Exact analysis for the effect of heat transfer on MHD and radiation Marangoni boundary layer nanofluid flow past a surface embedded in a porous medium

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

“…Rashidi et al [57] investigated the buoyancy effect on MHD flow of water based nanofluid over a stretching sheet with thermal radiation effect. Very recently, it has been proved that the effective electrical conductivity parameter is mandatory and should be taken into account on applying the magnetic field; otherwise a spurious physical sight is to be gained [58]. This means also that any published results that dropped this term (see for example the recent papers [59], [60], [61], and [62]) have to be reinvestigated.…”

“…Therefore, these figures clarify that Eq. (4c) is mandatory, especially with its presence in the solutions' conditions as in Section 3, and should be taken into account on applying the magnetic field in nanofluids' study, otherwise a false and useless physical view is expected to be obtained [58].…”

Thermal radiation effect on boundary layer over a flat plate having convective surface boundary condition

“…Some recent work on the impact of thermal radiation on the fluid flow considering different geometries includes Cao and Baker [22] who examined heat transfer by radiation on boundary layer through optical fluid past a vertical wall. Aly and Ebaid [23] in their report presented on the role of thermal radiation and suction/injection on boundary layer nanofluid flow over a porous medium considering the induced magnetic field effect concluded that the velocity of the nanofluid flow decreases with volume fraction augment. Hayat et al [24] also presented the role of radiation in a stagnation point flow of carbon nanofluid considering a stretching cylinder.…”

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

“…The basic mechanism and the heat transfer process of Marangoni boundary layer flow have been extensively investigated in many literatures . The nanofluid of Marangoni convection on various occasions has been investigated . Lin and colleagues and Ellahi and colleagues presented research on particle shape effects on Marangoni convection boundary layer flow of a nanofluid.…”

“…[40][41][42] The nanofluid of Marangoni convection on various occasions has been investigated. [43][44][45] Lin and colleagues 46 and Ellahi and colleagues 47 presented research on particle shape effects on Marangoni convection boundary layer flow of a nanofluid. Motivated by the above research, this paper aims to explore the heat transfer characteristics of Marangoni boundary layer flow of a copper-water nanofluid, using the Cattaneo-Christov heat flux model.…”