Thermal analysis of magnetized Walter's-B fluid with the application of Prabhakar fractional derivative over an exponentially moving inclined plate

Abstract

The field of fractional calculus communicates with the conversion of regular derivatives to non-local derivatives with non-integer order. This emerging field has various applications, including population models, electrochemistry, signals processing, and optics. Due to the realistic practices of fractional derivatives, this study focuses on the Walter's-B non-Newtonian fluid flow in terms of fractional-based analysis. Through an exponential movable inclined plate, the magnetized unsteady flow behavior of Walter's-B incompressible fluid is examined. The mass and heat transport mechanisms are scrutinized with the association of chemical reaction and heat absorption/generation, respectively. The conversion of constitutive equations to dimensionless equations is accomplished through the application of dimensionless ansatz. The dimensionless equations are explored through the fractional approach of the Prabhakar derivative with the three-parametric Mittag-Leffler function. Both the Laplace transform and Stehfest methodologies are adopted to address equations based on fractional derivative. The consequence of the physical parameters with distinct time intervals on the concentration, flow field, and temperature distribution is physically visualized through graphics. According to the findings of this study, the velocity distribution decreases as fractional parameter values increase. Moreover, the concentration field exhibits a declining behavior with the improved chemical reaction parameter.