Free surface dynamics of MHD third‐grade fluid model over a heated stretching sheet with variable fluid properties

Abstract

AbstractA thorough investigation of MHD third‐grade differential‐type fluid flow over a heated stretching sheet is performed in this work. In particular, we analyze the film thinning process, when the thermal sensitive fluid parameters vary due to the effect of heat supplied to the stretching sheet. Starting with a two‐dimensional (2D) free surface boundary value problem of non‐Newtonian third‐grade fluid, we present a systematic derivation of a 1D transient thin‐film height equation using longwave analysis with respect to the small aspect ratio of the fluid domain. The derived model is used to study the impact of Newtonian and non‐Newtonian parameters with variable fluid properties on the thin film height. The model is discretized using an upwind discretization in space and implicit time integration to guarantee first‐order convergence. The model is analyzed thoroughly with the help of numeric computing software MATLAB. The existing findings for a Newtonian fluid are in excellent agreement with derived evidence. In comparison to Newtonian fluid, the study finds that the third‐grade parameter causes thinning under different parametric restrictions. Simulations on the coupling effect explain that, the film thickness can be reduced with a high Marangoni number for highly viscous fluids. Also, since the effect of the conductivity parameter can be reduced at a low Prandtl number, the fluid shows a thinning effect. The film thinning rate, on the other hand, is reduced by the magnetic field.