Two-step exothermic reaction–diffusion of hydromagnetic Prandtl–Eyring viscous heating fluid in a channel

Abstract

The impact of toxic emission on the ecosystem and environmental degradation cannot be overstressed. This resulted from the rising incomplete hydrocarbon combustion of human activities. Thus, this study investigates temperature distribution of Prandtl–Eyring viscous heating fluid in a channel. A two-step exothermic reaction–diffusion of the viscoelastic fluid is assumed to enhance combustion process. Without reactant consumption, the fluid flow is pressure driven and influenced by an induced Lorentz force and pre-exponential factor. The model is governed by partial derivative equations subject to fixed walls and non-isothermal boundary conditions. A non-dimensional invariant model is obtained using dimensionless quantities, which is then solved by a semi-implicit difference method. The presented results in tables and graphs revealed that the second step exothermic reaction raised the heat distribution that assist in the complete combustion process. Also, the fluid viscosity is improved with rising material dilatant term. Hence, terms that induced heat generation should be guided to circumvent excessive heat that can lead to blowup.

Keywords

• Prandtl–Eyring fluid
• Two-step diffusion
• Exothermic reaction
• Viscous heating