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This study is to examine the impact of viscous dissipation, thermal radiation and Ohmic heating on the magnetohydrodynamic (MHD) flow with thermal and mass transport over a horizontally stretching surface. Cattaneo–Christov heat flux model on a non-Newtonian viscous fluid along with two viscosity models and convective boundary condition has been employed. Tri-hybrid nanofluid has been used to increase thermal performance.

Governing mathematical model has been transposed into a dimensionless system of ordinary differential equations (ODEs) by applying suitable similarity transformation. Numerical solution has been found by applying the bvp4c shooting method in MATLAB software.

Velocity and thermal profiles of Model-I dominate the profiles of Model-II whereas opposite behavior is noticed for concentration profiles. It is concluded that there is an increase in temperature due to thermal radiation, viscous dissipation and convective boundary condition.

The novelty of presented work is to examine the impact of Ohmic heating, viscous dissipation, thermal radiation, chemical reaction and two models of viscosity on Cattaneo–Christov heat flux model of tri-hybrid non-Newtonian nanofluid with convective boundary constraint. The accuracy and effectiveness of presented model have been compared with already published research.

The present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.

The governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (T_h) left wall and a cold (T_c) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (10⁴ ≤ Ra ≤ 10⁵) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θ_f = 0.5) and volume fraction (ϕ = 0.04).

The findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 10⁴ to 10⁵, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.

This research is for two-dimensioal laminar flow only.

PCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.

As per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

The article aims to provide an accurate and efficient numerical algorithm for viscous flows in power-law fluids under various thermal boundary and partial slip conditions.

We are conducting a numerical investigation using the Taylor–Galerkin/pressure correction finite element method, which builds upon the work of previous researchers. Here, attention is therefore given to the interplay of various thermal boundary and stick-slip conditions and their impact on non-isothermal inelastic fluid.

The results demonstrate the influence of the Prandtl, Brinkman and Reynolds numbers on the flow’s thermal and hydrodynamic behavior, concentrating on the impact of slip at the wall. Furthermore, we have presented the effects of these dimensionless parameters on the detailed local and average Nusselt numbers, illustrated the high accuracy we obtained for numerical convergence, and compared our results with those of previous papers, observing excellent agreement.

We have successfully tested the code under the presented industrial conditions. Future research directions on this topic aim for efficient and robust solvers for non-Newtonian thermal rheological models; this algorithm can be used for that purpose.

This algorithm has never been used for numerical analysis of such a problem previously.

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.

The purpose of this study is to investigate the dynamics of capillary underfill flow (CUF) in flip-chip packaging, particularly in a multi-chip configuration. The study aims to understand how various parameters, such as chip-to-chip spacing (S12), chip thickness (tc) and others, affect the underfill flow process. By using computational fluid dynamics (CFD) simulations and experimental studies, the goal is to provide insights into understanding the dynamics of CUF in heterogeneous electronic packaging.

The paper introduces a CFD analysis and experimental study on CUF in a multi-chip configuration, aiming to understand underfill flow dynamics. A 3D geometry models of multi-chip arrangement are created using computer-aided design (CAD) software. After that, the CAD models are meshed and simulated in Ansys Fluent using incompressible and non-Newtonian fluid properties. The study maintains S12 of 2.86 and tc of 22.29 between experimental and simulation data for results validation. Next, a various of S12 values (1.14, 2.86, 5.71, 8.57, 14.29 and 20) which focus on tc of 22.29 have been investigated. Further studies have been conduct using S12 of 5.71 and tc of 8.00, 14.29 and 22.29.

Results show a strong correlation between simulation and experiment which validate the correctness and robustness of simulation. Further parameter’s studies using simulation for various of S12 indicated that higher S12 values lead to faster flow. This effect is due to large underfill weight from reservoir able to flow into S12 region which contributed to higher mass momentum movement. Furthermore, the effect of various of tc shows that the thicker the chip the faster the underfill to flow in S12 region.

The intentional exclusion of solder bump pattern arrangements from the experiment and simulation may limit the study's ability to fully understand the impact of solder bump patterns on underfill flow. Therefore, more parameters can be investigated such as solder bump pattern, underfill weight and dispense pattern in the future using CFD.

The manuscript provides a comprehensive examination of the contributions of CFD to the advancement of knowledge regarding CUF phenomena in heterogeneous electronic packaging assemblies. Moreover, it delineates the utilization of CFD methodologies to assess the influence of chip-to-chip spacing (S12) and the thickness of the chip (tc) on the underfill flow characteristics.

This paper fulfills an identified need of computational fluid dynamics method to study capillary underfill flow dynamics in heterogenous electronic packaging.

The coating process increases the durability, quality and effectiveness of the web, is used in manufacturing of wallpapers, adhesive tapes, wrapping, protection of fabrics and metals, X-ray and photographic films, beautification, books and magazines, film foils, magnetic records, coated paper, etc.

This paper gives a detailed study of the Oldroyd-4 constant fluid rheology during blade coating technique to check the sensitivity of velocity slippage on blade surface and magnetohydrodynamics (MHD) on final coating thickness and other mechanical properties. Heat transfer effects are also considered with viscous dissipation. The governing expressions under Lubrication Approximation Theory (LAT) are shortened and non-dimensionalized. A numerical technique with root finding algorithm is employed to determine the velocity profile, pressure and pressure gradient, shear stress, coating thickness, blade load and temperature profile. Figures and tables are exploited to show and discuss the effects of Hartmann number, slip parameter, geometrical parameter and viscoelastic fluid parameters on the flow and mechanical quantities. Comparison is also presented with previous literature under specific conditions.

From a technical vantage point, blade load and pressure are significant results of research as they lead to varying coating thickness, which gives an efficient coating process and extends substrate life. Shear stress is directly proportional to the magnetic parameter and inversely proportional to velocity slippage on blade surface. Temperature curve increases with increment in magnetic parameter and Brinkman number, while decrease in temperature is detected from slip parameter.

In literature, this investigation fills a gap in the numerical prediction of slip and MHD effects on the thin layer coating of rheological viscoelastic fluid during blade coating phenomena.

This study aims to investigate magnetohydrodynamic (MHD) conjugate pure mixed convection considering interior heat production and resistive heating inside a square closed/open cavity featuring a rotating cylinder for aiding (clockwise) and opposing (counterclockwise) flow configurations. Moreover, the impacts of altering cylinder size and conductivity on the system’s overall performance to determine optimum conditions are examined in this investigation.

The closed chamber is differentially heated by keeping high and low temperatures at the vertical boundaries. In contrast, the open cavity has a heated left wall and an open right boundary. The Galerkin finite element method is used to solve the Navier–Stokes and the thermal energy equations, which construct the present study’s mathematical framework. Numerical simulations are conducted for the specified ranges of several controlling parameters: Reynolds (31.62 ≤ Re ≤ 1000), Grashof (10³ ≤ Gr ≤ 10⁶) and Hartmann numbers (0 ≤ Ha ≤ 31.62), and volumetric heat generation coefficient (Δ = 0, 3).

When Gr, Re and Ha simultaneously increase, the average Nusselt number along the warmed boundary rises accordingly. Conversely, interior heat production lowers heat transmission within the computational domain, which is also monitored regarding mean fluid temperature, overall entropy production and thermal performance criterion. Finally, the open cavity confirms better thermal performance than the closed cavity.

Comprehending the impacts of the magnetic field, Joule heating, internal heat generation and enclosed or open boundary on pure MHD combined free-forced convective flow offers valuable understandings of temperature fluctuations, velocity propagations, heat transport and irretrievable energy loss in numerous engineering applications.

This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

This study aims to investigate the flow and heat transfer characteristics of a Bingham viscoplastic fluid subjected to the combined effects of axial rotation and radial stretching of a circular disk. Building upon existing models for Bingham fluids on stationary walls, we extend the formulation to incorporate the effects of a linearly stretching disk using von Kármán similarity transformations.

The resulting system of nonlinear ordinary differential equations is solved to characterize the flow and thermal fields. Three dimensionless parameters govern the momentum layer: a swirling number capturing the balance between rotation and stretching, a Bingham number characterizing the fluid’s yield stress and a modified Reynolds number incorporating the disk stretching. The Prandtl number controls the thermal response.

For purely stretching flows, a two-dimensional flow structure emerges. However, the introduction of rotation induces three-dimensional flow behavior. Unlike previous studies suggesting that moderate Bingham numbers are sufficient for non-Newtonian effects on purely revolving disks, the findings indicate that significantly higher yield stresses are required to observe non-Newtonian characteristics under radial stretching conditions. This difference can be attributed to the enhancing influence of wall movement on the fluid dynamics. At high Bingham numbers, a two-layer flow structure develops, comprising an unyielded plug region above the disk and a yielded shear layer adjacent to the wall. The von Kármán viscous pump mechanism drives the Bingham flow within this regime.

Physical quantities such as drag force due to wall shear stress, torque resulting from tangential shear stress and Nusselt number are extracted from the quantitative data.

Surface properties (smooth or roughness) play a critical role in controlling the wettability, surface area and other physical and chemical properties like fluid flow behaviour over the rough and smooth surfaces. It is reported that rough surfaces are offering more significant insights as compared to smooth surfaces. The purpose of this study is to examine the effects of surface roughness in the diverging channel on physiological fluid flows.

A mathematical formulation based on the conservation of mass and momentum equations is developed to derive exact solutions for the physical quantities under the assumption of low Reynolds numbers and long wavelengths, which are appropriate for biological transport scenarios.

The results reveal that an increase in surface roughness reduces axial velocity and volumetric flow rate while increasing pressure distribution and turbulence in skin friction.

These findings offer valuable insights for biological flow analysis, highlighting the effects of surface roughness, non-uniformity of the channel and magnetic fields.

These findings are very much applicable for designing the pumping devices for transportation of the fluids in non-uniform channels.

This study examines the impact of surface roughness on the peristaltic pumping of viscoelastic (Jeffrey) fluids in diverging channels with transverse magnetic fields.