The present study examines the impact of unsteady viscous flow in a squeezing channel. Silver–gold hybrid nanofluid particles with different shapes are inserted in the base fluid engine oil. Flow and heat transfer mechanism is detected in the presence of magnetohydrodynamics between the two parallel infinite plates. The thermal conductivity models, that is, Yamada–Ota and Hamilton–Crosser models are used to investigate various shapes (Blade, platelet, cylinder, and brick) of hybrid nanoparticles. The model is made up of paired high nonlinear partial differential equations that are then transformed into ordinary differential equations which are coupled and strong nonlinear using the boundary layer approximation. The MATLAB solver bvp4c package is used to solve the numerical solution of this coupled system. The influence of different parameters on the physical quantities is addressed via graphs. A comparison with already reported results is given in order to confirm the current findings. The analysis shows that surprisingly the Yamada–Ota model of the Hybrid nanofluid gains high temperature and velocity profile than the Hamilton–Crosser model of the hybrid nanofluid. Also, both the models show increasing trends toward increasing the volume fraction rate of silver‐gold hybrid nanoparticles. It is also inferred that the hybrid‐nanoparticles performance is far better than the common nanofluids.

A linear general rate model of two-component liquid chromatography is analyzed considering heterogenous reactions of types A→B and A⇄B. The model equations incorporate axial dispersion, external and intra particle pore diffusions, interfacial mass transfer, linear sorption kinetics, and first order heterogeneous chemical reactions. The solution methodology successively employs the Laplace transform and linear transformation steps to uncouple the governing set of coupled differential equations. The resulting system of uncoupled

The current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

This article presents semi-analytical solutions of a linear general rate model for fixed-bed liquid chromatographic reactors packed with core-shell particles. The model considers axial dispersion, interfacial mass transfer, intraparticle diffusion, linear adsorption, heterogeneous irreversible and reversible reactions, and injection of rectangular pulses. The Laplace transformation and eigen-decomposition technique are simultaneously applied to derive analytical solutions. The numerical Laplace inversion is applied for back transforming solutions in the actual time domain. A high resolution finite volume scheme is used to numerically approximate the model equations. Different case studies of reactive chromatography are considered to analyze the effect of core radius fraction on the elution profiles.

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This article presents analytical solutions of the general rate model (GRM), the lumped kinetic model (LKM), and the simpler equilibrium dispersive model (EDM) for core-shell particles and linear adsorption isotherms. The solutions in the Laplace domain are applied to derive analytical expressions for the temporal moments of these models. The results provide relations between the model specific kinetic parameters by matching one or more of the temporal moments. Several case studies are considered for illustration. The results show that simpler models are in many cases as good as the most detailed GRM if their kinetic parameters fulfill the matching relations. Thus, it is possible to reliably predict elution profiles using the simpler models. The derived analytical expressions can also be utilized to efficiently estimate model parameters from experimentally observed elution profiles to further optimize core-shell particles and to identify suitable column sizes and operating conditions. GRAPHICAL ABSTRACT 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 t [min] c [g/l] GRM LKM EDM u = 1 cm/min KEYWORDS Core-shell particles; Liquid chromatography; mathematical models; moment analysis; matching relations; semi-analytical solutions rate model (GRM), the lumped kinetic model (LKM), and the equilibrium dispersive model (EDM). [1,2] Hereby, the GRM is the most detailed model, while the LKM and EDM have less degrees of freedom and are simpler. It accounts for various mass transfer kinetics that influence the band profiles, namely external mass transfer resistance and intraparticle diffusion. In addition axial dispersion is

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