Similarity and Boubaker Polynomials Expansion SchemeBPEScomparative solutions to the heat transfer equation for incompressible non-Newtonian fluids: case of laminar boundary energy equation

MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation

“…The nanofluid is assumed incompressible and the flow is laminar, the base fluid and the nanoparticles are in thermal equilibrium and that no slippage occurs between them. Under these assumptions, the governing conservation equations of mass, momentum and energy in unsteady state can be expressed as [13][14][15][16][17][18][19][20][21][22][41][42][43][44][45][46][47][48][49][50][51][52] @u @x þ @v @y…”

“…The effects of power law viscosity on a temperature field are taken into account with a modified Fourier's law proposed by assuming that the temperature field is similar to the velocity field [41][42][43][44][45][46][47][48][49][50][51][52]. External magnetic field and internal heating effects are considered.…”

MHD Marangoni boundary layer flow and heat transfer of pseudo-plastic nanofluids over a porous medium with a modified model

“…A generalized Fourier law proposed by Zheng for varying thermal conductivity of nanofluids is taken into account (Zheng et al 2006(Zheng et al , 2008(Zheng et al , 2011. Unlike the classical Boussinesq effect on the body force term in buoyancy-induced flows, the Marangoni surface tension effect acts as a boundary condition on the governing equations of the flow field.…”

“…μU/(kρ nf ) is the porous medium item, k is the permeability of the porous medium (Zhang et al 2015), T is the temperature of the nanofluid, T ∞ is a reference temperature, and A is a positive constant; α = α nf |∂T /∂Y | n−1 is the thermal diffusivity proposed by Zheng for power-law fluid media (Zheng et al 2006(Zheng et al , 2008(Zheng et al , 2011, and k nf is the effective thermal conductivity of the nanofluid. The related parameters of the nanofluid are given by Palm et al (2006), Abu-Nada (2008), Abu-Nada et al (2008), Lin et al (2014Lin et al ( , 2015aLin et al ( , 2015b:…”

“…It is assumed that a variable magnetic field is applied along the interface. A generalized Fourier law proposed by Zheng (2006Zheng ( , 2008Zheng ( , 2011 for varying thermal conductivity of nanofluids is taken into account, and the surface tension is assumed to be a quadratic term function of the temperature (Slavtchev and Miladinova 1998). The Navier-Stokes momentum equations and the thermal energy equation are reduced to strongly nonlinear ODEs, and the solutions are studied numerically.…”