Susanta Maity

Development of thin Casson liquid (CL) film on a heated nonlinear flat stretching surface is examined under influences of thermal radiation and transverse magnetic field. The velocity and temperature at any point of the stretching surface are assumed as the generalized nonlinear functions of the distance of that point. The analytical expressions for velocity components and temperature are obtained using long-wave approximation technique. The numerical solution for nonlinear film evolution equation is incurred by the Newton–Kantorovich method. It is found that initial non-uniform film thickness becomes flat with due course of time. It is further observed that the film thinning rate enhances for larger values of the Marangoni number and radiation parameter. It is also discovered that the rate of film thinning diminishes for the larger Hartmann number and Casson parameter.

Most of the previous works on the thin nanoliquid-film (NLF) flow on a stretchable horizontal cylinder are limited to the boundary-layer flow (BLF) of infinite depth liquid. In this article, we have removed the above restrictions to examine the unsteady thin NLF flow on a porous stretchable cylinder by considering full momentum equations under the influence of thermal radiation and suction/injection. The implicit finite difference technique is utilized to obtain the numerical solutions to the problem. The present numerical solution is validated with the analytical solution obtained by Maity et al.⁴¹ for the isothermal case. It is found that the film thickness for Au/water nanoliquid is higher in comparison with Ag/water and Cu/water nanoliquids, respectively. The film thickness of nanoliquid enhances for rising magnitude of nanoparticle volume fraction (φ), porosity parameter (β), and Hartmann number (M_n). The film thickness of the nanoliquid increases or decreases as injection or suction (V) takes place through the surface of the cylinder. Furthermore, the sign of temperature gradient θ_R changes inside the nanoliquid depending on the values of other parameters. The percentage of changes in the film height is presented with the different parameters of the flow problem.