Nonlinear Mixed Convection in a Reactive Third-Grade Fluid Flow with Convective Wall Cooling and Variable Properties

Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the working environment becomes hazardous is presented in the present investigation together with the entropy generation analysis that guarantees the efficient management of expensive energy resources. In this regard, the nonlinear mixed convective flow behavior of a combustible third-grade fluid through a vertical channel with wall cooling by convection is investigated. The mathematical formulation captures the nonlinearities arising from second-order Boussinesq approximation and exponential dependence of internal heat generation, viscosity, and thermal conductivity on temperature. The resulting nonlinear boundary value problems were solved based on the spectral Chebyshev collocation method (SCCM) and validated with the shooting-Runge–Kutta method (RK4). The nonlinear effects on the flow velocity, temperature distribution, entropy generation, and Bejan heat irreversibility ratio are significant. Further analyses include the thermal stability of the fluid. Findings from the study revealed that flow, temperature, and entropy generation are enhanced byincreasing values of the Grashof number, the quadratic component of buoyancy, and the Frank-Kameneskii parameter, but are reducedbyincreasing the third-grade material parameter. Moreover, it was shown that increasing values of the third-grade parameter encourages the thermal stability of the flow, while increasing values of the linear and nonlinear buoyancy parameter destabilizes the flow. The present result is applicable to thick combustible polymers with increased molecular weight.