The magnetohydrodynamics (MHD) viscous Jeffrey heat transport flow past a permeable extending sheet is analyzed. The Alumina ([Formula: see text]) is chosen as nanoparticles immersed in sodium alginate ([Formula: see text]) as the based fluid. The effect of heat generation, Ohmic heating and viscous dissipation are also being investigated adopting Tiwari and Das model. The adequate similarity transformation is used to convert the governing equations to non-linear of higher-order ordinary differential equations (ODEs). The numerical solution of the transformed ODEs is accomplished using a finite-difference technique. The results are described in graphs according to selected parameters' values provided. The flow velocity reductions when the porosity parameter is augmented. The thermal distribution is affected by the presence of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Deborah number and the volume fraction of nanoparticles affect the skin friction coefficient in opposite ways. A higher volume percentage of nanoparticles and a higher Deborah number are both shown to boost the rate of heat transfer. These findings suggest that the concentration of nanoparticles can be used to manipulate heat transport and nanofluid motions.