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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 1
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Original Articles

Unsteady natural convection heat transfer of nanofluid in an annulus with a sinusoidally heated source

, , &
Pages 97-108 | Received 13 Feb 2015, Accepted 17 Apr 2015, Published online: 23 Sep 2015
 

ABSTRACT

We study the unsteady natural convection of nanofluid between the outer and inner surfaces of a concentric annulus. The inner surface is heated sinusoidally with time about a fixed mean temperature but the outer boundary is kept at a constant temperature. The effects of Brownian motion and thermophoresis are taken into account. Numerical solutions are presented using the continuous finite-element method. Results indicate that the heat and mass transfer rates are significantly influenced by inner wall temperature oscillation, which presents periodic triangle fluctuation for the considered parameters of amplitude A, inner circle radius R, and frequency F.

Nomenclature

a, A=

amplitude, dimensionless amplitude

Cp=

specific heat at constant pressure

DB=

Brownian diffusion coefficient

DT=

thermophoretic diffusion coefficient

F=

dimensionless oscillating frequency

g=

gravitational acceleration

k=

thermal conductivity

L=

gap between inner and outer boundaries of the enclosure (=r0ri)

Le=

Lewis number (=α/DB)

Nb=

Brownian motion parameter (=(ρc)pDB(ϕhϕc)/((ρc)f α))

Nt=

thermophoresis parameter (=(ρc)pDT(ThTc)/((ρc)f αTc))

Nu=

local surface Nusselt number

Nuave=

inner surface-averaged Nusselt number

Nuτ=

time-averaged Nusselt number

Nr=

buoyancy ratio number

p, P=

pressure, dimensionless pressure

Pr=

Prandtl number (=µ/ρfα)

r, R=

inner circle radius, dimensionless inner circle radius

Ra=

Rayleigh number

Sh=

local surface Sherwood number

Shave=

inner surface-averaged Sherwood number

Shτ=

time-averaged Sherwood number

t=

time

T=

temperature

u, v=

velocity components along x- and y-axes

U, V=

dimensionless velocity components in the X- and Y-directions

x, y & X, Y=

space coordinates and dimensionless space coordinates

α=

thermal diffusivity

β=

thermal expansion coefficient

ζ=

angular location

Θ=

dimensionless temperature

µ=

dynamic viscosity

ν=

kinematic viscosity

ρ=

density

τ=

dimensionless time

ϕ=

concentration

Φ=

dimensionless concentration

ψ=

stream function

ω=

oscillating frequency

Subscripts=
ave=

average

c=

cold

h=

hot

i=

inner

loc=

local

o=

outer

w=

condition on the sheet

τ=

time-averaged

=

condition far away from the plate

Nomenclature

a, A=

amplitude, dimensionless amplitude

Cp=

specific heat at constant pressure

DB=

Brownian diffusion coefficient

DT=

thermophoretic diffusion coefficient

F=

dimensionless oscillating frequency

g=

gravitational acceleration

k=

thermal conductivity

L=

gap between inner and outer boundaries of the enclosure (=r0ri)

Le=

Lewis number (=α/DB)

Nb=

Brownian motion parameter (=(ρc)pDB(ϕhϕc)/((ρc)f α))

Nt=

thermophoresis parameter (=(ρc)pDT(ThTc)/((ρc)f αTc))

Nu=

local surface Nusselt number

Nuave=

inner surface-averaged Nusselt number

Nuτ=

time-averaged Nusselt number

Nr=

buoyancy ratio number

p, P=

pressure, dimensionless pressure

Pr=

Prandtl number (=µ/ρfα)

r, R=

inner circle radius, dimensionless inner circle radius

Ra=

Rayleigh number

Sh=

local surface Sherwood number

Shave=

inner surface-averaged Sherwood number

Shτ=

time-averaged Sherwood number

t=

time

T=

temperature

u, v=

velocity components along x- and y-axes

U, V=

dimensionless velocity components in the X- and Y-directions

x, y & X, Y=

space coordinates and dimensionless space coordinates

α=

thermal diffusivity

β=

thermal expansion coefficient

ζ=

angular location

Θ=

dimensionless temperature

µ=

dynamic viscosity

ν=

kinematic viscosity

ρ=

density

τ=

dimensionless time

ϕ=

concentration

Φ=

dimensionless concentration

ψ=

stream function

ω=

oscillating frequency

Subscripts=
ave=

average

c=

cold

h=

hot

i=

inner

loc=

local

o=

outer

w=

condition on the sheet

τ=

time-averaged

=

condition far away from the plate

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