Generalized viscoelastic flow with thermal radiations and chemical reactions

Background: A generalized model of mathematical nature is considered to address the viscoelastic flow prob-lem using fractional derivatives. Control/freedom of the flow mechanism is achieved with these derivatives. In simulations of industrial interest, more variations are available with fractional derivatives when compared with ordinary derivatives. Relaxation times are incorporated to handle the abrupt changes in the flow domain. Fluid flow is carried out under the influence of thermal radiations and when a heat source or sink is present. Chemical reactions of the first order are observed in the mathematical modeling of the flow. Methods: Flow is induced with the movement of the lower surface while applying force on the x-plane. Simulations of the governing mathematical problem are computed with the combination of finite element and finite difference algorithms. Significant Findings: It is noted that velocity, temperature, and concentration change with the variation of fractional order derivatives which was not possible with the classical derivatives. Moreover, with greater relaxation times, velocity, temperature, and concentration remained at a lower level. The modeled mechanism can be considered to avoid costly trials in chemical and polymer casting industries.

Automated summary

In this study, a mathematical model using fractional derivatives is proposed to address the viscoelastic flow problem. The control/freedom of the flow mechanism is achieved by varying the fractional derivatives. Simulation results show that velocity, temperature, and concentration change with the variation of fractional order derivatives. Moreover, with greater relaxation times, these parameters remained at a lower level. The proposed model can help avoid costly trials in the chemical and polymer casting industries.