Mathematical analysis of a combustible viscoelastic material in a cylindrical channel taking into account induced electric field: A spectral approach

Abstract

Abstract In spite of the enormous applications of heating combustible materials due to exothermic chemical reactions, scientists and engineers still face a problem with these materials’ tendency to self-ignition, which can result in significant property damage if serious precautions are not taken. Therefore, the thermal decomposition of combustible viscoelastic material in a cylindrical channel is investigated in this study. With a third-order constitutive model considered for viscoelastic flow behavior, momentum and energy-balanced governing equations are provided. The chemical reaction of the material is assumed exothermic and thus follows Arrhenius’s kinetics. A numerical solution is provided for the boundary value problem via the bivariate spectral collocation method, and the impact of kinetics parameters on the combustible viscoelastic material is investigated. Our findings show that self-ignition is delayed with higher values of activation energy parameter ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>ε</m:mi> </m:math> \varepsilon ) and third-order parameter ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>γ</m:mi> </m:math> \gamma ), as well as lower values of magnetic field parameter ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>M</m:mi> </m:math> M ), current density parameter ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>δ</m:mi> </m:math> \delta ), and electrical conductivity exponent ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>m</m:mi> </m:math> m ).