We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the “rarefied gas” limit or the “molecular chaos” hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density (low density of elementary events). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann H-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.

Purpose: This paper aims to address the flow of Sisko nanofluid by an unsteady curved surface. Non-uniform heat source/sink is considered for heat transfer analysis. Design/methodology/approach: Numerical solutions are constructed using bvp4c procedure. Findings: Pressure profile inside boundary region is increased when A and K are enhanced. Originality/value: No such analysis is yet presented.

Mathematically, complex chemical reactions can be simplified by “model reduction,” that is, the rigorous way of approximating and representing a complex model in simplified form. Furthermore, to reduce the dimension of the reaction mechanism there are different available model reduction techniques (MRT). Two MRT Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM) are applied here. Both techniques are good approximation techniques but not completely analytical. While for a case study, the complex behavior of the two-route reaction mechanism allied graphically. The characteristic properties of nodes and trees of reaction mechanism are addressed with the graph theory. The invariant solution curves and their comparison for two-route reaction mechanism have never been reported so far. Therefore, the aim of this article is to study such facts. The possible approaches to their solution and key problems are based on the Horiuti’s rules and their slow invariants. Both model-reduction techniques are applied to solve the high dimensional complex problem and comparison between invariant curves of both routes are presented graphically. The efficiency of ILDM with respect to time is compared with the SQEM graphically and in tabulated form by using MATLAB.