Numerical study of entropy generation in MHD water-based carbon nanotubes along an inclined permeable surface

  • Feroz Ahmed Soomro
  • Rizwan-ul-Haq
  • Z. H. Khan
  • Qiang Zhang
Regular Article


Main theme of the article is to examine the entropy generation analysis for the magneto-hydrodynamic mixed convection flow of water functionalized carbon nanotubes along an inclined stretching surface. Thermophysical properties of both particles and working fluid are incorporated in the system of governing partial differential equations. Rehabilitation of nonlinear system of equations is obtained via similarity transformations. Moreover, solutions of these equations are further utilized to determine the volumetric entropy and characteristic entropy generation. Solutions of governing boundary layer equations are obtained numerically using the finite difference method. Effects of two types of carbon nanotubes, namely, single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) with water as base fluid have been analyzed over the physical quantities of interest, namely, surface skin friction, heat transfer rate and entropy generation coefficients. Influential results of velocities, temperature, entropy generation and isotherms are plotted against the emerging parameter, namely, nanoparticle fraction \(0\le \phi \le 0.2\), thermal convective parameter \(0\le \lambda \le 5\), Hartmann number \(0\le M\le 2\), suction/injection parameter \(-1\le S\le 1\), and Eckert number \(0\le Ec \le 2\). It is finally concluded that skin friction increases due to the increase in the magnetic parameter, suction/injection and nanoparticle volume fraction, whereas the Nusselt number shows an increasing trend due to the increase in the suction parameter, mixed convection parameter and nanoparticle volume fraction. Similarly, entropy generation shows an opposite behavior for the Hartmann number and mixed convection parameter for both single-wall and multi-wall carbon nanotubes.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of Electrical EngineeringBahria UniversityIslamabadPakistan
  3. 3.Department of MathematicsUniversity of Malakand, Dir (Lower)Khyber PakhtunkhwaPakistan

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