Abstract
The mass and thermal flow of an unsteady Jeffery fluid over a surface having variable thickness with the presence of magneto-hydrodynamics is considered here. For this physical problem, we develop a mathematical formulation using Buongiorno's model for the Jeffery fluid. Characteristics of pedesis motion and thermo-migration of nanoparticles with the thermal link of heat source/sink are also examined. An arrangement of similarity variables is introduced to transform the transport equations into solvable forms in Cartesian configuration. A numerical solution of the differential system is obtained by using the algorithm of Runge-Kutta-Fehlberg fourth-fifth (RKF-45) method. Physical interpretations of obtained outcomes are established with the help of various plots, isotherms, and streamlines. Flow velocity reduces wall-thickness and unsteadiness parameters. Temperature enhances with the advances of radiation parameters, whereas regresses for the progression of Deborah number. Concentration improves with the progression of the activation energy parameter. Nusselt number condenses for velocity index and Eckert number. A comparison benchmark is also presented for solution validation.