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Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu–water nanofluid

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Abstract

In this work, the influences of heat generation/absorption and nanofluid volume fraction on the entropy generation and MHD combined convection heat transfer in a porous enclosure filled with a Cu–water nanofluid are studied numerically with of partial slip effect. The finite volume technique is utilized to solve the dimensionless equations governing the problem. A comparison with already published studies is conducted, and the data are found to be in an excellent agreement. The minimization of entropy generation and the local heat transfer according to various values of the controlling parameters are reported in detail. The outcome indicates that an augmentation in the heat generation/absorption parameter decreases the Nusselt number. Also, when the volume fraction is raised, the Nusselt number and entropy generation are reduced. The impact of Hartmann number on heat transfer and the Richardson number on the entropy generation and the thermal rendering criteria are also presented and discussed.

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Abbreviations

B :

Dimensionless of heat source/sink length

\( B_{0} \) :

Magnetic field strength (T)

\( Be \) :

Bejan number

\( b \) :

Length of heat source (m)

\( C_{\text{p}} \) :

Specific heat at constant pressure \( ( {\text{J}}\;{\text{kg}}\;{\text{K}}^{ - 1} ) \)

D :

Dimensionless heat source position

Da :

Darcy number

d :

Location of heat sink and source (m)

H :

Length of cavity (m)

Ha :

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

Gr :

Grashof number, \( g\beta_{\text{f}} H^{3} \Delta T/\upsilon^{2}_{\text{f}} \)

g :

Acceleration due to gravity (m s−2)

K :

Permeability of porous medium (m2)

k :

Thermal conductivity (W m−1 K−1)

Nu :

Local Nusselt number

\( Nu_{\text{m}} \) :

Average Nusselt number of heat source

\( p \) :

Fluid pressure (Pa)

\( P \) :

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

Pr :

Prandtl number, \( \upsilon_{\text{f}} /\alpha_{\text{f}} \)

Re :

Reynolds number, \( V_{0} H/\upsilon_{\text{f}} \)

S :

Entropy generation (W K−1 m−3)

T :

Temperature (K)

\( T_{\text{c}} \) :

Cold wall temperature (K)

\( T_{\text{h}} \) :

Heated wall temperature (K)

u,v :

Velocity components in x, y directions (m s−1)

\( U,V \) :

Dimensionless velocity components, u/V 0, v/V 0

\( x,y \) :

Cartesian coordinates (m)

\( X,Y \) :

Dimensionless coordinates, x/L, y/L

\( \alpha \) :

Thermal diffusivity, \( {\text{m}}^{2} \;{\text{s}}^{ - 1} ,{\text{k}}/\rho c_{\text{p}} \)

\( \beta \) :

Thermal expansion coefficient, K−1

\( \phi \) :

Solid volume fraction

σ :

Effective electrical conductivity \( (\upmu {\text{S}}\;{\text{cm}}^{ - 1} ) \)

\( \theta \) :

Dimensionless temperature, \( {{(T - T_{\text{c}} )} \mathord{\left/ {\vphantom {{(T - T_{\text{c}} )} {(T_{\text{h}} - T_{\text{c}} }}} \right. \kern-0pt} {(T_{\text{h}} - T_{\text{c}} }}) \)

\( \mu \) :

Dynamic viscosity (N s m−2)

\( \nu \) :

Kinematic viscosity \( ( {\text{m}}^{2} \;{\text{s}}^{ - 1} ) \)

\( \rho \) :

Density (kg m−3)

c:

Cold

0:

Reference

f:

Pure fluid

h:

Hot

m:

Average

nf:

Nanofluid

p:

Nanoparticle

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Authors and Affiliations

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

    A. J. Chamkha

  2. Rak Research and Innovation Center, American University of Ras Al Khaimah, Ras Al Khaimah, United Arab Emirates

    A. J. Chamkha

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

    A. M. Rashad

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

    T. Armaghani

  5. Department of Mathematics, Faculty of Science, Assuit University, Assuit, Egypt

    M. A. Mansour

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  1. A. J. Chamkha
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Correspondence to T. Armaghani.

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Chamkha, A.J., Rashad, A.M., Armaghani, T. et al. Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu–water nanofluid. J Therm Anal Calorim 132, 1291–1306 (2018). https://doi.org/10.1007/s10973-017-6918-8

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