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Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media

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Abstract

A numerical investigation of entropy generation due to MHD-free convective of Cu–water nanofluid in a porous I-shaped cavity is reported. The cavity is under Darcy law with inclined uniform magnetic field. The cavity is cooled from the top and a part of bottom wall subjected to uniform heat flux, while the other parts of walls of the cavity are adiabatic. Mathematical pattern formulated employing the single-phase nanofluid approach in governing equations the problem has been solved by finite difference technique. Prime efforts have been concentrated on the impacts of the pertinent parameters on the fluid flow and heat transfer inside the cavity. Numerical data have been plotted in the form of streamlines, isotherms, and average Nusselt numbers. The results show that the Nu number decreases via increasing the Ha number. It increases when the Ra number is increased. The maximum and minimum values of Nusselt occur at B = 0.2 and B = 0.8, respectively. Exerting an angle for magnetic flux leads to the improvement in thermal performance for all amount of B. The effects of Ha, nanofluid volume fraction, heat source size, location and angle of magnetic field on heat transfer, entropy generation, and thermal performance are completely studied and discussed.

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Abbreviations

B :

Dimensionless of heat source/sink length

B 0 :

Magnetic field strength, T

b :

Length of heat source, m

C p :

Specific heat, J kg−1 K−1

C T :

Difference temperature

D :

Dimensionless heat source position

d :

Location of heat sink and source, m

Da:

Darcy number

g :

Acceleration due to gravity, m s−2

H :

Length of cavity, m

Ha:

Hartmann number, \( B_{0} L\sqrt {\sigma_{\text{f}} /\rho_{\text{f}} \nu_{\text{f}} } \)

K :

Permeability of porous medium, m2

k :

Thermal conductivity, Wm−1 K−1

Nus :

Local Nusselt number

Num :

Average Nusselt number of heat source

p :

Fluid pressure, Pa

P :

Dimensionless pressure, \( {\text{pH}}/\rho_{\text{nf}} \,\alpha_{\text{f}}^{2} \)

Pr:

Prandtl number, vf/αf

Q 0 :

Heat generation coefficient, W m−2

\(q''\) :

Heat flux

Ra:

Rayleigh number, gβf (Th − Tc)H3/αfνf

S :

Entropy generation, WK−1 m−3

T :

Temperature, K

T c :

Cold wall temperature, K

T h :

Heated wall temperature, K

u, v :

Velocity components in x, y directions, m2 s−1

U, V :

Dimensionless velocity components, u/v0, v/v0

x, y :

Cartesian coordinates, m

X, Y :

Dimensionless coordinates, x/L, y/L

\( \alpha \) :

Thermal diffusivity, m2 s−1, k/ρcp

\( \beta \) :

Thermal expansion coefficient, K−1

ϕ :

Solid volume fraction

σ :

Effective electrical conductivity, μS cm−1

\( \theta \) :

Dimensionless temperature, (T − Tc)/(Th − Tc)

\( \mu \) :

Dynamic viscosity, N s m−2

\( \nu \) :

Kinematic viscosity, m2 s−1

\( \rho \) :

Density, kg m−3

Ф:

Angle of enclosure

c:

Cold

0:

Reference

f:

Pure fluid

h:

Hot

m:

Average

nf:

Nanofluid

p:

Nanoparticle

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Author information

Authors and Affiliations

  1. Department of Engineering, Mahdishahr Branch, Islamic Azad University, Mahdishahr, Iran

    T. Armaghani

  2. Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University (PMU), Al-Khobar, 31952, Kingdom of Saudi Arabia

    Ali Chamkha

  3. Department of Mathematics, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    A. M. Rashad

  4. Department of Mathematics, Faculty of Science, Assuit University, Assuit, 71515, Egypt

    M. A. Mansour

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  1. T. Armaghani
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  2. Ali Chamkha
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Armaghani, T., Chamkha, A., Rashad, A.M. et al. Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media. J Therm Anal Calorim 142, 2273–2285 (2020). https://doi.org/10.1007/s10973-020-09449-6

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