The present study examines the stagnation point flow of a non-Newtonian fluid along with the Cattaneo–Christov heat flux model. The coupled system is simplified using suitable similar solutions and solved numerically by incorporating the shooting method with the Runge–Kutta of order five. The motivation is to analyse the heat transfer using an amended form of Fourier law of heat conduction known as the Cattaneo–Christov heat flux model. The influences of significant parameters are taken into the account. The computed results of velocity and temperature profiles are displayed by means of graphs. The notable findings are as follows. The viscous and thermal boundary layer exhibits opposite trends for Reynolds number, Deborah number and power-law index. The shear stress at the wall displays reverse patterns for shear thinning and shear thickening fluids. The Prandtl number contributes to increasing the Nusselt number while the Deborah number of heat flux plays the role of reducing it.

In the current study, the flow of Casson liquid thin film, together with heat transfer towards a stretching surface extracting out from a narrow slit in the presence of a magnetic field, viscous dissipation and thermal radiation effects, is examined. The contribution of nanoparticles is investigated by employing the Buongiorno model. Mathematical modelling is carried out in the Cartesian coordinate system and similarity analysis is opted for simplification. The numerical analysis is performed in the reduced system using the shooting method. The effects of the prominent parameters are discussed using line and bar graphs. The key finding is that the temperature drop is prominent in the case of Casson nanofluid compared to the nanofluid.