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# Investigation of free convection heat transfer and entropy generation of nanofluid flow inside a cavity affected by magnetic field and thermal radiation

• Ahmad Hajatzadeh Pordanjani
• Saeed Aghakhani
• Arash Karimipour
• Masoud Afrand
• Marjan Goodarzi
Article
• 37 Downloads

## Abstract

In this paper, the effect of the presence of radiation on the convection heat transfer rate and the nanofluid entropy generation within a diagonal rectangular chamber is investigated numerically in the presence of a magnetic field. The governing equations have been solved via finite volume method using the simple algorithm. In this paper, the effects of Rayleigh number, Hartmann number, magnetic field angle changes, chamber angle changes, entropy parameter, radiation parameter and volume percent of nanoparticles on the entropy generation and heat transfer have been investigated. The results show that with increasing Rayleigh number and decreasing the Hartmann number, the Nusselt number and entropy generation increase and the Bejan number decreases. By increasing the angle of the magnetic field, the heat transfer rate and the entropy generation are reduced and the Bejan number increases. By increasing the angle of the chamber at high Rayleigh numbers, the heat transfer rate increases, or by adding 6% of the nanoparticles to the base fluid, the heat transfer rate increases by 9.3% and the entropy generation increases by 15.5% in the absence of radiation. This increase in the Rd = 3 radiation parameter is 5.4% and 6.2%, respectively. It was also observed that the Nusselt number and the entropy generation increased, and with increasing the radiation parameter, the Bejan number decreased. Increasing the heat transfer rate is more significant at higher Rayleigh numbers by increasing the radiation parameter.

## Keywords

Radiation effects Entropy generation Magnetic field Nanofluid

## List of symbols

B

Magnetic field strength

Be

Bejan number, $$Be = {\raise0.7ex\hbox{{S_{\text{gen,T}} }} \!\mathord{\left/ {\vphantom {{S_{\text{gen,T}} } {S_{\text{Total}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{S_{\text{Total}} }}}$$

$$C_{\text{p}}$$

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

g

Gravity (m s−2)

H

Enclosure height

Ha

Hartmann number, $$Ha = B_{0} l\sqrt {\frac{{\sigma_{\text{f}} }}{{\rho_{\text{f}} \vartheta_{\text{f}} }}}$$

k

Thermal conductivity (W mK−1)

L

Thickness of enclosure

Nu

Nusselt number, hl/k

P

Pressure (Pa)

Pr

Prandtl number, $${\raise0.7ex\hbox{{\vartheta_{\text{f}} }} \!\mathord{\left/ {\vphantom {{\vartheta_{\text{f}} } {\alpha_{\text{f}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{\alpha_{\text{f}} }}}$$

Ra

Rayleigh number, $$Ra = \frac{{g\beta_{\text{f}} l^{3} (T_{\text{h}} - T_{\text{c}} )}}{{\alpha_{\text{f}} \vartheta_{\text{f}} }}$$

Rd

Radiation parameter, $${\text{Rd}} = \frac{{\sigma_{\text{e}} }}{{\beta_{\text{R}} }}\left( {\left( {\rho C_{\text{P}} } \right)_{\text{f}} } \right)$$

S

Entropy (J K−1)

T

Temperature (K)

u

Velocity in x direction (m s−1)

v

Velocity in y direction (m s−1)

xy

Cartesian coordinates (m)

## Greek letters

$$\sigma$$

The electrical conductivity [(Ω m)−1]

$$\varphi$$

Solid volume fraction

$$\alpha$$

Thermal diffusivity (m2 s−1), $${\raise0.7ex\hbox{k} \!\mathord{\left/ {\vphantom {k {\rho C_{\text{p}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{{\rho C_{\text{p}} }}}$$

$$\rho$$

Density (kg m−2)

$$\mu$$

Dynamic viscosity (kg m−2)

$$\psi$$

Stream function value

## Subscripts

C

Cold

f

Fluid (pure water)

H

Hot

m

Average

nf

Nanofluid

p

Nanoparticle

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## Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

## Authors and Affiliations

• Ahmad Hajatzadeh Pordanjani
• 1
• Saeed Aghakhani
• 2
• Arash Karimipour
• 2
• Masoud Afrand
• 2
• Marjan Goodarzi
• 3
Email author
1. 1.Department of Mechanical EngineeringShahrekord UniversityShahrekordIran
2. 2.Department of Mechanical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran
3. 3.Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour SafetyTon Duc Thang UniversityHo Chi Minh CityVietnam