The present work investigates the transfer of heat, mass and fluid flow at the boundary layer of a nanofluid past a wedge in the presence of a variable magnetic field, temperature-dependent heat source and chemical reaction. The study is entirely theoretical and the proposed model describes the influence of Brownian motion and thermophoresis in the case of nanofluids. This study also includes the impact of thermal radiation. The partial differential equations relating to the flow are nonlinear and hence are numerically solved after transforming them into ordinary differential equations with similar variables. The outcome of the present study is given in tabular form and depicted graphically. It is found that the nanofluid flow along the wedge is accelerated by enhancing the Falkner–Skan parameter. The study further reveals that the magnetic field has an improved effect on the velocity. The Brownian motion parameter raises the profile of temperature but decreases the profile of volume fractions. Thermal radiation decreases the energy transport rate to the fluid and hence reduces the degree of heat present in the fluid. It is also observed that heat sink blankets the surface with a layer of cold fluid.

This work focusses on deriving exact analytic solutions for an oscillatory flow of an elastico-viscous conducting fluid in a porous medium over a moving plate with variable suction. The momentum equation is enhanced with the resisting force offered by the permeability of the medium by incorporating the Darcy model. The energy transfer is equipped with volumetric heat generation/absorption and thermal radiation. Exact solutions for the governing equations are obtained by employing Cardan’s method, and comparative discussion is made by using the perturbation technique. The temperature distribution is evaluated by solving the energy equation considering relaxation time. Solutions of velocity fields are obtained for any value of viscoelastic parameter k$_1$. The results obtained from the analytical and approximation methods for any value of viscosity parameter are compared and found to be in good agreement. The physical behaviour of the pertinent parameters is obtained and displayed in graphs.