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This particular study focuses on investigating the heat and mass transport characteristics of a liquid flow across the conical gap (CG) of a cone-disk apparatus (CDA). The cone and disk may be taken as stationary or rotating at varying angular velocities. Consideration is given to heat transport affected by solar radiation. The Rosseland approximation is used for heat radiation calculations in the current work. To observe the mass deposition variation on the surface, the effect of thermophoresis is taken into account. Appropriate similarity transformations are used to convert the three-dimensional boundary-layer governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs) system. Particularly for the flow, thermal and concentration profiles, plots are provided and examined. Results reveal that the flow field upsurges significantly with upward values of Reynolds numbers for both cone and disk rotations. The increase in values of the radiation parameter improves heat transport. Moreover, it is detected that the stationary cone and rotating disk model shows improved heat transport for an increase in the values of the radiation parameter.

The time-dependent Maxwell nanofluid flow with thermophoretic particle deposition is examined in this study by considering the solid–liquid interfacial layer and nanoparticle diameter. The governing partial differential equations are reduced to ordinary differential equations using suitable similarity transformations. Later, these reduced equations are solved using Runge–Kutta–Fehlberg’s fourth and fifth-order method via a shooting approach. An artificial neural network serves as a surrogate model, making quick and precise predictions about the behaviour of nanofluid flow for various input parameters. The impact of dimensionless parameters on flow, heat, and mass transport is determined via graphs. The results reveal that the velocity profile drops with an upsurge in unsteadiness parameter values and Deborah number values. The rise in space and temperature-dependent heat source/sink parameters value increases the temperature. The concentration profile decreases as the thermophoretic parameter upsurges. Finally, the method’s correctness and stability are confirmed by the fact that the maximum number of values is near the zero-line error. The zero error is attained near the values 2.68×10−6, 2.14×10−9, and 8.5×10−7 for the velocity, thermal, and concentration profiles, respectively.

Fins are utilized to considerably increase the surface area available for heat emission between a heat source and the surrounding fluid. In this study, radial annular fins are considered to investigate the rate of heat emission from the surface to the surroundings. The effects of a ternary nanofluid, magnetic field, permeable medium and thermal radiation are considered to formulate the nonlinear ordinary differential equation. The differential transformation method, one of the most efficient approaches, has been used to arrive at the analytical answer. Graphical analysis has been performed to show how nondimensional characteristics dominate the thermal gradient of the fin. The thickness and inner radius of a fin are crucial factors that impact the heat transmission rate. Based on the analysis, it can be concluded that a cost-effective annular rectangular fin can be achieved by maintaining a thickness of 0.1 cm and an inner radius of 0.2 cm.

This work examines the second law analysis of an electrically conducting reactive third-grade fluid flow embedded with the porous medium in a microchannel with the influence of variable thermal conductivity, activation energy, viscous dissipation, joule heating, and radiative heat flux. A suitable non-dimensional variable is included into the governing equations to transform them into an ensemble of equations that are devoid of dimensions. The acquired equations are then tackled using the Runge Kutta Felhberg 4th and 5th order (RKF-45) approach in conjunction with the shooting methodology. Through comparison with the current results, the numerical results are verified, which provides a good agreement. From the present outcomes, it is established that the entropy generation is supreme for the viscous heating constraint, variable thermal conductivity, Frank Kameneski, heat source ratio parameter and third-grade fluid material constraint. The Bejan number boosts up with larger values of activation energy, and Frank Kameneski constraint and the decreasing nature is noticed for increasing third-grade material parameter, viscous heating parameter. With magnetism, the fluid’s velocity slows down because of a resistive force. A similar impact in the channel on velocity is noticed for larger third-grade fluid, activation energy parameter, and Frank-Kameniski parameters and increasing behavior is noticed for variable thermal conductivity, and permeability parameter. Further, it is cleared that the variable thermal conductivity assumption in the channel plate leads to a significant under prediction of the irreversibility rate.

In the present article, we investigate the free convective flow of a ternary hybrid nanofluid in a two-phase inclined channel saturated with a porous medium. The flow has been propelled using the pressure gradient, thermal radiation, and buoyancy force. The flow model’s governing equations are resolved using the regular perturbation approach. The governing equations are solved with the help of the regular perturbation method. Polyethylene glycol and water (at a ratio of 50%:50%) fill up Region I, while a ternary hybrid nanofluid based on zirconium dioxide, magnesium oxide, and carbon nanotubes occupies Region II. The ternary hybrid nanofluids are defined with a mixture model in which three different shapes of nanoparticles, namely spherical, platelet, and cylindrical, are incorporated. The consequences of the most significant variables have been examined using both visual and tabular data. The main finding of this work is that utilising a ternary hybrid nanofluid at the plate y = 1 increases the rate of heat transfers by 753%, demonstrating the potential thermal efficiency. The overall heat and volume flow rates are amplified by buoyant forces and viscous dissipations and dampened by the thermal radiation parameter. The optimum enhancement of temperature is achieved by the influence of buoyancy forces. A ternary nanofluid region experiences the maximum temperature increase compared to a clear fluid region. To ensure the study’s efficiency, we validated it with prior studies.

In the current examination, the impact of the radiation on MHD convective fluid flow stream in a permeable medium over a semi-infinite inclined plate with the impact of the Joule heating. The governing Equation changed into nonlinear ODE's with the assistance of the similarity transformation. By utilizing the Runge-Kutta fourth order with shooting technique. The effect of the fluid parameters on velocity and temperature along with concentration profilesexamined through graphs.

The present research analyzes the impact of nanoparticle diameter and the interfacial layer on the nanofluid flow over a rough rotating disk with melting. Additionally, homogeneous and heterogeneous reactions play an essential part in comprehending the dynamics of mass transfer. Appropriate similarity variables are utilized to convert nonlinear governing equations into ordinary differential equations. The reduced equations are solved numerically by using a shooting approach and Runge–Kutta–Fehlberg fourth-fifth (RKF-45)-order method. In addition, an advanced intelligent numerical computing solver that interprets heat transfer and surface drag force is offered. This solution uses artificial neural networks with multilayer perceptron, feed-forward, back-propagation, and the Levenberg–Marquardt method. The plotted histograms display the error distribution for each of these predicted values from a zero-error point. More values that are close to the zero-error line will be present in a solution method that is more exact and precise. The results reveal that the radial velocity profile’s oscillatory behavior is shown to diminish close to the disk as the viscous force rises with higher slip parameter values. The axial component of velocity decreases as the slip parameter upsurges, which is to be expected as less fluid is radially released. The increase in melting parameter diminishes the temperature profile.

A comprehensive understanding of the behaviour of nanoparticles in a fluid flow may be necessary to design more efficient medication delivery devices. The behaviour of nanofluids in a variety of environments, including those affected by magnetic fields and temperature gradients, may have an impact on the targeted distribution of medications inside the body. The three-dimensional nanofluid flow via an expanding/contracting permeable slider with the consequence of magnetic field, thermophoresis and Brownian motion is explored in this study. The quantity of liquid injected to make the slider levitate is not constant; instead, it changes over time according to where the slider is at any given moment. The time-dependent governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) with the aid of similarity variables. Runge Kutta Fehlberg’s fourth-fifth-order (RKF-45) methodology is utilized to solve the resulting ODEs numerically. It is discovered that the reverse effect of slider contraction is seen when flat slider expansion results in the suppression of lift and drag. The velocity profile is decreased with an upsurge in the magnetic and wall-dilation parameters. The rise in Brownian motion and thermophoretic parameters improves the heat transfer. The rise in Brownian motion and thermophoretic parameters declines the concentration profile.

The Aligned magnetic field with Williamson fluid has been analyzed using a stretching sheet with Newtonian heating. The governing partial differential equations are transformed to the nonlinear ordinary differential equation by employing the similarity transformations and then solved by using the MATLAB inbuilt solver bvp4c. The influence of various parameters on dimensionless velocity and temperature was graphically explored. Comparisons of all conditions for a particular situation have been made and a very effective agreement has been reached.

The current study explores the magnetohydrodynamic flow and heat transport enhancement due to convection in a ferrofluid stream across a permeable vertical plate with thermal radiation, thermal diffusion, and a magnetic field. This examination considers the suspension of magnetite and cobalt ferrite nanoparticles in water as a base liquid. Strong magnetic capabilities are exhibited by cobalt ferrite and magnetite nanoparticles, which makes them attractive options for uses requiring magnetic manipulation of liquid flows. Understanding the relationship between the fluid flow and external magnetic fields requires the ability to regulate and modulate the fluid behaviour, which is made possible by the existence of a magnetic field in the system. Understanding the trajectory of drug-loaded particles and enhancing targeting efficiency need a knowledge of how ferrofluid flow behaves when subjected to an external magnetic field. The modelling equations are transformed into dimensionless form and solutions for flow and thermal fields are attained by applying the regular perturbation method. The outcome of physical factors on the flow and derived quantities has been introduced as tables and graphs. The heat transfer rate of magnetite is higher than that of cobalt ferrite due to the large thermal conductivity of magnetite particles. The thickness of the fluid increases by increasing the Grashof number.