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Natural convection in a horizontal cylindrical annulus filled with a porous medium saturated by a nanofluid using Tiwari and Das’ nanofluid model

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Abstract

This paper deals with a numerical study of natural convection flow and heat transfer inside a concentric horizontal annulus filled with a porous medium saturated by a cuprum (Cu)-water nanofluid. The inner and outer cylinders are kept at different constant temperatures. First, the governing partial differential equations in dimensional formulation in a polar coordinate system for the physical domain are transformed in dimensionless form in terms of stream function-temperature formulation. These equations along with the corresponding boundary conditions were solved numerically by the finite difference method. Particular efforts have been focused on the effects of the Rayleigh number, porosity of the porous medium, solid volume fraction parameter of nanoparticles, annulus radius ratio, and the solid matrix of the porous medium (glass balls and aluminum foam) on the local and average Nusselt numbers, streamlines and isotherms. It is found that a very good agreement exists between the present results and those from the open literature.

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Abbreviations

C p :

specific heat at a constant pressure

g :

gravitational acceleration

H(φ):

special function

K :

permeability of the porous medium

k :

thermal conductivity

Nu :

local Nusselt number along the internal cylindrical surface

\(\overline {Nu}\) :

average Nusselt number at the internal cylindrical surface

r :

dimensionless radial coordinate

\(\bar r\) :

dimensional radial coordinate

\(\bar r_1\) :

radius of internal cylinder

\(\bar r_2\) :

radius of external cylinder

R :

annulus radius ratio

Ra :

Rayleigh number for the porous medium

T :

dimensional temperature

T c :

temperature of cold external cylinder

Th :

temperature of hot internal cylinder

u, v :

dimensionless Darcian velocity components

\(\bar u,\bar v\) :

dimensional Darcian velocity components

α :

thermal diffusivity

β :

thermal expansion coefficient

γ :

azimuthal coordinate

Δr :

step along r-coordinate

Δγ :

step along γ-coordinate

ε :

porosity of the porous medium

θ :

dimensionless temperature

μ :

dynamic viscosity

ρ :

density

ρC p :

heat capacitance

ρβ :

buoyancy coefficient

φ :

uniform concentration of the nanoparticles

ψ :

dimensionless stream function

c :

cold

f :

fluid

h :

hot

m :

clear fluid saturated with porous medium

max :

maximum value

min :

minimum value

mnf :

nanofluid saturated with porous medium

nf :

nanofluid

p :

(nano) particle

s :

solid matrix of the porous medium

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Author information

Authors and Affiliations

  1. Department of Theoretical Mechanics, Faculty of Mechanics and Mathematics, Tomsk State University, 634050, Tomsk, Russia

    M. A. Sheremet

  2. Institute of Power Engineering, Tomsk Polytechnic University, 634050, Tomsk, Russia

    M. A. Sheremet

  3. Department of Applied Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Ioan Pop

Authors
  1. M. A. Sheremet
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  2. Ioan Pop
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Correspondence to Ioan Pop.

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Sheremet, M.A., Pop, I. Natural convection in a horizontal cylindrical annulus filled with a porous medium saturated by a nanofluid using Tiwari and Das’ nanofluid model. Eur. Phys. J. Plus 130, 107 (2015). https://doi.org/10.1140/epjp/i2015-15107-4

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