This study investigates the qualitative behavior of a mathematical model describing bidirectional nonlinear wave propagation in a water channel. The non-integrability of the model is proved by using Painlev & eacute; singularity analysis. By applying a suitable wave transformation, the original system is reduced to a planar dynamical system equivalent to a Hamiltonian system. Within this framework, a bifurcation analysis is performed, leading to a theorem that specifies the conditions for the existence of periodic, solitary, and kink/anti-kink wave solutions. New exact solutions are constructed under parameter constraints derived from the bifurcation analysis. The influence of physical parameters on these solutions is examined, and graphical representations are provided. Furthermore, the effects of external periodic forcing are explored, revealing quasi-periodic and chaotic dynamics through phase portraits, Poincar & eacute; sections, and Lyapunov exponents. Numerical simulations demonstrate that the system's behavior is highly sensitive to the frequency and amplitude of the external forcing.
This interesting analysis takes into consideration the characteristics of heat and mass transfer of silver and alumina nanoparticles in base fluid water across an extending sheet, that is, permeable with slip effects, Brownian motion, MHD effect, and thermophoresis. This remarkable study, which has not yet been discussed by any author, examines the phenomena of mass and heat flux of hybrid nanofluid by combining slip and convective conditions. Furthermore, the behaviors of relevant parameters are taken into account, including Brownian motion, thermophoretic diffusion, joule heating, activation energy, viscous dissipation, and thermal radiation. A hybrid nanofluid is made by mixing silver and alumina nanoparticles with the base fluid water. The flow model is written in the form of PDEs, which are then solved by bvp4c to become ODEs through the appropriate transformation. The obtained result illustrates that the heat transfer rate and temperature distribution of the fluid escalates with sundry parameters of thermal radiation. It is found that hybrid nanoparticles show better results than nanofluids.
In this article, we investigate certain subcritical and critical equations involving the fractional -Laplace operator. More precisely, using fibering maps and the Nehari manifold, we establish the multiplicity of solutions for the following problem: where is a smooth bounded domain, is the fractional -Laplacian, and are positive parameters, and are homogeneous functions of degrees and with . Our results are novel and extend previous works by considering more general growth conditions.
This article explores B & ouml;dewadt flow of both Newtonian and second-grade nanomaterials (based on the Buongiorno model) over the radial stretching disk subjected to suction velocity and MHD effects. Influences of Joule heating, viscous dissipation, thermal radiation, and convective heat and mass conditions on heat and mass transport are investigated. The governed PDEs (continuity, energy, and momentum equations) are reduced to a set of ODEs (BVP) using similarity transformation, which are then solved via the semi-analytical technique OHAM (BVPH-2.0: A Mathematica package based on HAM). The key focus in this study is to perform a comparison between Newtonian nanofluid and second-grade nanofluid behavior under variations in key physical parameters. The results provide new insight for enhancing the thermal efficiency of nanofluid-based systems in the presence of magnetohydrodynamic and radiation environments.
Heat transfer enhancement in non-Newtonian fluids flowing through porous structures is crucial in various engineering applications such as geothermal energy systems, polymer processing, and thermal coating technologies. In this study, the mixed convective boundary-layer flow of a Casson fluid over an inclined vertical plate in a non-Darcy porous medium is analyzed by incorporating nonlinear thermal convection effects, along with thermal dispersion, convective surface heating (Biot number), and nonlinear density variation with temperature. The novelty of the present work lies in analyzing these coupled effects within a non-similar framework, which has not been sufficiently explored in earlier studies. The governing nonlinear partial differential equations are transformed into dimensionless form using appropriate non-similar transformations and solved numerically via the Spectral Quasi-Linearization Method (SQLM). The results reveal that an increase in the thermal dispersion parameter significantly enhances the fluid velocity and heat transfer rate while reducing the temperature distribution within the boundary layer. Higher Biot numbers intensify the convective heat exchange at the surface, leading to increased temperature, skin friction, and Nusselt number. It is also observed that increasing the inclination angle weakens the buoyancy force, resulting in a reduction in both velocity and heat transfer rate. These findings provide important physical insights into the control of heat and momentum transport in Casson-type fluids within porous media, with direct relevance to industrial processes such as high-temperature coating systems, geothermal heat extraction, and chemical thermal processing applications.
Thermal enhancement is required in many engineering processes, such as thermal and cooling systems, radiators, heat exchangers, and so forth. Therefore, thermal analysis regarding thermal enhancement in shear-thinning/shear-thickening fluid past over a heated cone is studied. Nanoparticles significantly enhance the fluid's thermal conductivity. The efficient transfer of heat depends on the thermal conductivity. The formulation of the problem is carried out through conservation laws of fluid dynamics. The coupled and nonlinear problems are solved numerically using bvp4c. Mesh analysis and result validation are carried out. The role of , and on thermal transfer optimization is studied. The presence of Darcy and Forchheimer porous media in the fluids causes a reduction in the Nusselt number, whereas a remarkable increase in the skin friction coefficient. Thus, aerodynamic stability of the flow can be controlled through appropriate values of parameters affecting the skin friction coefficient. In heat exchangers or cooling systems, an increase in skin friction coefficient transitions laminar flow into turbulent flow, which is crucial in enhancing convective heat transfer. The fluids with ternary nanoparticles exert the highest drag on the solid's surface to which they interact. The Lorentz force results in an increase in drag on the flow of the fluid. Therefore, the Lorentz force can be used in controlling the thickness of the momentum boundary layer. The tangent hyperbolic fluids with Joule heating and viscous dissipation characteristics are less efficient working fluids than fluids that do not exhibit Joule heating and viscous effects. Thus, tangent hyperbolic fluids with Joule heating and viscous dissipation are not recommended for optimal thermal transport of heat. In thermal and cooling systems using fluid for the transfer of heat, porous medium affects the efficiency of the working fluid adversely. Moreover, the dispersion of tri-nanoparticles results in an 8.5003% increase in the Nusselt number.
Efficient thermal management is crucial in modern engineering systems such as energy devices, cooling technologies, and chemical processing, where advanced nanofluids offer improved heat transfer performance. Entropy generation in magnetohydrodynamic flow of ternary hybrid nanoliquid over a stretching disk is the main focus of the current study. The analysis incorporates copper , alumina , and titanium dioxide as three distinct nanoparticles. Various thermal aspects, including viscous dissipation, Ohmic heating, and variable thermal conductivity, are also studied. The thermal energy analysis incorporates the utilization of the Xue model. The nonlinear partial differential equations governing velocity and temperature profiles are transformed into ordinary differential equations using appropriate similarity transformations. The numerical solution to the current problem is computed using the Matlab routine, which implements the finite difference method. The impact of relevant parameters, including unsteadiness parameter , magnetic parameter , volume fraction of and , Eckert number , Biot number , thermal conductivity parameter , temperature ratio parameter , and Brinkmann number on flow dynamic, heat transfer, entropy, and the Bejan number are analyzed. The results show that the thermal conductivity variation parameter showed significant effects on , temperature profile, and thermodynamic irreversibility. Entropy generation is augmented with higher magnetic number, Brinkman number, and thermal conductivity parameter. The Nusselt number demonstrated higher values within the ternary hybrid nanofluid compared to both the nanofluid and hybrid nanofluid across various parameters. The Nusselt number increases by approximately - with increasing the thermal conductivity parameter. In comparison to the nanofluid and the hybrid nanofluid, the ternary hybrid nanofluid showed enhancement in both heat transmission and the irreversibility effects. The findings of this study are beneficial for the design of advanced thermal systems, including heat exchangers, cooling devices, and energy systems where enhanced heat transfer and controlled entropy generation are required.
In this paper, we investigate a nonlinear thermoelastic Timoshenko system involving thermodiffusion effects, second sound propagation, infinite hereditary memory, distributed delay, and nonlinear logarithmic damping. The model describes the evolution of the transverse displacement , the rotational angle , the temperature variation , the heat flux governed by Cattaneo's law, and the diffusive variable associated with thermodiffusion phenomena. The considered coupled thermo-viscoelastic system is governed by for .The thermal component is modeled through the Cattaneo heat conduction law which introduces finite propagation speed of thermal waves and incorporates second sound effects. The viscoelastic behavior is described by an infinite memory operator of the form while the distributed delay contribution generates additional hereditary interactions depending on the past history of the rotational velocity. First, the problem is reformulated as an abstract evolution equation in a suitable Hilbert space involving weighted history spaces associated with the infinite memory term. By combining semigroup theory, dissipativity methods, variational arguments, and the Lumer-Phillips theorem, we establish the global well-posedness of the coupled thermoelastic system. Next, suitable Lyapunov functionals are constructed in order to compensate the strong coupling generated by the hereditary memory operator, the second sound mechanism, the thermodiffusion effects, and the distributed delay contribution. The stability analysis is particularly delicate because the logarithmic damping term does not satisfy standard coercivity assumptions near the origin, while the infinite memory contribution introduces highly nonlocal effects depending on the entire past history of the solution. Using refined multiplier techniques, weighted energy estimates, and suitable compensating inequalities, we derive a general decay estimate for the total energy. More precisely, under the relaxation assumption where is a positive nonincreasing function, we prove that the total energy satisfies The obtained result provides a unified stability framework that includes exponential, polynomial, and more general decay rates as particular cases according to the asymptotic behavior of the relaxation kernel. Several numerical simulations and computational experiments are also developed through fully implicit finite difference approximations preserving the dissipative structure of the continuous model. The numerical tables and energy profiles clearly illustrate the influence of second sound effects, distributed delay, hereditary memory, and logarithmic damping on the asymptotic behavior and stabilization properties of the thermoelastic system. The computational results are shown to be in complete agreement with the theoretical analysis. The present contribution considerably extends and improves several previous works devoted to thermoelastic Timoshenko systems by simultaneously combining thermodiffusion coupling, second sound propagation, infinite hereditary memory, distributed delay, and nonlinear logarithmic dissipation within a unified analytical and numerical framework.
The complex applications of nanofluids have made them a prominent subject in both engineering and scientific research, inspiring multidisciplinary modeling efforts supported by rapid developments in nanotechnology. The core purpose of the ongoing research is to examine the thermal behavior of carbon nanotubes (CNTs) -based hybrid nanofluids flowing along vertically stretching surfaces, considering the influence of Darcy-Forchheimer resistance and an inclined magnetic field. Owing to their remarkable thermal and electrical conductivity, along with high strength, stiffness, and toughness, CNTs have become an essential element in advanced engineering applications. A mathematical model is developed to examine the effects of porous media, magnetic fields, and nonlinear thermal radiation on velocity and temperature profiles in stagnation-point hybrid nanofluid flow. By applying appropriate transformations, the governing equations are reduced to dimensionless system, which is then tackled numerically using the MATLAB bvp4c technique. The impacts of relevant flow parameters on the velocity and temperature fields are analyzed through graphical plots. During this exertion, results indicate that elevated mixed convection parameter intensifies fluid velocity, whereas thermal characteristics weaken under more substantial radiative effects. The local Nusselt number and skin friction coefficient are analyzed, with their variations and implications comprehensively evaluated. Additionally, it is evident from the results that hybrid nanofluids facilitate more rapid heat transfer compared to conventional nanofluids. This research provides valuable insights for optimizing energy systems and industrial operations by utilizing nanofluids and hybrid nanofluids for efficient thermal control.
This paper's objective is to present a comprehensive and intricate comparative numerical analysis of the heat exchange performances and flow behaviors of ternary hybridized nanofluid, hybridized nanofluid, and nanofluid flows in the presence of an oblique Lorentz force, with a focus on a nonlinear deformable wedge-shaped geometry. The thermal radiation, viscous-Ohmic dissipation, and first-order velocity slip boundary condition on the surface have all contributed to the regulation of the flow governing boundary-layer equations. This has allowed for the flow to be regulated. The study employed a rigorous methodological approach, using the self-similar transformation to change the governing coupled nonlinear PDEs into a collection of ODEs, which were then numerically solved using the fifth-order Runge-Kutta method with the shot approach. The robustness of our methodology ensures the validity of our findings. In conclusion, our comparative research on nanofluids has been conducted using a rigorous methodology to analyze the influence of governing parameters on simple, hybridized, and ternary hybridized nanofluids. Our findings, presented in tables, offer a numerical observation of local skin friction and the rate of heat transmit coefficients. We have concluded that the progressiveness of the velocity profile improves for the Hartree pressure gradient, the velocity slip parameter, the velocity ratio parameter, and the magnetic parameter. Conversely, the magnetic parameter, Eckert number, and thermal radiation parameter all contribute to a rise in the temperature profiles. This work examines the effects of many unexamined variables, such as thermal radiation, oblique Lorentz force, viscous-Ohmic dissipation, and first-order velocity slip boundary conditions, on the heat exchange performance of fluids, employing numerical analysis. The potential impact of this work is significant, with applications in fields such as space technology, high-temperature and cooling operations, paints, conductive coatings, medications, biosensors, cosmetics, and many more showcasing the versatility of the research.
The novel theoretical insights into the time-dependent hydromagnetic Couette flow of engine-oil based MoS2 nanofluid under the effects thermal radiation, energy dissipation, Dufour, and Soret effects including temperature-dependent fluid properties are analyzed. Unlike the conventional persistent property models, this study integrates the variable viscosity and thermal conductivity to accurately model the nanofluid performance in high-temperature lubrication and regulation systems. The models nonlinearly coupled PDEs governing momentum, energy, and species transport are tackled numerically using an efficient implicit finite difference scheme with stable and convergent structure. The comprehensive parametric analysis of the problem reveals that momentum profiles are significantly enhanced by increasing the Dufour and Soret numbers and thermal Grashof number, whereas they decrease with by the magnetic parameter and variable viscosity effects. The temperature distribution noticeably increases with radiation parameter, nanoparticle volume fraction, and Eckert number, but decreases with thermal absorption. The primary wall friction decreased by magnetic and thermal and mass buoyancy effects but the secondary wall-friction increased by these parameters. Sensitivity analysis and optimization accomplished via response surface methodology (RSM) identified that the thermal radiation and nanoparticle concentrations are most influential parameters in maximization of thermal transport performance. Remarkably, in comparison to the base fluid, the dispersion of 4% MoS2 nanoparticles yields a significant 7.13% increase in the heat transport rate. Further, findings of the study offer novel revelations into the combined influences of the radiative thermal transport, cross-diffusion, and variable properties in nanofluid lubrication, with direct implications for advanced thermal management in automotive engines, aerospace components, and industrial cooling systems.
This study investigates the unsteady two-dimensional Heimenz flow of a Casson fluid over a semi-infinite Riga horizontal plate, considering leading-edge accretion and ablation effects. A ternary hybrid nanofluid model is used, where sodium alginate (SA) serves as the base Casson fluid containing titanium oxide, copper, and silver nanoparticles. The effects of Stefan blowing on microorganism transport, Newtonian heating, nonlinear thermal radiation, activation energy, non-uniform heat source/sink, and Soret (thermal-diffusion) effects are examined to analyze momentum, heat, mass, and motile organism transfers in the boundary layer under stagnation-point conditions. The governing partial differential equations (PDEs) are transformed into dimensionless nonlinear ordinary differential equations (ODEs) using an appropriate nondimensionalization technique and solved numerically via the bvp4c method in MATLAB. Validation against existing literature confirms the accuracy of the solutions. The results show that increasing the Casson fluid parameter reduces velocity due to enhanced Newtonian-like behavior, while stagnation-point flow, non-uniform heating, Soret effects, and electromagnetic forcing from the Riga surface significantly influence the thermal, nanoparticle, and microorganism distributions in the boundary layer. Increasing the leading-edge parameter slows down the fluid but strengthens temperature and nanoparticle/microorganism accumulation near the wall. Higher activation energy enhances velocity, temperature, and nanoparticle concentration while slightly reducing microorganism density. The Stefan blowing parameter adds mass to the boundary layer, enriching nanoparticles and microorganisms, whereas suction or injection controls the local flow and boundary thickness. Notably, the modified Hartmann number from the Riga surface propels the fluid, increasing velocity and heat transfer.
Due to their stimuli-responsive behavior and superior thermal conductivity, as well as low inherent toxicity and chemical stability, the ferrite oxide nanoparticles are useful in the cooling systems, microfluidics, and energy systems. The colloidal suspensions of single-domain magnetic nanoparticles, with water known as ferro-nanofluids, find more applications in biology, emerging technologies, and other engineering disciplines. This study examines the time-dependent two-dimensional flow of electrically conducting, magnetic-type ferro-nanofluid over a vertically expanding sheet, influenced by a heat source, and Lorentz force effect. The governing equations of the present problem are reduced to ordinary differential equations through similarity transformations and solved using the Runge Kutta Fehlberg 5th order method with shooting approach. Additionally, an artificial neural network (ANN) model is utilized to optimize the thermal transfer rate within the system. The developed ANN model proves to be reliable, as it exhibits excellent accuracy during the training, validation, and testing phases. Moreover, the results indicate that suction and nanoparticle concentration reduce the velocity distribution, whereas the unsteady parameter and heat source parameter enhance the thermal distribution. Finally, the agreement between the present results and existing findings reinforces their credibility.
In this paper, we have discussed the pulsatile, unsteady blood (containing nanoparticles) flow via an artery that has a combined effect of aneurysm and stenosis, also using the Cattaneo-Christov heat flux to analyze the heat transfer effects within the physical system. Making the assumption that the stenotic condition is mild simplifies the coupled non-linear partial differential equations. The method of finite difference is implemented to resolve the coupled differential equations numerically. Graphs are developed to illustrate the impacts of nanoparticles, in addition to stenosis/aneurysm on flow rate of blood, impedance, and wall shear stress. A comparison of pure blood profiles with the graphical results of the nanoparticle fluid profiles shows a significant deviation. The instantaneous behavior of streamline patterns for various parameters of interest designates the variation in the circulating regions within the flow field. Thermal therapies like cryotherapy or hyperthermia are used in the principles of heat transfer to treat the different vascular diseases. Nanoparticles can be utilized to sense the temperature differences, thermal therapies, and transfer of heat in the examination of vascular disease.
The investigation into blood flow through stenotic arteries holds significant importance in the realm of mathematical fluid dynamics, particularly in the field of biological medicine. In this study, the focus is on understanding the impact of human blood circulation on a stenosed vessel. The chosen model for human blood is a micropolar liquid. The objective of this research is to scrutinize the significance of mixed convection in micropolar fluid as it flows through a stenosed artery. To computationally model the concentration and temperature distributions induced by blood flow via MATLAB, the structural equations and boundaries are reduced into non-dimensional notation by similarity transformations. The low Reynolds number and long wavelength techniques are used to simplify partial differential equations. The Crank-Nicolson method is employed to handle the evaluation of boundary conditions and governing equations for fluid flow. A specific geometry is assumed to understand the impact of the stenosis configuration. The study contains a graphical analysis of the influence of various physical parameters on the axial velocity graph, as well as the heat and mass fields. These variables include the coupling number, micropolar parameter, Prandtl number, Schmidt number, thermal Grashof number, and solutal Grashof number. The key findings include the observation that velocity increases with enhancements in the concentration number. Additionally, an increase in the coupling parameter and the thermal Grashof number within the confined region leads to a reduction in axial velocity. The temperature distribution experiences a rise with an increased Prandtl number. Notably, the concentration profile remains unchanged with an increase in Schmidt number values.
The conversion of solar radiation into thermal energy has attracted considerable interest because of the increasing worldwide need for renewable and sustainable energy sources. The remarkable heat transfer characteristics of nanofluids make them essential for improving solar-thermal system efficiency. This is achieved through the use of copper (Cu) and silver (Ag) nanoparticles to produce a Casson hybrid nanofluid (HNF), which is suspended in a 50:50 (water + ethylene glycol) base fluid. The thermal performance of this fluid is then studied on a non-Darcy porous curved stretching surface that is shown to an angled magnetic field. The methodology takes into account the combined effects of viscous dissipation, Forchheimer resistance, thermal radiation, heat source/sink, and Cattaneo-Christov heat flux. The governing nonlinear equations are simplified using similarity transformations and solved numerically using MATLAB's bvp4c solver. The findings demonstrate that augmenting magnetic field strength amplifies Lorentz forces, thereby decreasing fluid velocity and raising temperature owing to resistive heating. Increased nanoparticle concentration and curvature parameters markedly enhance heat transmission properties, whereas viscous dissipation elevates entropy production and diminishes the Bejan number, signifying more thermal irreversibility. The results provide an insightful understanding of the advancement and enhancement of HNF-based solar thermal systems and curved sheet heat transfer in advanced energy applications.
Minimizing entropy generation and optimizing nanofluid performance are critical strategies for improving thermal management in advanced energy systems, including nuclear reactors, aerospace platforms, and automotive heat exchangers. This study examines the thermofluidic behavior of a Casson trihybrid nanofluid within an accelerating microchannel, focusing on entropy generation influenced by Darcy-Forchheimer drag effects and Cattaneo-Christove heat flux. The governing system of coupled nonlinear partial differential equations is transformed into a set of ordinary differential equations utilizing similarity transformations and solved numerically using the spectral local linearization method. Convergence and validation evaluate approve the accuracy and stability of the approach through comparison with established literature. Entropy generation is assessed with thermal conduction, viscous dissipation, and Joule heating as primary irreversibility mechanisms. Parametric investigations exhibit that the Brinkman number significantly improves the temperature distribution, while the Darcy-Forchheimer parameter reduces it due to increased flow resistance. The Reynolds number is shown to advance entropy generation, indicating greater thermodynamic irreversibility at higher velocities. Conversely, the Bejan number raises with both thermal radiation and Reynolds number, while declines under increased magnetic field strength and viscous dissipation effects. Furthermore, multiple linear regression and sensitivity analyses are employed to assess the influence of critical dimensionless parameters, posing statistical validation of the model's predictive capability. The findings emphasize the advanced thermophysical performance of trihybrid nanofluids and provide constructive insights into optimizing entropy generation and heat transfer characteristics in nanofluid-based thermal systems under complex flow conditions.
This paper focuses on the numerical modeling of the shock absorbers' dynamic response under road excitations. The nonlinear characteristics of the shock absorber represent a critical aspect of vehicle suspension systems; therefore, their effects on the dynamic system's behavior are thoroughly investigated. The study considers various rheological models of the shock absorber, including linear symmetric, linear asymmetric, nonlinear symmetric, and nonlinear asymmetric configurations. The dynamic behavior of the vehicle is analyzed using a quarter-car model to investigate the linear and nonlinear damping characteristics. These damping properties are incorporated into a two-degree-of-freedom quarter-car suspension model. Modeling and simulations are conducted in the MATLAB environment, where a bump-type road profile is used to excite the system. Performance metrics, such as ride comfort, suspension working space, and road holding, are evaluated for both linear and nonlinear suspension systems based on the deflections of sprung and unsprung masses as well as the damping force. The obtained results indicate that the linear asymmetric shock absorber configuration is more effective in reducing the shock absorber suspension dynamic deflection, enhancing road holding, and maintaining the ride comfort. The systematic assessments of the shock absorber characteristics can guide engineers in selecting the most appropriate damping coefficient. These findings emphasize the importance of accurately capturing the nonlinear behavior of damping for reliable vehicle dynamics analysis.
One of the critical aspects of peristaltic transport is analyzing the influence of surface roughness on fluid motion. Rough surfaces promote heat transfer since they disturb the boundary layer, unlike smooth channels. With this perspective, the current work considers the electro-osmotic peristaltic flow of Bingham fluid in a rough channel, along with the effects of temperature-dependent properties. The fluid motion is modeled using lubrication theory approximations in order to guarantee the accurate description of low Reynolds number and long-wavelength assumptions. The influence of slip and convective boundary conditions, heat source coefficient, and Helmholtz-Smoluchowski velocity on flow dynamics is examined. The nonlinear transformed equations are solved using OHAM to render computations efficient and accurate. Graphical analysis shows the effect of various parameters on velocity, temperature, entropy generation, wall shear stress, and Nusselt number. Results indicate that a hike in yield stress diminishes temperature and entropy generation, while higher roughness factors enhance fluid flow in the center and drop at the walls of the channel. Further, the role of thermal conductivity in temperature to regulate heat exchange efficiency is most dominant. These results are important to optimize the performance of peristaltic transport systems within microfluidics, industrial fluids, and heat exchange applications.
An analysis has been carried out for the three-dimensional flow of tri-hybrid nanofluid (THNF) , , /water in the presence of magnetic field, thermal radiation, heat source, and velocity slip are examined. By using an appropriate transformation, the governing nonlinear partial differential equations (PDEs) are transformed into a set of nonlinear ordinary differential equations (ODEs). The reduced dimensionless nonlinear system are numerically solved by using the shooting technique via MATLAB's bvp4c built-in function. The effects of key parameters, including magnetic field strength, Daracy porous medium, dimensionless Prandtl number, radiation parameter, and velocity slip parameter, on the velocity components and temperature distribution are analyzed. The properties of flow controlling parameters via velocity and thermal profiles are elaborated through graphs. The findings showed that the velocity slip parameter in the x-direction and y-direction decreases the velocity. The momentum profile decreases when increasing the magnetic parameter, while thermal profile improved. Furthermore, the thermal profile boosted up the higher values of the thermal radiation parameter and magnetic parameter. The outcomes of this study have potential applications in cooling of microelectronic devices, thermal regulation in biomedical systems, and enhancement of heat exchangers and solar thermal collectors, where magnetic field and radiation effects are significant.
