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The purpose of this study is to develop a new numerical algorithm to simulate the phase-field model.

First, the derivative of the temporal direction is discretized by a second-order linearized finite difference scheme where it conserves the energy stability of the mathematical model. Then, the isogeometric collocation (IGC) method is used to approximate the derivative of spacial direction. The IGC procedure can be applied on irregular physical domains. The IGC method is constructed based upon the nonuniform rational B-splines (NURBS). Each curve and surface can be approximated by the NURBS. Also, a map will be defined to project the physical domain to a simple computational domain. In this procedure, the partial derivatives will be transformed to the new domain by the Jacobian and Hessian matrices. According to the mentioned procedure, the first- and second-order differential matrices are built. Furthermore, the pseudo-spectral algorithm is used to derive the first- and second-order nodal differential matrices. In the end, the Greville Abscissae points are used to the collocation method.

In the numerical experiments, the efficiency and accuracy of the proposed method are assessed through two examples, demonstrating its performance on both rectangular and nonrectangular domains.

This research work introduces the IGC method as a simulation technique for the phase-field crystal model.

The hybrid nanofluid flow due to a rotating disk has numerous applications, including centrifugal pumps, paper production, polymers dying, air filtration systems, automobile cooling and solar collectors. This study aims to investigate the convective heat transport and magnetohydrodynamics (MHD) hybrid nanofluid flow past a stretchable rotating surface using the Yamada-Ota and Xue models with the impacts of heat generation and thermal radiation.

The carbon nanotubes such as single-wall carbon nanotubes and multi-wall carbon nanotubes are suspended in a base fluid like water to make the hybrid nanofluid. The problem’s governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. Then, the numerical solutions are found with a bvp4c function in MATLAB software. The impacts of pertinent parameters on the flow and temperature fields are depicted in tables and graphs.

Two solution branches are discovered in a certain range of unsteadiness parameters. The fluid temperature and the rate of heat transport are enhanced when the thermal radiation and heat generation effects are increased. The Yamada-Ota model has a higher temperature than the Xue model. Furthermore, it is observed that only the first solution remains stable when the stability analysis is implemented.

To the best of the authors’ knowledge, the results stated are original and new with the investigation of MHD hybrid nanofluid flow with convective heat transfer using the extended version of Yamada-Ota and Xue models. Moreover, the novelty of the present study is improved by taking the impacts of heat generation and thermal radiation.

This study aims to investigate numerically the impact of the three-dimensional convective nanoliquid flow on a rotating frame embedded in the non-Darcy porous medium in the presence of activation energy. The cross-diffusion effects, i.e. Soret and Dufour effects, and heat generation are included in the study. The convective heating condition is applied on the bounding surface.

The control model consisted of a system of partial differential equations (PDE) with boundary constraints. Using suitable similarity transformation, the PDE transformed into an ordinary differential equation and solved numerically by the Runge–Kutta–Fehlberg method. The obtained results of velocity, temperature and solute concentration characteristics plotted to show the impact of the pertinent parameters. The heat and mass transfer rate and skin friction are also calculated.

It is found that both Biot numbers enhance the heat and mass distribution inside the boundary layer region. The temperature increases by increasing the Dufour number, while concentration decreases by increasing the Dufour number. The heat transfer is increased up to 8.1% in the presence of activation energy parameter (E). But, mass transfer rate declines up to 16.6% in the presence of E.

The applications of combined Dufour and Soret effects are in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The nanofluid with porous medium can be used in chemical engineering, heat exchangers and nuclear reactor.

This study is mainly useful for thermal sciences and chemical engineering.

The uniqueness in this research is the study of the impact of activation energy and cross-diffusion on rotating nanoliquid flow with heat generation and convective heating condition. The obtained results are unique and valuable, and it can be used in various fields of science and technology.

Scientists have been conducting trials to find ways to reduce fuel consumption and enhance heat transfer rates to make heating systems more efficient and cheaper. Adding solid nanoparticles to conventional liquids may greatly improve their thermal conductivity, according to the available evidence. This study aims to examine the influence of external magnetic flux on the flow of a mixed convective Maxwell hybrid non-Newtonian nanofluid over a linearly extending porous flat plate. The investigation considers the effects of thermal radiation, Dufour and Soret.

The mathematical model is formulated based on the fundamental assumptions of mass, energy and momentum conservation. The implicit models are epitomized by a set of interconnected nonlinear partial differential equations, which include a suitable and comparable adjustment. The numerical solution to these equations is assessed for approximate convergence by the Runge−Kutta−Fehlberg method based on the shooting technique embedded with the MATLAB software.

The findings are presented through graphical representations, offering a visual exploration of the effects of various dynamic parameters on the flow field. These parameters encompass a wide range of factors, including radiation, thermal and Brownian diffusion parameters, Eckert, Lewis and Soret numbers, magnetic parameters, Maxwell fluid parameters, Darcy numbers, thermal and solutal buoyancy factors, Dufour and Prandtl numbers. Notably, the authors observed that nanoparticles with a spherical shape exerted a significant influence on the stream function, highlighting the importance of nanoparticle geometry in fluid dynamics. Furthermore, the analysis revealed that temperature profiles of nanomaterials were notably affected by their shape factor, while concentration profiles exhibited an opposite trend, providing valuable insights into the behavior of nanofluids in porous media.

A distinctive aspect of the research lies in its novel exploration of the impact of external magnetic flux on the flow of a mixed convective Maxwell hybrid non-Newtonian nanofluid over a linearly extending porous flat plate. By considering variables such as solar radiation, external magnetic flux, thermal and Brownian diffusion parameters and nanoparticle shape factor, the authors ventured into uncharted territory within the realm of fluid dynamics. These variables, despite their significant relevance, have not been extensively studied in previous research, thus underscoring the originality and value of the authors’ contribution to the field.

The purpose of this paper is to investigate the thermoelastic interactions in a homogeneous, transversely isotropic infinite medium with a spherical cavity in the context of two temperature Lord-Shulman (2TLS) generalized theory of thermoelasticity considering Eringen’s nonlocal theory and memory dependent derivative (MDD). Memory-dependent derivative is found to be better than fractional calculus for reflecting the memory effect which leads us to the current investigation.

The governing field equations of the problem are solved analytically using the eigenvalue approach in the transformed domain of Laplace when the cavity’s boundary is being loaded thermomechanically. Using MATLAB software the numerical solution in real space-time domain is obtained by Stehfest method.

Numerical results for the different thermophysical quantities are presented in graphs and the effects of delay time parameter, non-local parameter and two temperature parameters are studied thereafter. The outcomes of this study convince that the displacement u, conductive temperature ϕ, thermodynamic temperature θ are concave upward whereas radial stress τ_rr is concave downward for every choice of delay time parameter ω, two temperature parameter η and non-local parameter “ζ”. As a specific instance of our findings, the conclusions of an equivalent problem involving integer order thermoelasticity theory can be obtained, and the corresponding results of this article can be readily inferred for isotropic materials.

The novelty of this research lies in the adoption of generalized thermoelastic theory with memory dependent derivative and Eringen’s nonlocality for analyzing the thermoelastic interactions in an infinite body with spherical cavity by employing eigenvalue approach. It has applications to many thermo-dynamical systems.

In this study, we investigate the effects of an extended ternary hybrid Tiwari and Das nanofluid model on ethylene glycol flow, with a focus on heat transfer. Using the Cross non-Newtonian fluid model, we explore the heat transfer characteristics of this unique fluid in various applications such as pharmaceutical solvents, vaccine preservatives, and medical imaging techniques.

Our investigation reveals that the flow of this ternary hybrid nanofluid follows a laminar Cross model flow pattern, influenced by heat radiation and occurring around a stretched cylinder in a porous medium. We apply a non-similarity transformation to the nonlinear partial differential equations, converting them into non-dimensional PDEs. These equations are subsequently solved as ordinary differential equations (ODEs) using MATLAB’s bvp4c tools. In addition, the magnetic number in this study spans from 0 to 5, volume fraction of nanoparticles varies from 5% to 10%, and Prandtl number for EG as 204. This approach allows us to examine the impact of temperature on heat transfer and distribution within the fluid.

Graphical depictions illustrate the effects of parameters such as the Weissenberg number, porous parameter, Schmidt number, thermal conductivity parameter, Soret number, magnetic parameter, Eckert number, Lewis number, and Peclet number on velocity, temperature, concentration, and microorganism profiles. Our results highlight the significant influence of thermal radiation and ohmic heating on heat transmission, particularly in relation to magnetic and Darcy parameters. A higher Lewis number corresponds to faster heat diffusion compared to mass diffusion, while increases in the Soret number are associated with higher concentration profiles. Additionally, rapid temperature dissipation inhibits microbial development, reducing the microbial profile.

The numerical analysis of skin friction coefficients and Nusselt numbers in tabular form further validates our approach. Overall, our findings demonstrate the effectiveness of our numerical technique in providing a comprehensive understanding of flow and heat transfer processes in ternary hybrid nanofluids, offering valuable insights for various practical applications.

Analyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.

The dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.

The numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.

This study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.

Powder bed density is a key parameter in powder bed additive manufacturing (AM) processes but is not easily monitored. This research evaluates the possibility of non-invasively estimating the density of an AM powder bed via its thermal properties measured using flash thermography (FT).

The thermal diffusivity and conductivity of the samples were found by fitting an analytical model to the measured surface temperature after flash of the powder on a polymer substrate, enabling the estimation of the powder bed density.

FT estimated powder bed was within 8% of weight-based density measurements and the inferred thermal properties are consistent with literature findings. However, multiple flashes were necessary to ensure precise measurements due to noise in the experimental data and the similarity of thermal properties between the powder and substrate.

This paper emphasizes the capability of Flash Thermography (FT) for non-contact measurement of SS 316 L powder bed density, offering a pathway to in-situ monitoring for powder bed AM methods including binder jetting (BJ) and powder bed fusion. Despite the limitations of the current approach, the density knowledge and thermal properties measurements have the potential to enhance process development and thermal modeling powder bed AM processes, aiding in understanding the powder packing and thermal behavior.

This study aims to explore entropy evaluation in the bi-directional flow of Casson hybrid nanofluids within a stagnated domain, a topic of significant importance for optimizing thermal systems. The aim is to investigate the behavior of unsteady, magnetized and laminar flow using a parametric model based on the thermo-physical properties of alumina and copper nanoparticles.

The research uses boundary layer approximations and the Keller-box method to solve the derived ordinary differential equations, ensuring numerical accuracy through convergence and stability analysis. A comparison benchmark has been used to authenticate the accuracy of the numerical outcomes.

Results indicate that increasing the Casson fluid parameter (ranging from 0.1 to 1.0) reduces velocity, the Bejan number decreases with higher bidirectional flow parameter (ranging from 0.1 to 0.9) and the Nusselt number increases with higher nanoparticle concentrations (ranging from 1% to 4%).

This study has limitations, including the assumption of laminar flow and the neglect of possible turbulent effects, which could be significant in practical applications.

The findings offer insights for optimizing thermal management systems, particularly in industries where precise control of heat transfer is crucial. The Keller-box simulation method proves to be effective in accurately predicting the behavior of such complex systems, and the entropy evaluation aids in assessing thermodynamic irreversibilities, which can enhance the efficiency of engineering designs.

These findings provide valuable insights into the thermal management of hybrid nanofluid systems, marking a novel contribution to the field.

This study aims to focuse on the flow behavior of a specific nanofluid composed of blood-based iron oxide nanoparticles, combined with motile gyrotactic microorganisms, in a ciliated channel with electroosmosis.

This study applies a powerful mathematical model to examine the combined impacts of bio convection and electrokinetic forces on nanofluid flow. The presence of cilia, which are described as wave-like motions on the channel walls, promotes fluid propulsion, which improves mixing and mass transport. The velocity and dispersion of nanoparticles and microbes are modified by the inclusion of electroosmosis, which is stimulated by an applied electric field. This adds a significant level of complexity.

To ascertain their impact on flow characteristics, important factors such as bio convection Rayleigh number, Grashoff number, Peclet number and Lewis number are varied. The results demonstrate that while the gyrotactic activity of microorganisms contributes to the stability and homogeneity of the nanofluid distribution, electroosmotic forces significantly enhance fluid mixing and nanoparticle dispersion. This thorough study clarifies how to take advantage of electroosmosis and bio convection in ciliated micro channels to optimize nanofluid-based biomedical applications, such as targeted drug administration and improved diagnostic processes.

First paper discussed “Numerical Computation of Cilia Transport of Prandtl Nanofluid (Blood-Fe₃O₄) Enhancing Convective Heat Transfer along Micro Organisms under Electroosmotic effects in Wavy Capillaries”.