Zero and nonzero normal uxes of thermal radiative boundary layer ow of nano uid over a radially stretched surface

The axisymmetric ow of a nanoparticles-saturated uid with existence of thermic radiation over a stretched sheet is investigated. The eects of zero (passive control) as well as nonzero uxes (active control) of nanoparticles on the plate on distributions of temperature and volumetric fraction of nanoparticles are investigated together comparatively. Through the supposition of boundary layer, the Navier-Stokes equations are simplied hence converted into non-dimensional form by similarity transformation. A shooting technique is engaged to deal with the emerging nonlinear system of ordinary dierential equations numerically in MATLAB software. Several distributions of velocity, thermal energy, and volumetric fraction of nanoparticles under zero/nonzero normal ux are graphically demonstrated. The impact of the parameters on the reduced coecient of skin friction, Nur and Shr, are also investigated. The presence of thermic radiation under consideration of both zero and nonzero normal uxes has signicant eects on the intensication of the ow heat transfer. Thermophoresis enhances the heat conductivity performance in the case of zero uxes of nanoparticles.