Wavy mathematical modeling of dynamically reactive shear thinning materials under the influence of gravity and wavy structures amplitude

Abstract

PurposeResultant leading equations are formed with non-linear partial differential equations by adopting a low Reynolds theory approximation. For a better and easier understanding of the role of physical features of the main problem, the equations are reduced to non-dimensional ordinary differential equations by incorporating the locally similar and non-similar dimensionless variables. In light of practical importance, all the significant findings are approximated by solving the equations with the assistance of a modified bvp4c built-in package. The effective speed, temperature and volume fraction of the same materials are displayed to address the behaviors of different controlling influences.Design/methodology/approachThis work is inaugurated to investigate thermal cycling, thermal striping and thermal stratification, which cause thermally induced damage during the wavy confined flow domains. Such physical constraints are imposed on the wavy surface while considering the wavy dynamics of shear thinning materials. The impact of gravity is assumed on the vertical wavy surface, which is observed as the main source for the wavy flow occurrence. The surface’s amplitude plays a critical role in generating a high temperature difference. The same phenomenon is further extended with the applications of thermal radiation, mixed convection and dynamical homogeneous/heterogeneous reactions.FindingsFor instance, the higher stratification factor causes a reduction in the liquid wavy speed and temperature, and the rising chemically reactive rate factor declines the volume fraction during the typical wavy motion of the materials. Moreover, the larger amplitude and mixed convective factor reduced and uplifted the speed of the materials, respectively. The surface resistive forces are monitored with the graphical visualization of local similar skin friction and are determined larger by varying the Weissenberg and mixed convective factors. The affective liquid speed, temperature and volume fraction are plotted to address the behaviors of different controlling factors. These impacts are listed, i.e. with higher stratification factors, a reduction is noticed in the liquid velocity and temperature. On the other hand, an opposite depict is noticed for higher heat generation factors. The reduction in volume fraction is reported with variation in the reaction factor and Schmidt number.Originality/valueAfter carefully assessing the previously referenced work, it is evident that the literature has yet to incorporate thermally stratified Williamson fluid. Meanwhile, the motion of the materials is noticed due to the gravitationally affected wavy surface. Such physical phenomenon is further approximated by testing a dynamical reaction during its motion. An effective presentation of all the outcomes is portrayed via graphs and approximated numerical results.