Multiple solutions for non-Newtonian nanofluid flow over a stretching sheet with nonlinear thermal radiation: Application in transdermal drug delivery


We have explored multiple solutions for non-Newtonian Casson nanofluid flow past a moving extending sheet under the influence of variable thermal conductivity and nonlinear radiation through a permeable medium with convective boundary conditions. The governing equations are transformed to ODEs by similarity transformations and then solved numerically by the Chebyshev pseudospectral (CPS) method. Dual solutions are obtained for velocity, temperature and nanoparticle concentration distributions with different values of physical parameters. In the present analysis, it was found that, the nonlinearity formula for thermal radiation gives a realistic description of nanofluid mathematical model depending on the existence of nanoscale particles. Furthermore, the concentration of nanoparticles is highly influenced by nonlinear thermal radiation due to the sizes of nanofluid, where linear radiation has a weak effect on the concentration distributions of nanoparticles. These results are very important in medicine, and more specifically for reinforcing the delivery of drugs through the skin, as the nanoparticle entrapment of drugs enhances delivery to, or absorption by, target cells. The transdermal drug delivery system offers huge clinical advantages over other dosage forms. As transdermal drug delivery offers controlled as well as predetermined rate of release of the drug into the patient, it can keep up steady-state nanofluid concentration.

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The authors are thankful to the reviewers for their constructive suggestions and encouraging comments to improve the final form of this manuscript.

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Correspondence to Nasser S Elgazery.

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Elgazery, N.S., Elelamy, A.F. Multiple solutions for non-Newtonian nanofluid flow over a stretching sheet with nonlinear thermal radiation: Application in transdermal drug delivery. Pramana - J Phys 94, 68 (2020).

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  • Multiple solutions
  • non-Newtonian nanofluid
  • variable thermal conductivity
  • nonlinear radiation
  • convective boundary condition
  • Chebyshev pseudospectral method
  • porous medium


  • 44.20.+b
  • 65.80.–g
  • 02.20.–a
  • 47.50.–d