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The purpose of this study is two-fold. First, it aims to differentiate the response of a stretching jet encountering a quadratic air resistance from the classical jet shape formed in a frictionless medium. Second, it investigates how the resulting jet forms with and without air resistance, seeking evidence that supports the similarity flows frequently studied for stretching/moving thin bodies under the boundary layer approximation.

This study extends the established electrohydrodynamic stretching jet theory, used to model electrospinning or jet printing in the absence of air resistance, to encompass the impact of the retarding force on the jet stretching in both the cone and final regimes before it impinges on a substrate.

A close examination of the nonlinear governing equations reveals that the jet rapidly thins near the nozzle because of the combined action of viscous and electrical forces. In this region, the exponentially decaying jet receives further support from the air resistance, resulting in a closer alignment with the observed experimental jet. This exponential decay, accelerated by the inversely quadratic speed of the liquid particles, serves as clear evidence for the existence of a similarity flow over an exponentially stretching sheet. Furthermore, in the final regime, the jet stretching exhibits an algebraic decay in the absence of air friction, while with air resistance, it decays exponentially to reach a limiting speed. In the former case, a square root dependence of the stretching jet speed leads to the emergence of a similarity flow over a thin stretching jet, while in the latter case, a Sakiadis’ similarity flow appears over a continuously moving flat surface.

The analysis goes beyond jet hydrodynamics, delving into the interplay of electrostatic forces (including Coulomb’s law) and quadratic air drag, drawing upon experimental data on glycerol liquid presented in earlier publications.

Finally, the asymptotic behavior of the stretching jet under the combined influence of electrostatic pull and its electric currents because of bulk conduction and surface convection is validated through a comprehensive numerical simulation of the nonlinear system.

This work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.

Through the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.

Numerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.

The fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

This paper aims to present a numerical investigation into heat transfer and entropy generation resulting from magnetohydrodynamic laminar flow through a microchannel under asymmetric boundary conditions. Furthermore, the authors consider the effects of viscous dissipation and Joule heating.

The finite difference method is used to obtain the numerical solution. Simulations are conducted across a broad range of Hartmann (Ha = 0 ∼ 40) and Brinkman (Br = 0.01 ∼ 1) numbers, along with various asymmetric isothermal boundaries characterized by a heating ratio denoted as ϕ.

The findings indicate a significant increase in the Nusselt number with increasing Hartmann number, regardless of whether Br equals zero or not. In addition, it is demonstrated that temperature differences between the microchannel walls can lead to substantial distortions in fluid temperature distribution and heat transfer. The results reveal that the maximum entropy generation occurs at the highest values of Ha and η (a dimensionless parameter emerging from the formulation) obtained for ϕ = −1. Moreover, it is observed that local entropy generation rates are highest near the channel wall at the entrance region.

The study provides valuable insights into the complex interactions between magnetic fields, viscous dissipation and Joule heating in microchannel flows, particularly under asymmetric heating conditions. This contributes to a better understanding of heat transfer and entropy generation in advanced microfluidic systems, which is essential for optimizing their design and performance.

This paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.

The treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.

Analysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.

Linear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

The present findings aim to investigate the thermal behavior of water-based nanofluid flow over a rotating surface, focusing on understanding the effects of different types of nanoparticles on thermal efficiency, considering thermal radiation and variable viscosity effects. By considering four distinct nanoparticles – silicon dioxide titanium dioxide, aluminum oxide and molybdenum disulfide – the study aims to provide insights into how nanoparticle addition influences heat production, thermal boundary layer thickness and overall thermal performance.

The study employs computational methods, utilizing the BVP mid-rich algorithm for the solution procedure. The computational approach allows for a detailed investigation of the thermal behavior of nanofluid flows across a rotating surface under varying conditions.

The study concludes that adding nanoparticles in the base liquid increases heat production in the system, resulting in enhanced thermal boundary layer thickness. The comparative analysis shows that different nanoparticle types exhibit varying effects on thermal efficiency, suggesting that careful selection of nanoparticles can optimize heat transport and thermal management processes. Moreover, there's a noteworthy uptrend in the radial velocity profile concerning the stretching parameter, whereas a converse trend is observed in the thermal profile.

This study contributes original insights by comprehensively investigating the thermal behavior of water-based hybrid nanofluid flow over a rotating surface.

The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.

Enzymes play a pivotal role in orchestrating essential biochemical processes and influencing various cellular activities in tissue. This paper aims to provide the process of enzyme diffusion within the tissue matrix and enhance the nano system performance by means of the effectiveness of enzymatic functions. The diffusion phenomena are also documented, providing chemical insights into the complex processes governing enzyme movement.

A computational analysis is used to develop and simulate an optimal control model using numerical algorithms, systematically regulating enzyme concentrations within the tissue scaffold.

The accompanying videographic footages offer detailed insights into the dynamic complexity of the system, enriching the reader’s understanding. This comprehensive exploration not only contributes valuable knowledge to the field but also advances computational analysis in tissue engineering and biomimetic systems. The work is linked to biomolecular structures and dynamics, offering a detailed understanding of how these elements influence enzymatic functions, ultimately bridging the gap between theoretical insights and practical implications.

A computational predictive model for nanozyme that describes the reaction diffusion dynamics process with enzyme catalysts is yet not available in existing literature.

Transient response of continuous composite material (CCM) fin made of high thermally conductive composite material is presented. The continuously varying effective properties of composite material such as thermal conductivity, heat capacity and density have been modelled using the Mori-Tanaka homogenization theory and rule of mixture. Additionally, temperature dependency of thermal conductivity, heat generation (composite materials) and convection coefficient (fluid properties) have also been incorporated. Different base boundary conditions are addressed such as oscillating heat flow, oscillating temperature, step-changing heat flow and step-changing temperature. At the other boundary, the fin is assumed to have a convective tip.

Lattice Boltzmann method is implemented using an in-house source code for obtaining the numerical solution of typical non-linear heat balance equation of the aforementioned problem under various transient base boundary conditions.

The effects of various thermal parameters such as material diffusivity ratio and conductivity ratio, area ratio and Biot number on transient response of fin and temperature distribution of fins are studied and interpreted. The heat transfer rate and time for attainment of steady state temperature of metal matrix composite (MMC) fin are found to be proportionally dependent on their diffusivity ratio. Additionally for higher values of area ratio and biot number, MMC fins are reported to dissipate the heat more efficiently in comparision to homogeneous fins in terms of time required to attain the steady state and surface temperature.

Response of transient fin associated with advanced class of material can facilitates the practicing engineers for designing high-performance and/or miniaturized thermal management devices as used in electronic packaging industries.

Studies of composite fin consisting of laminating second layer of material over the first layer have been reported previously, however transient response of CCM fin fabricated by continuously varying the volume fraction of two materials along the fin length has not been reported till date. Such material finds its application in thermal management and electronic packaging industries. Results are plotted in form of a graph for different application-wise material combinations that have not been reported earlier, and it can be treated as design data.

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.