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Current study examined the magnetohydrodynamic (MHD) Prandtl nanofluid of a thermal double-diffusive flow through an exponentially vertical surface in association with heat generation, and thermophoresis effect. The novelty of this study is due to the analysis of Prandtl nanofluid model with Soret mechanism and chemically responding fluids. The fluid flow phenomenon is characterized by nonlinear coupled differential equations involving two or more independent variables. A suitable numerical technique is used to handle the set of governing equations along with a stability and convergence analysis. According to recent study, the fluid velocity increases since all the parameters are set to higher levels. For the various parametric values, isotherms and streamlines have been explored. This suggested model is beneficial since it can significantly advance the domains of thermal and industrial engineering. For instance, thermal radiation is crucial in designing sophisticated energy-transformed systems that operate at high temperatures. On the other hand, the phenomenon of Soret is useful in separating isotopes in chemical engineering. These studies have several applications in the manufacturing and biomedical fields, petrochemical industries, automobiles, medical sciences, and various production processes in industries.

A novel study of interdiffusion analysis in multicomponent alloys is presented. A custom written Matlab fitting program (MFP) is used as the main tool for the present study. The interdiffusion matrices are obtained using a newly developed mathematical approach based on the fitting into the closed form solution for the composition profiles. Overall, the new fitting method gives very good outcomes and allows the probing of multiple solutions (validated by back tests) that exist when a single diffusion couple is used in a multicomponent system. An important finding of the present investigations is that small differences in composition profiles may lead to large differences in the interdiffusion coefficients.

A novel study of analysis interdiffusion in multicomponent alloys is investigated by means of closed form solutions and numerical simulations. Quaternary as well as selected CoCrFeMnNi (HEAs) quinary metallic systems are analysed using one, two and three diffusion couples with the full set of interdiffusion coefficients being calculated. A custom written Matlab fitting program (MFP) is used as the main tool for the simultaneous fitting into multiple composition profiles in both systems. The retrieved interdiffusion matrices are obtained using a newly developed approach that is interlinked with composition vectors, eigenvalues and eigenvector. On average, it can be concluded that the accuracy of the obtained matrices steadily improves with the increase of the number of couples used in the analysis.

The interdiffusion process in a three-component alloy system has been studied by means of numerical analysis. The composition profiles for a ternary system were generated making use of the closed-form solution with a constant interdiffusion matrix with the accompanying analysis of the diffusion paths. Two methods [the Fitting Method and the modified square root diffusivity (MSQRD) method] have been considered to investigate the inverse interdiffusion problem for application to a single interdiffusion couple measurement. The Fitting Method simultaneously fits the required functional form into the data obtained for two composition profiles. Such fitted parameters are used to determine the constant interdiffusion matrix. The MSQRD method has been applied to the generated composition profiles and performs very well for all the cases considered. It was found that the errors of the MSQRD method are, in general, lower than in the use of the Fitting Method even without imposing artificial noise on the composition profiles to mimic the experimental data. In addition, it has been shown that the back-tests of the composition profiles must not be used as the only proof of the reliability of the methods used.

High entropy alloys (HEAs) are composed of five or more principal elements with equal (or nearly equal) compositions. In this paper, interdiffusion phenomenon in the HEAs is investigated. Two composition dependent (as well as composition independent) interdiffusion matrices have been used for detailed studying of the diffusion behaviour in CoCrFeMnNi HEAs. These matrices are calculated according to the Darken and Manning formalisms and are used in combination with the explicit finite difference method (EFDM) to obtain interdiffusion profiles. First, the interdiffusion profiles are calculated for the case of the terminal binary diffusion couple. A significant difference in the composition profiles is found between predictions according to the Darken and Manning formalisms. Next, the interdiffusion problem in the 5-component alloy is addressed numerically by considering the interdiffusion coefficients as constant, independent of composition, in CoCrFeMnNi alloys for several diffusion couples (mainly quasi-binary and quasi-ternary). The simulated composition profiles are found to be in a very good agreement with the available experimental results [1, 2]. It should be pointed out that the independence on composition of the interdiffusion matrix should be used for diffusion couples under two conditions: relatively small changes in composition, and the non-zero/non-dilute terminal compositions. The composition dependent interdiffusion matrix should be used in the diffusion couple if the composition differences are large and/or zero/dilute terminal compositions. In this paper, the Darken and Manning formalisms are used for modelling the composition dependent interdiffusion matrices. The purpose of this modelling is to systematically investigate interdiffusion in CoCrFeMnNi alloys in diffusion couples with substantial changes in composition. The main application of the present research is in the prediction of possible interdiffusion profiles in the framework of the random alloy model.

Analysis of interdiffusion in multicomponent alloys is addressed by developing a new and elegant mathematical approach that is based on the fitting of composition profiles into a closed-form solution where interdiffusion coefficients are independent of composition. As examples, ternary metallic systems are analysed using one and two diffusion couples with the full set of interdiffusion coefficients being determined. Overall, the new fitting method gives excellent outcomes and allows the probing of multiple solutions (validated by back-testing) that exist when a single diffusion couple is used in multicomponent (>2) systems. Important findings of the present investigation show that small differences in composition profiles may lead to large differences in the interdiffusion coefficients. In addition, the newly developed approach is successfully applied to experimental results for the Cu-Ni-Zn alloys annealed at 775 °C for 48 h.