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Integral treatment for forced convection heat and mass transfer of nanofluids over linear stretching sheet

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Abstract

An integral treatment is proposed for the analysis of the forced convection flow of a nanofluid over a stretching sheet. The obtained results agree well with the numerical results. The results of the presented solution provide an analytic solution, which can be conveniently used in engineering applications. Four types of nanoparticles, i.e., alumina (Al2O3), silicon dioxide (SiO2), silver (Ag), and copper (Cu), dispersed in the base fluid of water are examined. The analytical results show that an increase in the volume fraction of nanoparticles increases the thickness of the thermal boundary layer. The reduced Nusselt number is a decreasing function of the volume fraction of nanoparticles.

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Abbreviations

(ρc)f :

heat capacity of the fluid

(ρc)p :

effective heat capacity of the nanoparticle material

(ρc p )nf :

heat capacity of the nanofluid

∞ :

condition at infinity

D B :

Brownian diffusion coefficient

d p :

nanoparticle diameter

D T :

thermophoretic diffusion coefficient

g :

gravitational acceleration vector

h :

local heat transfer coefficient

h m :

local mass transfer coefficient

h nf :

heat transfer coefficient of the nanofluid

K :

thermal conductivity

K B :

Boltzmann constant

k f :

thermal conductivity of the fluid

k nf :

nanofluid thermal conductivity

k p :

nanoparticle thermal conductivity

Le :

Lewis number

N B :

Brownian motion parameter

N T :

thermophoresis parameter

Nu :

Nusselt number

P :

pressure

Pr :

Prandtl number

Re x :

local Reynolds number

Sh x :

local Sherwood number

T :

temperature

T ∞ :

ambient temperature attained as y tends to infinity

T w :

temperature at the stretching surface

u, v :

velocitycomponents

u w :

velocity of the stretching sheet

w:

condition at the stretching surface

x, y :

Cartesian coordinates

α :

thermal diffusivity

β :

volumetric expansion coefficient of the fluid

Δ:

boundary-layer thickness ratio

δ c :

concentration boundary-layer thickness

δ T :

thermal boundary-layer thickness

τ :

heat capacity ration (ρc)p/(ρc)f

θ(η):

dimensionless temperature profile

μ f :

viscosity of the fluid

μ nf :

viscosity of the nanofluid

ρ f :

fluid density

ρ nf :

nanofluid density

ρ p :

nanoparticle mass density

υ :

kinematic viscosity of the fluid

φ :

nanoparticle volume fraction

φ(η):

dimensionless concentration profile

φ ∞ :

ambient concentration attained as y tends to infinity

φ w :

ambient nanoparticle volume fraction

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 6135743337, Iran

    A. Noghrehabadi, P. Salamat & M. Ghalambaz

Authors
  1. A. Noghrehabadi
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  2. P. Salamat
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  3. M. Ghalambaz
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Correspondence to A. Noghrehabadi.

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Noghrehabadi, A., Salamat, P. & Ghalambaz, M. Integral treatment for forced convection heat and mass transfer of nanofluids over linear stretching sheet. Appl. Math. Mech.-Engl. Ed. 36, 337–352 (2015). https://doi.org/10.1007/s10483-015-1919-6

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  • DOI: https://doi.org/10.1007/s10483-015-1919-6

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