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One of the major and abundant environmental elements is water, which life existence on earth is depending on. However, degradation of water quality arising from natural occurrences due to anthropogenic that resulted in eutrophication needs to be guided. Indiscriminate harmful waste discharge and dispersion into the water bodies leads to water pollution. As such, constant management and monitoring of water resources for an enhanced quality and quantity is essential. Therefore, this study employed a coupled derivative mathematical model to investigate soluble and insoluble water pollutants. The insoluble pollutants are converted to soluble pollutants through an applied control or treatment. To optimize the water quality, parametric sensitivities in relation to reproduction number are examined. From the computational analysis carried out, it was revealed that treatment still remains the only remedy for safe water.

The research examines the intricate between Eyring-Powell microfluidic heat transfer, electromagnetic radiation and viscous heating in a Riga slippery device as applied in heat exchangers, cooling systems, biomedical devices, energy generation, polymer processing, and others. The viscoelastic property of the fluid is characterized by the Eyring-Powell Cauchy fluid model with shear-thickening and shear-thinning phenomena that are useful in several heat transport processes and thermal management. The developed governing model is taken from the constitutive relations and conservation principles and solved via an adaptive partition weighted residual method. The essential fluid term sensitivities are systematically investigated on the flow and thermal distribution characteristics. An appropriate validation and comparison of results is done and found to agree quantitatively, this confirmed the correctness of the presented outcomes. The results reveal the significant impact of the thermofluidic terms interaction on the viscous flowing fluid and thermal behaviour. As seen, slip conditions momentously increase the flow rate gradients for about 1.7% to 2.4% close to the boundary wall and consequently raise the microfluidic thermal propagation rates with 3.7% non-Newtonian fluid and thickness of the boundary layer. Moreover, the thermal gradient and distribution complexities are modulated within the fluid regime due to radiation and Lorentz force.

The use of a hybrid nanofluid, a relatively new invention in the field of nanofluids, results in better heat transmission. In the ongoing investigation, a hybrid nanofluid stagnation point flow involving Fe3O4-CoFe2O4 nanoparticles is utilized. To ensure novelty, the study incorporates reliable thermal properties on a stretching (or shrinking) wedge with variable magnetic fields and heat production, aiming to explore unique features of heat transfer. A set of relevant similarity transformation is utilized to generate ordinary differential equations and further solved numerically to obtain simulation results. The transformed dimensionless equations tackled numerically adopting the bvp5c MATLAB tool. Influence of several pertinent parameters on velocity and thermal distributions is analysed graphically. Surface plot and streamlines is presented for volume fraction and stretching/shrinking effects. It has been shown that magnetic field inclined the flow velocity across the domain due to sheet flow velocity. The wedge term boosted the velocity field, but the temperature distribution is decreased. The internal heating of the energy equation is influenced strongly by the entrenched thermofluidic terms. Computed numerical values are presented as a table for drag force coefficient and rate of heat transfer.

The need to enhance industrial working fluid and material thermal strength for quality output of engineering and domestic devices, has increased diverse studies on non-Newtonian viscous fluid under different constraints. Various architectures and geometries have been considered for thermal propagation of fluid particles. As such, this study addresses thermal motility of tiny particles in magnetized chemically reacting upper-convective Maxwell stagnation point fluid with radiation owing to its usages. A partial-differential model is formulated under some certain assumptions and conditions, and with applicable similarity variables, a transformed invariant coupled ordinary-differential model is obtained. The solutions to the model are determined using Galerkin-weighted residual method. The computed outcomes are quantitatively tabulated and qualitatively demonstrated in graphs. The analysis revealed that the hydrodynamic bounding surface alongside with velocity profiles declines due to augmentation of the magnetic field and Deborah number terms.

The core motive of the investigation is to scrutinize the precise outcome of an unsteady motion of a convective Casson fluid of the non-Newtonian type when thermo-diffusion and diffusion-thermo are present through an infinite vertical plate. The convection of binary diffusivity is exemplified via thermal-diffusion and Diffusion-thermal parameter. The numerical modeling of delimited stream yields a set of non-linear PDEs, these are transmuted into dimensionless PDEs via non-dimensional quantities. The dimensionless quasilinear PDEs defining the flow model are handled numerically, adopting an effectual finite difference schema. The behavior of different aspects, i.e., velocity, thermal and solutal transport, is presented via a graphical illustration using the MAPLE program. The results finding are likened to earlier investigations that have already been published, and a high level of precision is found. The concluding outcomes revealed that increasing the permeability term, thermal and species buoyancy forces fasten the flow velocity whilst the opposite behavior is taking down with escalating magnetic parameters. Enhancing the Dufour and heat source parameters raise thermal fluid, where the Prandtl number oppositely affect the heat transfer. The thermo-diffusion parameter speeds up the species mass and the liquid velocity.

The analysis of melting heat transfer over an expansive sheet of variable thickness is of the utmost importance in various industrial and engineering sectors, such as injection molding of polymers and composites, cooling of nuclear reactors, hot rolling, etc. Thus, the current work examines the flow dynamics, melting heat transport, and entropy generation of a magneto-hybrid nanofluid over a stretching device with variable thickness in porous media. A water-based hybridized nanofluid is formed using copper (Cu) and aluminium oxide (Al2O3) nanoparticles in the presence of thermal radiation, viscous dissipation, and Joulean heating. The transport partial derivatives were transmuted to ordinary derivatives using appropriate similarity quantities. These equations were numerically solved through shooting techniques combined with the Runge–Kutta–Fehlberg (RKF) method. Diverse figures and tables are sketched to illustrate the outcomes of the various parameters involved in the study. The investigation reveals an enlargement in the heat-bounding surface with an escalation in the magnitude of volume fraction, melting heat transfer, and magnetic field terms. In contrast, the momentum-bounding surface depletes with these parameters. Furthermore, as thermal radiation and Eckert numbers rise, the thermal gradient increases. The entropy generation increases with higher Brikman number and porosity term, but the melting heat parameter causes a decline in the entropy profiles.

The heat and mass transfer mechanism of motile tiny particles in nonlinear porosity media is significant in geosciences, bioremediation, soil mechanism, acoustics, and others to create an advection flow variable velocity field. Thus, the need to improve industrial species mixtures, thermal stability, conductivity strength for an enhanced productivity cannot be overstressed. As such, this study investigates thermal radiating and Joule heating on heat and mass transfer of magnetized tiny particles in tangent hyperbolic nonlinear porosity flow with the Riga plate and Arrhenius reaction. The developed model is appropriately transformed into an invariant derivative model, which is then solved by a Chebyshev wavelets technique. The presented graphical and tabular outcomes are verified and justified by comparing them with previous studies and are found to be accurate. As noticed from the analysis, the modified magnetization of magnet and magnetic field at low and high medium porosity, the velocity field decreased. The embedded energy equation terms inspired heat transfer while tiny particles Brownian motion damped the mass transfer at low and high viscous heating.

The experimental and theoretical analysis of viscous dissipation and heat generation/absorption management is crucial in engineering, medical, biological, and exploration activities. This study investigates the analytical solution of viscous heating and thermal gyration of magneto-micropolar fluid particles across a resistive medium with internal non-uniform heat generation/absorption. The formulated partial differential equations were appropriately converted into coupled ordinary differential equations employing similarity variables along with the boundary conditions. The simulation of the resultant equations is carried out using the collocating weighted residual scheme, and the result is validated using the shooting technique via the Runge-Kutta method of order four, Adomian decomposition technique, variational iteration scheme, differential transform method, and quasi-linearization technique as the control methods. Tabular and graphical representations are provided to illustrate the flow characteristics. Taking from the results, the existence of a magnetic field retards the gyration of the fluid particle motion. The spin gradient and vortex viscosity terms reveal the reverse occurrence of micro-rotation distribution, and it is seen that the porosity term suppresses the velocity field. Furthermore, it is observed that the parameters that enhance internal heat generation decrease the viscosity of the fluid in the region. Hence, these findings will assist scientists and engineers to effectively manage heat generation/absorption in industries where effective heat transfer activities are crucial to achieving ideal performance and reducing energy waste.

The current work concentrates on increasing the thermal and solutal performance in exponentially accelerating vertical surfaces via the utilization of nanofluids containing the mixtures of base water fluid and Aluminum oxide (Al2O3), Copper (Cu), Titanium dioxide (TiO2) and Silver (Ag) nanoparticles. During the fully utilize the capabilities of nanoparticles in a variety of applications and to evaluate the effects that they will have on the environment and biological systems, it is crucial to comprehend and manage heat transmission. This motivation allows us to investigate the nanofluid boundary layer flows under cross-diffusion effects, as this model study earlier was not conducted, thus the results of this work are new, which describe the novelty of the current problem. The partial differential equations for the developed model are altered into dimensionless statements first via non-dimensionalization. The numerical simulations implementing a finite difference scheme are applied for the solution description. The physical description of the variation of momentum, temperature, and mass fields for different factors is computed and presented graphically for ramped temperature and isothermal heat cases. Convergence and validation of the problem are checked with the help of tables. We found that enhancement in the Reynolds number, Brinkman parameter and magnetic field mark a downward trend in the fluid velocity, but it strengthens with the porosity parameter and time factor. The temperature distribution expands for advancing diffusion-thermal and radiation effects, whereas a contrary pattern was noted with the Prandtl number and heat consumption parameter. The thermo-diffusion effect enlarges the concentration distribution but decays with chemical reaction and Schmidt number.

In the cause of enhancing the heat and mass transfer of blood, nanoparticles are being introduced to give an improved heat exchanger in human systems. Nanofluid is a viable heat-carrier fluid, which serves as a cooling agent in drug delivery systems and improves their performances. However, the stability of nanoparticles in the base fluid is one of its challenges that needs more attention. This work investigates the aggregate of gold nanoparticles and blood-based fluid in the presence of both thermal radiation and magnetic fields. To have a better understanding and prediction of this physical phenomenon, a mathematical model of the system of governing Partial Differential Equations (PDEs) were formulated and transformed into a system of coupled third-order non-linear boundary values differential equations by similarity techniques. The boundary value in Ordinary Differential equations (ODEs) were reduced into the system of first-order initial value ODEs using the shooting approach alongside the Runge-Kutta Fehlberg fourth-fifth order (rkf45) method with the help of Python 3.0 software. The numerical results of the influence of aggregate nanoparticles on the velocity and temperature profiles were displayed graphically and the effect of thermo-physical parameters on skin friction coefficient and Nusselt number were shown in tables. It was found that as thermal radiation upsurges the temperature profile escalates for both with and without aggregate nanoparticles. Likewise, rises in magnetic fields raise the temperature profile of the gold-blood nanofluid. Nevertheless, the velocity profile declines as the magnetic field intensifies. This present work can be of great help in the medical field where drug delivery is paramount. Also the result has a significant impact on the possibility of utilizing the interaction between aggregate gold nanoparticles in blood-based fluid, which improved the system's mass and heat transfer.

The global threat of environmental degradation from harmful waste discharge is evident, leading to unusual diseases and natural disasters. Some of these toxic emissions result from human activities, such as the incomplete combustion of hydrocarbons. As such, this study aims to explore the analysis of electromagnetic and radiative heat sources on tangential hyperbolic fluid under Arrhenius kinetic with convective cooling. The transformed momentum and heat equations are solved using a rigorous computational approach called the Galerkin integration approximation with weighted residual method. This computational methodology ensures the reliability and accuracy of the results. Various graphs illustrate the results, showing parametric sensitivity profiles for the velocity, temperature, skin friction, thermal gradient, Bejan, and entropy generation. As noticed from the outcomes, electric field loading increases heat dispersion by about 3.25 % as heat source terms are enhanced. Increasing magnetic field, radiation, and electric field loading parameters strengthened thermodynamic equilibrium and minimized entropy generation. The tangential hyperbolic combustion process is 6.11 % increased with rising Brinkman number and electric field loading terms. The flow rate and temperature field are increased to the peak along the middle of the channel for increasing pressure gradient.

Ternary hybrid nanofluids offer promising roles in biomedical engineering, solar energy, atomic reactors, automobiles, and heat pipes. Through these facts and influenced by recent work in nanotechnology and their rich utilization, this particular research emphasizes the MWCNT (Multi wall carbon nano tube)-Au-Ag/blood ternary nanofluid flow through a bidirectional stretching sheet. The coupled non-linear partial differential equations (PDEs) for the developed model are altered into dimensionless ordinary differential equations (ODEs) via similarity transformations, also subsequently undertaken computationally via the spectral linearization methodology. The physical description of parameters is presented against the flow parameters graphically, also related physical quantities such as the Sherwood quantity and surface frictional force are exhibited. Furthermore, surface plots are presented to examine the boundary layer effect. The study reveals that increasing the stretchable ratio of the surface upsurges the y− velocity as a result of the thinning of the surface in this same direction, which reduces the resistance to fluid movement. Trihybrid nanofluid rapidity is less than the rapidity of hybrid nanofluid due to the increment of the number of molecules in the fluid which reduces the interspace between these molecules. Enhancing the Lorentz force and surface pores numbers reduces the surface frictional force factors of the ternary hybrid nanofluid.

The interest in improving the industrial and engineering working fluid for optimal productivity inspired studies on various fluid materials. Cauchy stress tensor fluids with suitable non-Newtonian rheological properties will enhance industrial fluids. Thus, Eyring-Powell fluid with applicable properties serves as a platform to promote engineering base fluid materials. As such, this study examines tiny particle thermal radiation and propagation in binary reactive Eyring-Powell with generalized Arrhenius kinetics fluid. A theoretical partial derivative boundary value model is developed and transformed into an applicable invariant model via similarity quantities. A Chebyshev collocation method is adopted to solve the model, and the outcomes quantitatively and qualitatively agree with the existing ones. The impact of fluidic terms on the Newtonian and non-Newtonian fluid cases is investigated, and the tiny particle propagation in the Eyring-Powell binary reactive fluid is enhanced with rising thermal radiation.

This study explores thermal criticality and dissipation involving a two-step reaction in a hyperbolic tangential fluid flow and quadratic Boussinesq approximation to model the complex internal heat transfer mechanisms during combustion. Subject to suitable convective boundary conditions, the transformed energy and momentum equations are numerically solved using Galerkin approximation integration coupled with a weighted residual scheme. The outcomes are disseminated using a variety of graphs to illustrate for parametric sensitivities of the thermal and velocity profiles. Based on the results, it is discovered that increases in the Frank-Kamenetskii parameter, Brinkman number, Weissenberg number, activation energy, activation ratio term, and second step term all aid in the complete combustion of hydrocarbons. Monitoring all terms that stimulate internal heat generation is essential to avoid system blow-ups.

The management of thermal propagation and preservation of heat energy are major challenges facing the industry and thermal science in recent times. Various studies have arisen on nanoparticles of different volume fraction for an enhanced heat transfer. Thus, limited reports have been offered on the dispersion of titanium dioxide TiO2, cylindrical magnesium oxide MgO and platelet aluminum Al nanoparticles in Prandtl-Eyring thermal water-based at different temperature experiencing force convection. Meanwhile, these nanoparticles’ hybridization served has essential materials to boost heat transfer for an improved industrial output and thermal engineering device. Hence, a partial derivative mathematical model is developed for the considered thermal fluid flow in dual wedge stretching sheets. An invariant transformed model is obtained via similarity variables, and a spectral quasi-linearization scheme solves the model. The results in tables and graphs are justified by validating with the existing ones and quantitatively discussed. It is seen with 200C at low and high-volume fraction (0.1 and 0.8), the ternary hybridized thermal gradient for unsteadiness decreases at 0.20 rate and increases at 0.07 rate respectively. Also, the heat transfer is strengthened with a rising induced magnetic field.

The theory of thermal radiation and viscous heating are crucial in space engineering and high temperature activities. This inquiry analyzes the consequence of energy source/sink on steady Magnetohydrodynamic(MHD) flow of stretchable surface via porous channel taken into account the introduction of thermal radiation and viscous heating. The transformed nondimensionalized nonlinear governing model is numerically classified and resolved to derive solutions for the physical terms using shooting techniques along with 4th order Runge Kutta method. The flow behavior represented through the physical parameters are discussed via tables and graphs. Examined are the effects of skin friction as well as Sherwood and Nusselt numbers. It is revealed from the research that increase in micropolar term leads to higher velocity and temperature while microrotation falls. Also, increase in temperature is observed for every increase in porosity, Eckert, radiative and heat source terms. It is deduced from the investigation that the temperature can be enhanced as both radiative and viscous heating terms improves.

Maintaining a continuous thermal convective power supply is very essential in many industries and thermal systems, this is because it helps in improving the efficiency of engineering machines and engines. Thus, hybridized electromagnetic nanoparticle in a heat supporting non-Newtonian fluid is a good platform to enhance thermal power energy. Based on its usefulness, this study focuses on the hybridization of zirconium dioxide (ZrO2) and copper (Cu) tangent hyperbolic nanofluid in ethylene-glycol(EG) (C2H6O2) solvent for thermal power optimization. With quadratic Boussinesq approximation, the fluid is influenced by electromagnetic induction and thermal convection. Via similarity quantities, an invariant derivative model is obtained. The model is completely solved using weighted residual method coupled with partition and one-third Simpson’s quadrature technique. The presented outputs revealed that entropy generation is minimized and thermodynamic equilibrium is achieved with rising values of the electric and magnetic field terms. Heat propagation is augmented with an enhanced electric field loading and nanoparticle volume fraction for hybrid nanofluid than unitary nanofluid. Also, current density is build-up for rising Williamson and thermal convection terms.

The implication of a stagnation-point flow together with the influence of activation energy in a Williamson fluid, which consists of tiny particles, over an expansive plate is analyzed numerically. Conditions of convective heat and mass motion with features of irregular movement and thermal-migration of particles influenced by viscous dissipation and convective heat surface condition are checked in the study. The conversion of the model equations from the initially formulated partial derivatives to ordinary ones is implemented by similarity transformations while an unconditionally stable Runge-Kutta-Fehlberg integration plus shooting technique are then used to complete the integration. Various interesting effects of the physical parameters are demonstrated graphically and explained appropriately in order to make accurate predictions. Moreover, the accuracy of the solution is verified by comparing the values of the skin friction factor with earlier reported ones in literature under limiting constraints. It is worth mentioning that the velocity profiles flatten down as the magnitude of the magnetic field factors expands but this causes a boost in the fluid’s temperature. The concentration field also appreciates with activation energy but depreciates with chemical reaction and Schmidt number.

Constant suction phenomenon has been executed in free convective Oldroyd-B material in an oscillatory flow mode over infinite vertical porous plate. For heat transfer, this study includes the influence of heat dissipation. The resulting governing equations are transferred into a set of dimensionless form of coupled-ordinary differential equations with appropriate non-dimensional variables. MAPLE code is developed for the regular perturbation method and executed to solve the set of non-dimensional couple-ordinary derivative equations. The impact of different embedded parameters on the mean, fluctuating, transient velocities and temperatures on the Oldroyd-B fluid have been discussed and depicted in graphical forms. The influence of some physical terms on the plate mean friction and plate heat mean gradient are computed and demonstrated in a tabular form. The attained results show that as an increase in relaxation time, greater amplitude of temperature fluctuations is observed. Remarkable enhancement is observed in all the parameters (Grashof, Prandtl and Eckert numbers) for transient temperature profiles.

The astronomical factors, geographical location, propensity, and temperature variability over time determined Nigeria's surface temperature and spatial distribution. As such, this investigation focuses on the harmonic temperature and sunshine of a northern and western station in Nigeria. The daily data for temperature and sunshine are collected for Ikeja (Western Nigeria) and Maiduguri (Northern Nigeria) from the Nigerian Meteorological Agency (NiMet) from the year 2010–2020. The data are studied and analyzed using a statistical tool. The harmonic analysis of the collected data is carried out using the Fourier series representation. From the temperature and sunshine of both Ikeja and Maiduguri, the peak periods for Maiduguri occur periodically, with maximums occurring every year at periods of every 3600 degrees depicting the months of December and January as months of high temperatures, while for Ikeja the peak periods occur periodically with maximums occurring every year at periods of 4000, depicting the months December to February as months of high temperatures. Sunshine for Maiduguri is observed to be at peak periods periodically, with maximum occurring every year at periods of every 3600 degrees depicting the months of December and January corresponding with temperature peaks. A peak minimum is observed in the year 2017. It is observed that the peak harmonic for temperature in Ikeja is higher than that of Maiduguri, as opposed to sunshine hours in Maiduguri, whose peak harmonic is higher than that of Ikeja. This could be due to population density or industrialization, but it is evident that Global warming effects are felt more in Ikeja than in Maiduguri.

Magnetohydrodynamic bioconvective micropolar nanofluid flow with migrating microorganisms opens up an intriguing new field in materials science. The distribution of particles during processing, such as metal casting, polymer extrusion, etc., can affect material characteristics and final product quality. So, the current research examines magnetohydrodynamic micropolar nanofluid flow over a vertically extending material in the presence of swimming microorganisms. The mathematical model also considers the temperature dependence of dynamic viscosity with thermal radiation using the Rosseland approximation, Brownian diffusion, and the thermo-migration of microscopic particles. Similarity variables are used to convert the partial derivatives to ordinary derivatives. Then the Runge-Kutta-Gill method is used with the shooting technique to obtain a numerical solution to the resulting set of equations. Various tables and graphs are included to illustrate the impact of the emerging parameters on the flow fields. Results show that an increase in the material parameter improves fluid mobility but decreases the skin friction coefficient, whereas the magnetic field term exhibits the opposite behaviour due to friction induced by the Lorentz force. The analysis shows that the thermal field significantly expands as the thermo-migration of tiny particles and Brownian motion get stronger.

The rising industrial demand for technological advancement in improving their working fluids and thermal augmentation has prompted studies on various non-Newtonian fluids and nanofluids. These play momentous role in many engineering devices and electronics development. Therefore, this study seeks to examine the thermal performance of ternary hybridized magneto-couple stress nanofluids in permeable media with nonlinear thermofluidic properties. The dispersion of suspended cobalt ferrite CoFe2O4, titanium dioxide TiO2 and magnesium oxide MgO nanoparticles occurs in H2O conventional solvent. With isothermal energy, the tri-hybrid nanofluid is controlled by stretchy velocity, magnetic field, gravity and Ohmic heating. An invariant transmutation of the partial derivative model is offered using similarity variables. The complete solutions to the model are obtained via Chebyshev technique coupled with integrated collocation method. From the graphically presented results, it is revealed that strong heat transfer is provided by ternary CoFe2O4+Ti02+MgO nanofluids compared to CoFe2O4+Ti02 and CoFe2O4 nanofluids. Also, the nanofluid concentration volume fraction enhanced thermal distribution and performance in the system.

Sequel to the industrial usage of ethylene-glycol conveying copper nanoparticles, nothing is known on how the dynamics differ from ethylene-glycol conveying copper and iron oxide nanoparticles when there is Coriolis force, slip and thermal jump. This report presents the outcome of a study on the motion and heat transfer across both non-Newtonian electro-conducting Carreau hybridized nanofluids via the porous medium on a three-dimensional rotating stretchable plate. The model for hybridization of the mixture of copper (Cu) and Iron oxide (Fe3O4) nanoparticles in the ethylene-glycol base fluid under thermal radiation, uneven heat source and wall slip attributes were developed and presented. The reduction of the model equations from partial into ordinary differential equations was carried out using similarity transformation variables. Pseudo-Spectral Method (PSM) was employed to solve the emerged boundary value problem. Exponential space-based heat source/sink, stretching rates, and temperature jump levels, heat transfer rates are maximal during ethylene-glycol conveying copper nanoparticles but minimal during ethylene-glycol motion conveying copper and iron oxide nanoparticles. The hybridization of the nanoparticles induces a higher heat propagation than the unitary nanofluid for all the physical parameters considered, whereas the strength of the surface drag force depreciates with a higher magnitude of the Weissenberg number.

This study examines the potential of using nanofluids in solar thermal energy systems. Nanofluids are known to exhibit high convection heat transfer coefficients, low specific heat, and density, making them ideal for improving the performance of solar thermal energy systems. However, this computational study investigates the application of Cattaneo-Christov heat flux on cylindrical surfaces using carbon nanotube (CNT) hybrid nanofluids, for use in a solar-powered ship. The work utilizes numerical simulations to analyze the heat transfer and fluid flow characteristics of the hybrid nanofluids. The research examines the use of single-walled and multi-walled carbon nanotubes (SWCNT and MWCNT) in engine oil (EO) as the working fluid. The Galerkin weighted residual method (GWRM) is utilized to solve the ordinary differential equations (ODEs) governing the system. The impact of various parameters, such as Cattaneo-Christov heat flux, solar thermal radiation, nonlinear stretching surface, slippery velocity, and porous media on the velocity equation, energy equation, and entropy generation are investigated and elaborated through detailed plots. The findings show that the MWCNT-SWCNT/EO hybrid nanofluid (HNF) exhibits maximum efficiency of around 2.4%, while the minimum efficiency is at 2.7%. This research provides valuable insights into the design and optimization of solar thermal systems for sustainable transportation.

Stoke's problems significantly impact several domains, including industrial manufacturing, geophysical flows, chemical engineering, and heat conduction. Stoke's second problem deals with the movement of a semi-infinite viscous incompressible fluid caused by an oscillating flat plate. Thus, this work examines Stoke's second problem for an unsteady hydromagnetic surface-driven flow along an infinite flat plate in the presence of thermal radiation and heat dissipation. The governing momentum and energy equations form an emerging nonlinear system of partial differential equations through dimensionless proxies. MAPLE 2022 is employed to solve the resulting system of nonlinear partial differential equations that control the flow both analytically and numerically in specific situations. The analytical solutions are displayed graphically, along with variations of skin friction and Nusselt number at the plate. It has been observed that momentum and thermal slips significantly diminished the flow characteristics to cause damping flow rate and temperature distributions. Rising the values of Magnetic and velocity slip parameters, an oscillatory motion is observed in skin friction. This is due to the periodic and wavy nature of the boundary wall. Furthermore, a rise in the Prandtl number and radiation value correspondingly boosted the wall heat gradient profiles. Finally, this study will assist industry and engineering in understanding the sensitivity of their working fluids to parameter variations and for the exact prediction of their base fluids.

An increasing interest in heat transfer of industrial working fluids and thermal applications of nanofluids propels the advancement of nanotechnology. Recently, focuses have been shifted to hybridization of nanofluids with the aim of enhancing heat propagation rate of conventional fluids. Hence, in this study, the elastic deformation of thermal radiation and convection for hybridized SWCNT-Ag and MWCNT-MoS4 magneto-nanomaterials in engine oil is examined. The thermal transfer of the hybrid nanofluids occurs in a vertical cylinder with thermofluidic features being considered in the model formulation. With appropriate variables, an invariant transformation of the model is obtained, which is then solved using Chebyshev Collocation Scheme (CCS). The data outcomes revealed that heat distribution is reduced with rising Prandtl number, elastic deformation and the viscoelastic term for both SWCNT-Ag and MWCNT-MoS4 hybrid nanofluids.

A theoretical study of hydromagnetic reaction of Oldroyd 8-constant exothermic liquid and explosion bifurcation slice is examined. The temperature distribution of the reactive molecular diffusion of the non-Newtonian liquid takes place in a plane bounded Couette. Without displacement of currents and material consumption, the viscoelastic fluid is completely exothermic with low thermal equilibrium. The dynamical flow momentum is not stimulated by the species reaction, but by the chain branched order, Arrhenius generalized kinetics, initiation rate and the flow medium upper plate motion. The nonlinear exothermic reaction differential model is completely solved by adopting a consistent and convergent collocation weighted residual analytical procedure. The qualitative results in graphs and tables are presented for the flow dynamic, heat propagation and ignition bifurcation slice. The results revealed that the viscoelastic property of the material is augmented by an increasing magnetic term. Also, exothermic heat diffusion is enhanced by initiation rate and reaction exponential factor. Hence, heat generation terms must be controlled to prevent thermal science and engineering devices from blowup.

An unsteady flow of heat and species transport through a porous medium in an infinite movable vertical permeable flat surface is considered. The hydromagnetic chemical reactive fluid flow is stimulated by the thermal and solutant convection, and propelled by the movement of the surface. The formulated nonlinear flow equations in time space are solved analytically by asymptotic expansions to obtain solutions for the flow momentum, energy and chemical concentration for various thermo-physical parameters. The existence of flow characteristic is defined with the assistance of the flow parameters. In the study, the impact of some pertinent flow terms is reported and discussed. The study revealed that the species boundary layer increases with a generative chemical reaction and decreases with a destructive chemical reaction. Also, arise in the generative species reaction term reduces the flow momentum for the cooling surface. The impact of other flow governing parameters is displayed graphically as well as the fluid wall friction, wall energy and species gradients. The results of this study are important in chemical thermal engineering for monitoring processes to avoid solution blow up.

This study examines Oldroyd 6-constant fluid and thermal explosion branch-chain criticality of a reactive flow in a generalized Couette device. With material consumption assumption, the reactive fluid is assumed to be actively exothermic, and the exchange of heat within the system is greater than the ambient heat exchange. Compared to the diffusion coefficient, the nondimensioned momentum and energy balance fields are influenced by a thermal Grashof number, non-Newtonian term, pressure gradient, branch-chain reaction order, and reaction initiation rate. The weighted residual collocation method is used to analytically obtain solutions to the dimensionless temperature and velocity equations as well as the bifurcation slice branch-chain solutions. The results are graphically presented, and it is revealed that a decrease in the fluid material terms will assist in managing the excessive heat generated by reaction initiation rate, and Frank Kamenetskii term. Also, a rise in the reaction branch order and reaction initiation rate can lead to system thermal runaway. Moreover, for industrial processes as obtained from the study, reactive non-Newtonian Oldroyd 6-constant fluid is thermally stable than reactive Newtonian fluid.

This study analyzes the second law of thermodynamic for entropy generation in an irreversible hydromagneto-micropolar flow system with non-homogenous heat generation. The non-symmetric microstructure fluid flow past a stretching sheet with saturated porous non-linear media under magnetic field influence. Ignoring the fluid particle deformation, the microstructure is assumed rigid with the viscous suspended medium. The reduced dimensionless nonlinear formulated model is computationally coded and solved to obtain solutions for the entropy volumetric production, Bejan number and heat transfer magneto-micropolar fluid. The parameter dependent solutions for the flow characteristics and irreversibility processes are plotted and discussed. It is revealed from the study that minimization of entropy generation in a magneto-micropolar flow system is possible by improving the thermodynamic equilibrium with low material variables, viscosity and hysteresis magnetic. Also, it is seen that the terms that encourage internal heat generation reduces the micropolar fluid viscosity in the system.

The numerical investigation of a Casson–Williamson reactive nanofluid species in a moving vertical medium is the subject of this study. The complete exothermic reaction of viscoplastic nanofluid material in a cylindrical system is considered using a generalized Arrhenius kinetic. Casson and Williamson fluids are combined to give the fluid its viscoelastic property. In collaboration with the bivariate overlapping multi-domain technique, the spectral quasi-linearization scheme is used to find solutions to dimensionless mathematical nonlinear formulated flow equations. The findings are displayed in tabular and graphical form, demonstrating the sensitivity of the thermofluid parameters. The study indicates that the flow motion is not caused by the activation energy or the material reaction. It was obtained that the magnetic field increased the viscosity of the material and the thermal conductivity of the nanoparticles. Also, Lewis number enhanced the fluid viscoplastic property. Thermal and chemical engineering, as well as nanotechnology development, will benefit from the findings of this investigation.

This paper examines the transport of nonlinear radiative Casson nanoliquid past a vertical electromagnetic actuator with temperature-dependent transport properties and entropy analysis. The model incorporates the Grinberg-term containing the influence of Lorentz force impinged by the actuator and the impact of the thermo-migration and Brownian motion of nanoparticles. The main equations are translated into non-dimensional forms via appropriate dimensionless variables and then solved using Chebyshev collocation method and verified by Galerkin type of weighted residual method and existing studies found in literature. From the study, the reactions of the embedded physical quantities of interest on the fields of velocity, temperature, nanoparticles concentration and entropy generation number are communicated graphically and deliberated upon. The implications of the results are that the modified Hartmann number aids the fluid flow as the Richardson number boosts the hydrodynamic boundary layer thickness whereas the converse occurs with Casson fluid material parameter. Also, the entropy generation is enhanced in the existence of viscous dissipation and suction while it declines with thermophoretic influence. Conclusively, it is found that the rate of entropy generation can be reduced by augmenting the magnitudes of the thermophoresis and Brownian motion parameters.

Theoretical study of inherent irreversibility and thermal runaway of an exothermic reactive Eyring–Powell fluid flow through a saturated porous fixed horizontal channel with thermal radiation and variable electrical conductivity is investigated. The reactive conducting fluid under bimolecular chemical rate law is propelled by pressure gradient. Ignoring the material assumptions, the governing dimensionless equations of the flow model are solved using semi discretization finite difference techniques coupled with weighted residual method. The results in terms of flow rate, temperature, thermal runaway, Bejan number and entropy generation are presented in graphical form. From the results, it is observed that parameter which argument the entropy production rate also enhances the Bejan number. Also, minimization of entropy generation is achieved at low values of thermal radiation, dissipation rate, electric field loading and viscosity variables. Keywords: Inherent irreversibility, Non-Newtonian, Thermal runaway, Reactive fluid, Thermal radiation

In this study, the viscous dissipation of heat transfer of poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel is investigated under different chemical kinetics. The flow is pressure-driven past fixed plates with heat generation. The upper wall surface is exposed to heat exchange with the temperature of the ambient aligning with the Newton’s law of cooling. The modeled coupled partial differential equations are non-dimensional and solved using stable and unconditional semi-implicit convergent finite difference method. The results are represented graphical and discussed accordingly for the velocity and temperature profiles showing the effect of some embodiment parameters entrenched in the system. From the results it was noticed that an increase in Frank-Kamenetskii parameters produces significant rises in the temperature distribution. Keywords: Dissipation, Poiseuille flow, Exothermic reaction, Convective cooling, Finite difference method

The study examines the thermal explosion branched-chain and entropy generation as a result of irreversibility of hydromagnetic reactive couple stress liquid with viscous heating and Navier slips. The reactive fluid flow is enhanced by heat dependent pre-exponential factor and axial pressure gradient in a porous wall. The flow equations for the non-Newtonian couple stress fluid model and heat transfer are solved by employing a semi-analytical collocation weighted residual method (CWRM). The efficiency and validity of the obtained results was verified with the existing results. The results reveal that at low hysteresis magnetic and viscous dissipation the irreversibility process is minimized and thermodynamic equilibrium is improved. The results from this study can assist in understanding the relationship between thermal and thermal explosions branched-chain. Keywords: Thermal criticality, Entropy generation, Viscous heating, Non-Newtonian fluid

Theoretical analysis of thermal stability and inherent irreversibility of reactive hydromagnetic Powell-Eyring fluid flow in a fixed vertical channel with variable electrical and thermal conductivities is examined. The conducting reactive fluid is influenced by gravity and axial pressure gradient under bimolecular kinetic rate law. Ignoring the material assumptions, the governing dimensionless equations are solved by finite semi-discretization difference scheme along with integration Fehlberg Runge-Kutta method. The results for the momentum and heat equations, Bejan number, thermal runaway, entropy generation and current density are graphically presented under different thermophysical parameters. The computational results for the shear stress and heat transfer at the wall is also presented and discussed quantitatively. It was observed that the parameter which enhance the rate of entropy generation also augment Bejan number with large pitch ratio. Hence, entropy generation can be minimized at low dissipation and material variables. Keywords: Thermal runaway, Reactive fluid, Chemical kinetic, Variable conductivity, Non-Newtonian

This study analyses current density and thermodynamics second law of double reaction of a magneto-Oldroyd 8-constant liquid in a convective asymmetric cooling medium. The viscoelastic properties of the liquid are prevented from distortion by convective cooling of the flow media device which is taken to satisfy Newton’s law of cooling. The flow momentum is motivated by exothermic reaction, chemical kinetics and energized by pressure gradient in the absence of material consumption. The dimensionless leading flow equations are solved using partition weighted residual analytical technique to reveal the parameters sensitivity and impacts on the viscoelastic flow liquid, exothermic combustible heat diffusion, entropy generation and current density. The solution results are presented in tables and graphs for clear understanding of the thermophysical parameters implication on the double reaction fluid considered. As observed, the second step reaction enhances exothermic reaction that in turn support complete combustion process in an engine. An improvement of thermodynamic equilibrium through reducing material terms and Frank-Kamenetskii will minimize the entropy generation and promote thermal engineering machine performance. Current density is augmented by rising second step reaction, electric field loading and activation energy ratio.

The study of nonlinear radiation and mixed convection of the MHD heat and mass transfer of Maxwell nanoliquid flow in porous media with Arrhenius kinetic reaction is examined. The non-Newtonian fluid is characterized by Maxwell model, and the species molecular mixture is inspired by the Arrhenius pre-exponential kinetics. Reaction mixture occurs in a boundless slippery plate subject to a considerable quantity of tension that can prevent material deformity. With appropriate similarity variables, the flow model reduces to quasilinear coupled system of derivatives. A numerical simulation of the flow characteristics is carried out, and the results presented in tables and graphs for various thermodynamic phenomena. The results show that the flow momentum is damped by the material term, but augmented by nonlinear heat convection and radiation. The heat transfer rate is significantly propelled by temperature ratio and viscous heating, while the Lewis number, molecular Brownian motion and the chemical reaction term encourage species mass transfer. As such, the study involving activation energy plays a critical part in the diffusion of binary chemical mixtures of energy and species transport which will assist the chemical engineering and others in their activities to prevent reaction blowup.

Parametric sensitivity of unsteady Maxwell magnetohydromagnetic nanofluid and second thermodynamic law analysis under Arrhenius kinetic is investigated in the presence of viscous heating and radiation. The porous flow channel is subjected to tension with material properties that vary with time without deformation. In the absence of fluid charge polarization, the conducting liquid is influenced by the sheet stretching velocity. The flow coupled derivatives model is reduced to dimensionless form by relevant transformation variables. These are computational solved by shooting numerical technique together with Fehlberg Runge-Kutta procedures. The essential characteristics of the flow and thermodynamic irreversibility are determined. The results are quantitatively and qualitatively compared with other studies and are established to agree well. The graphical results revealed that Lewis number increases the molecular species concentration and the thermodynamic stability for reversibility can be enhanced by the augmentation of magnetic field, thermophoresis, and radiation. Therefore, for thermal and chemical reaction systems, increasing heat propagation should be managed to keep the system from blowing up.

This study investigates hydromagnetic fourth-grade reactive diffusion, exothermic temperature distribution of the fluid flow and ignition criticality in a channel. This is important to improve the optimal efficiency of engineering devices and industrial machines. The fully exothermic combustible reaction occurs in a Couette medium with molecular diffusion. Ignoring material reacting consumption, the heat exchange in the system is greater than the ambient heat exchange, and the viscoelastic liquid is propelled by pre-exponential reaction rate and upper wall motion of the device. The resulted highly nonlinear dimensionless time variation, boundary value equations are solved by finite semi-discretization difference method. The obtained solutions for various parameters dependent flow characteristic are plotted and discussed. It is seen that activation energy increases the system thermal criticality while chemical kinetics decreases thermal ignition. Also, it is noticed from the study that the terms that raises the heat generation must be managed in order to prevent solution explosion and enhances optimal performance of engineering devices. The results from this study will assist in understanding the safe and unsafe regime of a system which can help in the chemical synthesis industries and thermal engineering operations.

Investigation into the mathematical analysis of affinity hemodialysis on T-cell depletion is considered to give more significant understanding on the infection dynamics of HIV. Our model revealed the possibility of more than two infected equilibriums with the incorporation of recovery through the affinity hemodialysis. The conditions for stable infected equilibrium to prevent full-blown of AIDS are obtained and stated as hypothesis. This work has, therefore, open the way for partnerships among modelers and clinicians to strengthening the insight into the nature and process of viral multiphasic decay noticed in some treated patients. The initial growth of virus, infected cells and glycoprotein as well as possibility of total viral clearance are examined in the study.

This study investigates the current density and branch-chain thermal criticality for a non-Newtonian hydromagnetic second-grade fluid flow in a Poiseuille device with varying electrical conductivity. The combustible reactive fluid is fully exothermic without material consumption, and the fluid is induced by electric and magnetic fields in the presence of axial gradient pressure. With suitable variables, the equations are translated to dimensionless form and solved by semi finite discretization difference scheme to provide solutions for the heat and velocity dependent parameters. The thermal ignition and slice bifurcation for the criticality, and the current density results are plotted for various dependent terms. It is obtained from the investigation that terms that increases current density in the flow system need to be augmented to improve the current carrying hydromagnetic fluid in order to improve its industrial usage.

Theoretical solutions of a thermal runaway and irreversibility thermodynamic analysis of a couple stress hydromagnetic reactive fluid with Navier slip conditions and variable properties are examined. Ignoring the material assumption, the fluid is taken to be actively exothermic under Bimolecular kinetics. The dimensionless modeled equations are analytically solved using weighted residual method coupled with collocation techniques to obtain the bifurcation branch chain for criticality, irreversibility rate, flow rate and heat distribution solutions. It was noticed that the variable properties have no significant influence on the couple stress reactive liquid and heat distribution. Also, at high thermodynamic equilibrium, entropy generation in the system is minimized. This study results will help in understanding the relationship that exist between thermal explosion and thermal branched-chain in managing industrial engines in order to avoid system blow up. Keywords: Thermal runaway, Irreversibility, Non-Newtonian fluid, Chemical kinetics, Hydromagnetic

The study examines the thermodynamic second law of a Powell-Eyring chemical reaction nanofluid flow with electric field loading and variable heat dependent electrical conductivity. The non-Newtonian radiative flow liquid is induced by electric and magnetic fields. The Powell-Erying Cauchy non-Newtonian model is employed for the viscoelastic effect. With suitable transformations, the modeled equations are successfully solved numerically. The results are plotted to investigate the influences of some emerging terms on the concentration, temperature, momentum, Bejan number and entropy generation. It is revealed from the study that entropy generation is minimized as the radiation, electric field loading and magnetic parameters are increased. Also, to avoid blowing up in the technology and industrial engines, the electric field loading as a current carrying hydromagnetic fluid needs to be encouraged for effective operations and performance of engineering and industrial machines. Keywords: Irreversibility, Viscous heating, Non-Newtonian, Bejan number, Electric field

In this study, the analysis of inherent irreversibility of chemical reactive third-grade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.

The amendibility of a spin-0 and spin-1 particle with a combined potential in the presence of the Duffin-Kemmer-Petiau wave equation is highly recommendable. Thus, the approximate bound state of the Duffin-Kemmer-Petiau equation and Schrӧdinger equation were obtained with a combination of Hulthẻn and Yukawa potentials in the framework of asymptotic iteration method and parametric Nikiforov-Uvarov method respectively for any arbitrary angular momentum quantum number J using a suitable approximate scheme to the centrifugal term. This was done when the second-order homogeneous differential equation was transformed to a form of recurrence relation from which a quantization condition obtained was used to calculate the eigenvalue energy equation and the corresponding wave function. In other to apply more application to this work, the scattering phase shift of the Duffin-Kemmer-Petiau equation was calculated and the thermodynamic properties of the potential under consideration were also calculated in view of the Schrӧdinger equation. It is noted that the results obtained by varying the two strengths of the potential differs due to the effect of the screening parameter. Keywords: Bound state, Wave equation, Eigensolutions, Scattering state, Phase shift, Thermodynamic properties