Abstract
The goal of current research is to better understanding how the thermal energy is transported in time-dependent axisymmetric flow that is created by a stretchable cylinder with thermophoretic particle deposition and Soret-Dufour effects. Due to the thermal gradient the occurrence of diffusion of species and concentration gradient cause of heat flux is one of the most fundamental mechanisms for transportation of energy. In present study the fluid flow reveals the relaxation and retardation phenomena. Moreover, the thermophoretic particle deposition is also considered in thermal analysis. The time-dependent partial differential equations for this flow dynamics are transformed into nonlinear ODEs (ordinary differential equations) and then solved analytically through homotopy analysis approach. The physical behavior of important parameters is studied in detail using graphical representations. The results show that as the values of the thermophoretic coefficient and thermophoretic parameter grow, the mass transfer rate declines. Further, the Soret and Dufour numbers are found to improve concentration and temperature distributions in the flow, respectively.