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Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

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Abstract

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

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Abbreviations

a, b :

wavy wall parameters

c p :

specific heat at constant pressure

g :

gravitational acceleration vector

Gr :

Grashof number

H 1,H 2,H 3 :

additional functions

k :

thermal conductivity

L,H :

cavity sizes (width, height)

Nu :

local Nusselt number

\(\overline {Nu} \) :

average Nusselt number

p :

dimensional pressure

Pr :

Prandtl number

Ra :

Rayleigh number

T :

dimensional temperature

t :

dimensional time

T c :

cold temperature of left and right vertical walls and upper wall

T w :

non-uniform temperature of the bottom wall

u, v :

dimensionless velocity components

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

dimensional velocity components

x, y :

dimensionless Cartesian coordinates

\(\bar x,\bar y\) :

dimensional Cartesian coordinates

α :

thermal diffusivity

β :

thermal expansion coefficient

γ :

cavity inclination angle

θ :

dimensionless temperature

κ :

undulation number

μ :

dynamic viscosity

ξ, η :

new independent variables

ρ :

density

ρc:

heat capacitance

ρβ :

buoyancy coefficient

τ :

dimensionless time

ϕ :

nanoparticles volume fraction

ψ :

dimensionless stream function

ω :

dimensionless

c:

cold

f:

fluid

nf:

nanofluid

p:

particle

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Acknowledgements

The work of Pop, Groşan, and Trîmbiţaş has been supported from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania. The authors also wish to express their thank to the very competent Reviewers for the valuable comments and suggestions.

Author information

Authors and Affiliations

  1. Laboratory on Convective Heat and Mass Transfer, Tomsk State University, Tomsk, 634050, Russia

    M. A. Sheremet

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

    R. Trîmbiţaş, T. Groşan & I. Pop

Authors
  1. M. A. Sheremet
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  2. R. Trîmbiţaş
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  3. T. Groşan
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  4. I. Pop
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Corresponding author

Correspondence to R. Trîmbiţaş.

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Citation: SHEREMET, M. A., TRÎMBIŢAŞ, R., GROŞAN, T., and POP, I. Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model. Applied Mathematics and Mechanics (English Edition), 39(10), 1425–1436 (2018) https://doi.org/10.1007/s10483-018-2377-7

Project supported by the Ministry of Education and Science of the Russian Federation (No. 13.6542.2017/6.7)

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Sheremet, M.A., Trîmbiţaş, R., Groşan, T. et al. Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model. Appl. Math. Mech.-Engl. Ed. 39, 1425–1436 (2018). https://doi.org/10.1007/s10483-018-2377-7

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  • DOI: https://doi.org/10.1007/s10483-018-2377-7

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