Hydromagnetic convective–radiative boundary layer flow of nanofluids induced by a non-linear vertical stretching/shrinking sheet with viscous–Ohmic dissipation

Existence of the multiple exact solutions for nanofluid flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects

“…Further, ( ) nf denotes the nanofluid quantities which are defined as follows (see [12], [13], [21], [71], [79])…”

“…Later, this subject becomes a classical type of fluid flow and has then a long history. For existence of the dual solutions in the shrinking case, it should be mentioned that many researchers have proved that the first solutions are stable and physically realizable, whilst those of the second solutions are not, see for example the research work done by Rosça and Pop [9], Rahman et al [10], Nandy and Pop [11], Pal and Mandal ([12], [13]), thermore, on studying the shrinking sheet, the resulting equations have been difficulty solved by a long analytical presentation [19], combination of a symbolic power series and Padé approximation [20], Runge-Kutta-Fehlberg fourth order technique or Dormand-Prince pair, both along with shooting method using software packages as BVP4C in MATLAB ( [9], [10]) or RFK45 in MAPLE [21] where guess starting values are needed. The other popular numerical methods applicable in this type of research have been listed by Kamyar et al [22] and Uddin et al [23].…”

Index, Volume 9, 2018

“…Pandey and Kumar (2018b) analyzed the influence of MHD flow of nanofluid through a stretching/shrinking convergent/divergent channel with viscous dissipation. Pal and Mandal (2015) analyzed the impact of magnetohydrodynamic and viscous dissipation on fluid flow past a vertical stretching/shrinking sheet in cooperation with thermal radiation and Ohmic heating. Mabood et al (2015) discussed the consequence of mass and heat transfer plus MHD flow of nanofluids past a nonlinear stretching surface numerically.…”

Flow and Heat Transfer of a Carbon Nanofluids Over Verticle Plate

“…They used convective boundary conditions for heat and mass transfer and classical transformation are used as well as a series of solutions of the problem are obtained. The author Pal and Mandal (2015) study deals with the MHD boundary layer flow of an electrically conducting convective nanofluid are used in a non-linear vertical shrinking sheet with viscous ohmic dissipation. They pointed various parameter in their studies and basic non-metallic nanoparticles like copper (cu), alumina (Al2O3) and titanium (TiO2) in the base fluid water.…”