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Thermal analysis of nanofluid saturated in inclined porous cavity cooled by rotating active cylinder subjected to convective condition

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Abstract

Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper.

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Abbreviations

C p :

Specific heat at constant pressure (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

L :

Length & height of the cavity (m)

Nu:

Nusselt number

P :

Dimensionless pressure

p :

Pressure (Pa)

Pr :

Prandtl number (νf/αf)

q :

Heat transfer rate (W m−2)

R :

Radius of the solid cylinder

Ra:

Rayleigh number \((g\beta _{{{\text{bf}}}} L^{3} (T_{{\text{h}}} - T_{\infty } )/\nu _{{{\text{bf}}}} \alpha _{{{\text{bf}}}} )\)

T :

Temperature (K)

U :

Dimensionless velocity component in x-direction

u :

Velocity component in x-direction (m s−1)

V :

Dimensionless velocity component in y-direction

v :

Velocity component in y-direction (m s−1)

X, Y :

Dimensionless coordinate

x, y :

Cartesian coordinates (m)

x 0, y 0 :

Cartesian coordinate of the rotating cylinder 

X 0,Y 0 :

Dimensionless coordinate of the rotating cylinder

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

θ :

Dimensionless temperature (T − T∞/Th − T∞)

μ :

Dynamic viscosity (kg s m−1)

ν :

Kinematic viscosity (μ /ρ)(Pa s−1)

ρ :

Density (kg m−3)

ϕ :

Nanoparticle volume fraction (%)

ψ :

Dimensional stream function (m2 s−1)

Ψ :

Dimensionless stream function

ω :

Angular velocity (rad s−1)

Ω :

Dimensionless angular velocity

ave:

Average

bf:

Base fluid (pure)

c:

Cold

h:

Hot

loc:

Local

na:

Nanofluid

so:

Conductive solid cylinder

sp:

Solid particle

Cond.:

Conduction

Conv.:

Convection

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Authors and Affiliations

  1. Mechanical Engineering Department, College of Engineering, University of Babylon, Hillah, Iraq

    Mohammed Y. Jabbar, Hameed K. Hamzah, Farooq H. Ali & Saba Y. Ahmed

  2. Mechanical Engineering Department, Engineering College, University of Basrah, Basrah, Iraq

    Muneer A. Ismael

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  1. Mohammed Y. Jabbar
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  2. Hameed K. Hamzah
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  3. Farooq H. Ali
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  5. Muneer A. Ismael
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Correspondence to Farooq H. Ali.

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Jabbar, M.Y., Hamzah, H.K., Ali, F.H. et al. Thermal analysis of nanofluid saturated in inclined porous cavity cooled by rotating active cylinder subjected to convective condition. J Therm Anal Calorim 144, 1299–1323 (2021). https://doi.org/10.1007/s10973-020-09668-x

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