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This work examines the behaviour of flow and heat transmission in the presence of hybrid nanofluid in thermal radiation, heat generation, and magnetohydrodynamics. The hybrid state in this model is represented by two different fluids, TiO2 (titanium dioxide) and Ag (silver). The enclosure is wavy and slanted, with curving walls on the left and right. The finite difference approximation method was utilized to resolve the fundamental equations after they were non-dimensionalized, which are further reduced to a fourth-order bi-harmonic equation and are numerically solved based on the biconjugate gradient-stabilized approach method. The simulations are performed with various Rayleigh numbers, Hartmann numbers, an inclination angle of the enclosure, radiation parameters, heat generation parameters, inclination angle of the magnetic field, and volume fraction of hybrid nanoparticles. The streamlines, isotherms, and average Nusselt number contours are used to depict the thermo-fluid patterns. The findings show that the average Nusselt number relies on ϕ and increases as ϕ rises. The investigation’s findings demonstrated that the transfer of heat on the heated bottom wall significantly increases with the Rayleigh number (Ra = 105 and 106). At a cavity inclination of 45°, interesting multi-vortex structures are observed. The results of this study may enhance the effectiveness of solar collectors, heat exchangers, and other similar systems that depend on convective heat transfer in nature.

Recently, experts have become particularly interested in the treatment of disorders caused by magnesium shortage. Hypomagnesemia is produced by a magnesium deficit in the blood, which is an additional stimulation for different diseases such as vomiting, drowsiness, nausea, loss of appetite, and so on. To compensate for this shortage, magnesium is injected as a nanoparticle in the blood (base fluid). The properties of these magnesium nanoparticles specifically their size, dispersion, and surface characteristics are crucial for optimizing their bioavailability and therapeutic efficacy. Advanced material characterization techniques ensure the stability and enhanced performance of these nanoparticles in the physiological environment. Based on these applications, the current research aims to address magnesium deficiency via Powell–Eyring nanofluid flow distorted by the linearly stretchable sheet in the region of the stagnation point. Linear thermal stratification, viscous dissipation, and Joule heating are used to reveal the heat transport features. The magnetic field is applied to the nanofluid at an angle α to further control the fluid dynamics and nanoparticle behavior. Transformations are used to create a set of dimensionless governing equations. Comparative graphs are used to explain the physical behaviors of temperature and velocity fields, demonstrating how material properties impact fluid dynamics. The well-known convergence method (homotopy analysis method) is used to solve the model by comparing graphs.

Nanofluids have many applications in industries as well as engineering such as biomedicine, manufacturing, and electronics. Nanofluid is used for improvement of thermal and mass transmission. Based on the aforementioned applications, in the present study, a two-dimensional Maxwell nanofluid with thermal radiation effect on the existence of motile microorganisms over a vertically stretchable surface is explored. The consequence of heat absorption, the efficiency of heat flux in a porous medium, viscous dissipations, and Joule heating impacts are considered. The Brownian and thermophoretic diffusion effects have been evaluated. In addition, the binary chemical reaction is taken into account to evaluate the magnetohydrodynamics (MHD) mixed convection flow. Graphene nanoparticles are suspended in so-called engine oil (base fluid). The proposed liquid model depends on the governing nonlinear equations of velocity, temperature, the concentration of nanoparticles, and motile gyrotactic microorganisms. In order to transform highly nonlinear partial differential equations into nonlinear ordinary differential equations, an appropriate similarity transformation is exploited. For the solution of the present study, the homotopy analysis method-technique in Mathematica-12 is used. The fluctuation of velocity, temperature, concentration, and gyrotactic microorganisms’ characteristics for numerous flow parameters is discussed in detail. Some important fallouts of the existing study are that the Maxwell liquid parameter, Eckert number, and magnetic parameter lessen the nanoliquid velocity. But the fluid temperature becomes higher for growing estimates of the Brownian motion and thermophoretic factors. The radiation and chemical reaction parameters have declining impacts on the solutal profile. The motile microorganism profile shows a decrement in bioconvection Lewis and Rayleigh numbers. The nanofluid thermal profile is improved but the nanofluid velocity declined through the augmentation of volume fraction. Also, the coefficient of skin friction and Nusselt number are obtained versus various flow parameters.

This theoretical work suggests a novel nonlinear thermal radiation and an applied magnetic feature-based three-dimensional Casson nanomaterial flow. This flow is assumed in the rotating frame design. Gyrotactic microorganisms (GMs) are utilized in the Casson nanofluid to investigate bioconvection applications. The altered Buongiorno thermal nano-model is used to understand the thermophoretic and Brownian mechanisms. Convective boundary conditions must be overcome to solve the flow problem. With suitable variables, the dimensionless pattern of equations is obtained. The solutions to the nonlinear formulations are then obtained using semi-analytical simulations using a homotopy analysis mechanism. It was found that the velocity outline is enhanced with the enhancing estimations of the buoyancy ratio, rotation factor, and Casson parameter while it is reduced with mixed convection, porosity, slippery parameters, and Rayleigh number. The temperature profile is increased with radiation, the temperature ratio, the thermophoretic parameter, the Brownian parameter, and the Biot number. The Brownian parameter reasons an improvement in the concentration outline contrary to the thermophoretic parameter. The concentration of GMs is decreased with the Peclet number inversely to the Lewis number effect, which causes an increase in the microorganisms’ concentration.

Our key objective in the present work is to elaborate the concept of activation energy in chemically reactive flow with the help of modeling and computation. The model investigated is fluid flow over a vertical cylinder in the porous medium with chemical reaction and radiation effect. The similarity transform converted the resulting constitutive equations and partial differential equations (PDEs) into ordinary differential equations (ODEs). The resulting non-linear momentum, heat transfer, and mass transfer coupled equations are computed with the Range–Kutta–Fehlberg method. Both assisting and non-assisting buoyant flow conditions are considered, and observed numeric solutions vary with the transport properties. Characteristics of momentum, heat, and concentration under the applied boundary conditions are analyzed. In addition, the increment in activation energy parameters boosts the Lorentz force and mass transfer rate.

More effective and lengthy energy storage systems have been highly desired by researchers. Waste heat recovery, renewable energy, and combined heating and power reactors all utilize energy storage technologies. There are three techniques that are more effective for storing thermal energy: Latent heat storage is one type of energy storage, along with sensible heat storage and chemical heat storage. Latent thermal energy storage is far more efficient and affordable with these methods. A method of storing heat energy in a substance is melting. The substance is frozen to release the heat energy it had been storing. A ground-based pump’s heat exchanger coils around the soil freezing, tundra melting, magma solidification, and semiconducting processes are examples of melting phenomenon. Due to the above importance, the present study scrutinizes the behavior of third-grade nanofluid in a stagnation point deformed by the Riga plate. The Riga plate, an electromagnetic actuator, is made up of alternating electrodes and a permanent magnet that is positioned on a flat surface. Graphene nanoparticles are put in the base fluid (Mineral oil) to make a homogenous mixture. Mathematical modeling is acquired in the presence of melting phenomenon, quadratic stratification, viscous dissipation, and slippage velocity. Suitable transformations are utilized to get the highly non-linear system of ODEs. The remedy of temperature and velocity is acquired via the homotopic approach. Graphical sketches of various pertinent parameters are obtained through Mathematica software. The range of various pertinent parameters is 1≤B1≤4,B2=1,3,5,7,B3=0.1,0.5,0.9,1.3,0.8≤A≤1.2,Re=1,3,5,7,S1=1,3,5,7,M1=1,6,11,16,0.1≤ϑ≤0.4,0.1≤Q≤0.4,Ec=1,3,5,7,0.1≤S≤0.4andNr=1,6,11,161\le {B}_{1}\le 4,\hspace{.5em}{B}_{2}=1,3,5,7,{B}_{3}=0.1,0.5,0.9,1.3,\hspace{.5em}0.8\le A\le 1.2,\mathrm{Re}=1,3,5,7,\hspace{.2em}{S}_{1}=1,3,5,7,\hspace{.5em}{M}_{1}=1,6,11,16,\hspace{.25em}0.1\le {\vartheta }\le 0.4,\hspace{.33em}0.1\le Q\le 0.4,\text{Ec}=1,3,5,7,\hspace{.5em}0.1\le S\le 0.4\hspace{.65em}\text{and}\hspace{.65em}\text{Nr}=1,6,11,16. Skin friction (drag forces) and Nusselt number (rate of heat transfer) are explained via graphs. The velocity is enhancing the function against melting parameter while temperature is the decelerating function as melting factor is amplified. The temperature field reduces with the accelerating estimations of stratified parameter. The energy and velocity profiles de-escalate with intensifying values of volume fraction parameter.

This work mainly deals with the effect of heat, mass transmission, and heat generating (sinking) on the time-independent two-dimensional boundary-layer flowing of radiative MHD over a sheet, which is dwindling including Joule heating. The governing formulas have been converted into nonlinear ordinary differential equations (NLODE). The final step aims to obtain the graphical numerical illustrations from the set of NLODE; this method is namely as shooting using MATLAB. The accuracy of the outcomes from this study are examines and the comparison have been made by using bvp4c routine of MATLAB. The effect of different material factors on the flow speed, energy, and concentricity have been depicted in diagrams and tables and also discussed in detail. It is found that velocity is enhanced by increasing suction, whereas temperature is increased due to radiation, heat source/sink, and Eckert number. Meanwhile, concentration profile is always being suppressed by magnetic fields, suction, Schmidt number, and chemical reaction parameter. The streamline of the velocity is intensified at the region close to the dwindling surface, whereas the density is the highest for the thicker boundary layer thickness for the temperature and concentration streamlines. [ABSTRACT FROM AUTHOR]

Mineral Oil [MO] has significant importance because of its vast variety of applications in various arenas of manufacturing, technology, and industrial processes. The applications of the Mineral Oil [MO] are PVC production, polystyrene production, as a lubricating, cutting fluid, thermoplastics rubber production, glossing product, wood products, cleaning products, lamp oil, glues, toys, veterinary, cosmetics, food preparation, as a brake fluid in some cars, and so forth. Due to these applications of Mineral Oil [MO], in the existing work, the two-dimensional mixed convective flow of micropolar fluid with the applications of the aluminum oxide nanoparticles in a Mineral Oil [MO] base liquid is taken into consideration. The melting heat phenomenon is discussed for the interpretation of heat transmission. Further, the flow analysis is discussed through the impacts of inclined magnetic field, heat generation, Joule heating and thermal radiation. Mass diffusivity is deliberated through the implementation of homogenous and heterogeneous chemical reactions. Entropic behavior is analyzed for the discussion of irreversibility analysis. Suitable similarity transformations are employed to renovate modeled systems of the PDEs into ODEs. Analytical simulation of the proposed model has been accomplished with the utilization of the homotopy analysis technique. Some significant outcomes from the existing work are that the velocity outline is reduced but the energy curve is greater for the melting parameter. Nanofluid entropy generation is increased due to the improvement of the Brinkman parameter and material parameter. Heat transportation is augmented due to the amplification of the radiation parameter, and nanoparticle volume fraction. The present study is useful in different fields of industries, technological processes, mechanical processes, and electrical processes due to the applications of mineral oil. [ABSTRACT FROM AUTHOR]