On the exact results of a non-linear model arising in catalytic reaction in a flat particle with power kinetics reaction rate

• The strongly non-linear mathematical model describing catalytic reaction in a flat particle with power kinetics n-th order reaction rate is revisited and new results for further physical interpretation are obtained.
• Three new functions namely MCR, MCR1 and MCR2 are introduced to discover exact analytical solutions of the model.
• A full discussion is given and, it is also revealed that the problem may admit no solution, unique, dual or even more triple solutions depending on the values of the parameters of the model.

The latest study of a model of heat and mass transfer for a catalytic reaction within a porous catalyst flat particle (Journal of the Taiwan Institute of Chemical Engineers 48 (2015) 49–55 [7]) shows that this model can be exactly solved when the reaction rate is taken linear term as f(y)=yf(y)=y, where y is heat within porous catalyst particle. In this paper, the mentioned model is revisited by considering the power kinetics nth order reaction rate instead of a linear reaction term. It is shown that the problem is still exactly tractable. Furthermore, it is revealed that previous results can be recovered from this exactly solvable generalization case. It is also proved that the problem might have multiple stationary solutions (unique, dual and triple solutions) depending on the values of the parameters of the model.