number

Nu :

Nusselt number

Pr :

Prandtl number

Ra :

Rayleigh number

C :

Free stream

f :

Property of base fluid

h :

Hot

nf :

Property of nanofluid

r :

Reference Section

s :

Property of nanoparticle added

t :

Test section

w :

Wall

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Calicut, Kerala, 673 601, India

    Dhairya R. Vyas & C. B. Sobhan

  2. School of Nano Science & Technology, National Institute of Technology Calicut, Kerala, 673 601, India

    C. B. Sobhan

  3. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    G. P. Peterson

Authors
  1. Dhairya R. Vyas
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  2. C. B. Sobhan
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  3. G. P. Peterson
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Correspondence to Dhairya R. Vyas.

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Vyas, D.R., Sobhan, C.B. & Peterson, G.P. An investigation of Marangoni-Benard convection in water based nanofluids. Heat Mass Transfer 55, 791–809 (2019). https://doi.org/10.1007/s00231-018-2452-x

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