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The purpose of this paper was the development of a model enabling precise determination of phosphorus concentration profile in the emitter layer of a silicon solar cell on the basis of diffusion doping process duration and temperature. Fick’s second law, which is fundamental for describing the diffusion process, was assumed as the basis for the model.

To establish a theoretical model of the process of phosphorus diffusion in silicon, real concentration profiles measured using the secondary ion mass spectrometry (SIMS) method were used. Samples with the phosphorus dopant source applied onto monocrystalline silicon surface were placed in the heat zone of the open quartz tube furnace, where the diffusion process took place in the temperature of 880°C-940°C. The measured real concentration profiles of these samples became template profiles for the model in development.

The model was developed based on phenomena described in the literature, such as the influence of the electric field of dopant ionized atoms and the influence of dopant atom concentration nearing the maximum concentration on the value of diffusion coefficient. It was proposed to divide the diffusion area into low and high dopant concentration region.

A model has been established which enabled obtaining a high level of consistency between the phosphorus concentration profile developed theoretically and the real profile measured using the SIMS method. A coefficient of diffusion of phosphorus in silicon dependent on dopant concentration was calculated. Additionally, a function describing the boundary between the low and high dopant concentration regions was determined.

The purpose of this paper is to focus on convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. The walls of the microchannel are subjected to constant asymmetric heat fluxes and also the first order catalytic reaction. To represent the non-equilibrium region near the surfaces, the Navier’s slip condition is considered at the surfaces because of the non-adherence of the fluid-solid interface and the microscopic roughness in microchannels.

Employing the Brinkman model for the flow in the porous medium and the “clear fluid compatible” model as a viscous dissipation model, the conservative partial differential equations have been transformed into a system of ordinary ones via the similarity variables. Closed form exact solutions are obtained analytically based on dimensionless parameters of velocity, temperature and species concentration.

Results show that the addition of Cu-nanoparticles to the fluid has a significant influence on decreasing concentration, temperature distribution at the both walls and velocity profile along the microchannel. In addition, total heat transfer in microchannel increases as nanoparticles add to the fluid. Slip parameter and Hartmann number have the decreasing effects on concentration and temperature distributions. Slip parameter leads to increase velocity profiles, while Hartmann number has an opposite trend in velocity profiles. These two parameters increase the total heat transfer rate significantly.

In the present study, a comprehensive analytical solution has been obtained for convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. Finally, the effects of several parameters such as Darcy number, nanoparticle volume fraction, slip parameter, Hartmann number, Brinkman number, asymmetric heat flux parameter, Soret and Damkohler numbers on total heat transfer rate and fluid flow profiles are studied in more detail. To the best of author’s knowledge, no study has been conducted to this subject and the results are original.

The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects.

Homotopy analysis method is used to find the series solutions of the governing equations.

Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field.

The present analysis has not been existed in the literature yet.

The purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

The purpose of this paper is to analyze theoretically the effects of thermal radiation with electrohydrodynamics through a Riga plate. An incompressible and irrotational fluid with constant density is taken into account. The governing flow problem is modeled with the help of linear momentum, thermal energy equation and nanoparticle concentration equation.

Numerical integration is used with the help of the shooting technique to examine the novel features of the velocity profile, temperature profile and nanoparticle concentration profile. The impact of all the emerging parameters is sketched with the help of graphs. The numerical values of local Nusselt number and Sherwood number are also presented.

The no-slip condition is considered for the present study. The effects of electromagnetohydrodynamics enhance the velocity profile while thermal radiation effects tend to raise the temperature profile. The present study depicts many interesting behaviors that warrant further study on Riga plates with different non-Newtonian fluid models. A comparison is also presented with the existing published results which confirms the validity of the presented methodology.

The results of this paper are new and original.

The aim of this paper is to find the optimal values of the reaction rates coefficients for the combustion of a methane/air mixture for a given reduced reaction mechanism which has a high appropriateness with full reaction mechanism.

A multi‐objective genetic algorithm (GA) was used to determine new reaction rate parameters (A's, β's, and E_a's in the non‐Arrhenius expressions). The employed multi‐objective structure of the GA allows for the incorporation of perfectly stirred reactor (PSR), laminar premixed flames, opposed flow diffusion flames, and homogeneous charge compression ignition (HCCI) engine data in the inversion process, thus enabling a greater confidence in the predictive capabilities of the reaction mechanisms obtained.

The results of this study demonstrate that the GA inversion process promises the ability to assess combustion behaviour for methane, where the reaction rate coefficients are not known. Moreover it is shown that GA can consider a confident method to be applied, straightforwardly, to the combustion chambers, in which complex reactions are occurred.

In this paper, GA is used in more complicated combustion models with fewer assumptions. Another consequence of this study is less CPU time in converging to final solutions.

Major land use changes can have a significant impact on the environment, e.g. increased leaching and run‐off losses of nutrients and water contamination. Nitrate (NO₃^–) can be easily leached and, when present at high concentrations in drinking water, can be a health hazard. This paper seeks to report an easy‐to‐use computer model designed to provide predictions of possible impacts on groundwater NO₃^– concentration on a regional scale.

The model takes into account NO₃^–‐N concentrations from various land use activities, land surface recharge rates (as affected by soil water retention capacity, land management, irrigation and rainfall), and mixing of surface recharge and river recharge. Spatial information on land use and groundwater recharge sources are lumped into groundwater management zones (100‐500 km²), and vertical concentration profiles of NO₃^– in groundwater are estimated from a one‐dimensional dispersion model. The model is applied to the 2,300 km² Central Canterbury Plains of New Zealand.

A scenario analysis for the Bankside groundwater management zone showed that the NO₃^–‐N concentration at the groundwater surface could increase from 7.8 mg N L^‐1 to 11.3 mg N L^‐1 if all the land used for sheep farming is replaced by dairy farming (increasing dairy land from 21 per cent to 64 per cent of the total land area). However, the impact of such land use changes on the NO₃^–‐N concentration 50 m below the groundwater surface was relatively small, resulting in an increase of NO₃^–‐N concentration from 0.4 to 0.5 mg N L^‐1. This is because of the significant mixing of surface recharge with river recharge at this depth.

The model can serve as a useful tool for first‐order estimation of possible trends of NO₃^–‐N concentration profiles in aquifers as a result of land use changes.

This paper aims to study turbulent dispersion of a passive plume emitting from a single elevated line source of different elevations in a plane channel flow by using direct numerical simulation (DNS).

The investigation was conducted in both physical and spectral spaces, which includes an analysis of statistical moments and pre-multiplied spectra of the velocity and concentration fields. The pre-multiplied power spectra of the velocity and concentration fields are compared to identify the transition of the plume development from the turbulent convective stage to the turbulent diffusive stage.

It is observed that due to the presence of wall shear, the mean plume drifts toward the wall for the near-wall source release case. It is also observed that streamwise development of the plume is sensitive to both the source elevation and the downstream distance from the source. For the line source placed near the center of the channel, the plume development is dominated by the bulk meandering effects. However, for the plume emitting from the near-wall line source, it hits the ground soon after its release and becomes dominated by the wall shear. As the downstream distance from the line source increases, the streamwise development of the plume released from the near-wall line source transitions from a turbulent convective stage to a turbulent diffusive stage.

This paper represents an original DNS study of turbulent mixing and dispersion of a passive plume emitting from a line source of different elevations in a wall-bounded flow. This paper proposes a practical method to identify the transition of the plume development from the turbulent convective to the turbulent diffusive stages.

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Numerical method is applied to find the results.

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

The purpose of this study is to analyze thermo-diffusion and diffusion-thermo effects, combined with first-order chemical reaction, in the flow of a micropolar fluid through an asymmetric channel with porous boundaries. Suction/injection velocities of upper and lower walls are taken to be different from each other. The channel exhibits a parting or embracing motion and the fluid enters, or leaves, the channel because of suction/injection through the permeable walls.

The solution of the problem is obtained by using the fourth-order Runge-Kutta method combined with the shooting technique.

The asymmetric nature of the channel that is caused by the different permeabilities of the walls deeply influences the flow. The temperature of the fluid rises significantly by increasing the absolute value of A for both Case I and Case II. While, for the concentration profile, the concentration drops near the lower vicinity of the center in Case I, and, it falls near the lower wall of the channel in Case II. Stronger Dufour effects increase the temperature of the fluid except for Case 1 at the center of the channel and for Case II in lower quarter of the channel.

It is confirmed that the presented work is original and is not under consideration by any other journal.