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Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid.

The ternary hybrid nanofluids have potential in different technological arenas such as biomedical engineering, solar energy, atomic reactors, the automotive industry, and heat pipes. Given these facts, along with the recent advancements in nanotechnology and their extensive applications, this research focuses on the MoS₂-Fe₃O₄-ZrO₂/CH₃OH ternary nanofluid flow through bidirectional stretching sheets. We have transformed the coupled nonlinear partial differential equations for the advanced model into nondimensional ordinary differential equations using similarity transformations, and then semi-analytically apply the homotopy analysis methodology (HAM). We have displayed the physical features of potential factors graphically alongside the flowing factors based on velocity and temperature. We presented a physical evaluation in tabular format for the rate of heat transmission and compared the results with existing work to ensure their validity. These meaningful outcomes indicate that the axial fluid velocity is compressed by the magnetic interaction, inertial drag, porosity and stretchable ratio, while it is augmented by the Powell-Eyring factor and the changed Hartmann value. The effect of increasing transverse speed boosts inertial drag.

The investigation delves into the examination of Jeffreys fluid flow within a porous medium, incorporating a temperature-dependent heat source and throughflow, while also taking into account the presence of an external electric field. The eigenfunction, also known as the critical Rayleigh number, is obtained to determine the initiation of convection by employing Galerkin processes during the linear stability analysis. Subsequently, the findings are scrutinized by means of graphical illustrations to explore the impacts of various factors, including the Jeffreys parameter, heat source, throughflow, and electric field. Upon careful examination of the outcomes, it becomes evident that specific parameters, such as the Jeffreys parameter, heat source, and throughflow parameters, exert an influence in stabilizing the system under consideration. The investigation evidently points toward an observation that an augmentation in the electric field parameter results in an accelerated onset of convection. This observation implies that the external electric field assumes a role as a destabilizing element within the system, thereby intensifying the convective tendencies exhibited within the medium. The results demonstrated that elevated throughflow characteristics played a significant role in the postponement of convection onset, while a rise in the heat source parameter dependent on temperature was found to enhance the overall stability of the system. Additionally, it was observed that the downward throughflow exhibited a greater stabilizing influence when juxtaposed with the upward throughflow, particularly in scenarios involving the Jeffreys term and electric fields. The implications of these findings suggest a complex interplay between throughflow parameters, temperature-dependent heat sources, and external forces, highlighting the intricate dynamics governing convection initiation and system stability in the studied environment.

This investigation predicts the assessment of mass and heat transfer due to Burgers nanofluid. The investigation is further supported by triple diffusion flow. Variable thermal conductivity is accounted to endorse the thermal flow. In the heat equation, the extension is suggested by utilizing the external heat source and nonlinear radiated phenomenon. Computations for modeled problems are achieved by the shooting method. The fundamental role of parameters governing flow is noticed which is physically attributed. It is observed that the heat transfer rate is enhanced due to the modified Dufour number. The solutal concentration declined for the regular Lewis number. Furthermore, the nanoparticles concentration reduces due to the nano-Lewis number. The depicted results convey novel applications in chemical processes, cooling control systems, refrigeration, solar energy, extrusion processes, etc.

This study explores heat and mass transport in natural convection of Casson fluid in a vertical annulus via porous medium. Impacts of thermal radiation, heat source and chemical reaction are taken into consideration. The equations representing the model reduced into nondimensional ordinary differential equations under adequate transformations are solved analytically. Closed form solutions are obtained for the problem in terms of Bessel’s functions. Influences of various arising parameters such as porous medium parameter, heat generation, thermal radiation, thermal Grashof number, solutal Grashof number, etc. on flow, temperature and concentration fields are exhibited by graphs and discussed. Also, we have solved the problem numerically on MATLAB software employing the bvp4c technique along with shooting technique. The exact and numerical solutions compared found a good match. Moreover, the effects of numerous parameters on quantities of physical importance such as skin-friction coefficient, Nusselt number and Sherwood number are also portrayed and discussed. Heat exchangers, energy storage systems such as batteries and inverters, thermal storage and thermal protection systems are some examples of applications of the study.

In this analysis, the stability of MHD stagnation point flow and heat transfer of an electrically conducting viscous incompressible fluid on a horizontally stretching/shrinking permeable cylinder with volumetric heat source are investigated. The cylindrical surface is subjected to a cross flow and a heat flux. This analysis finds applications in the areas of polymeric processing unit due to stretching/shrinking of surface and biofluid flows with therapeutic effects through the arteries, vein and digestive system that have a tube-like structure. Other aspects of the analysis are: magnetic field intensity whose strength can be remotely controlled and embodied generating/absorbing thermal power. The solution of the boundary value problems (BVP) is carried out with MATLAB’s inbuilt solver bvp4c. The most significant findings are recorded as: an increase in magnetic field strength increases the skin friction at the solid surface which is consistent with progressive thinning of boundary layer. This striking result is of interest in industrial applications because it is easy to regulate the magnetic field strength by electromagnetic devices such as controlling the voltage in the electric circuit. There is a point of neutrality of thermal energy distribution during the high fluctuation of temperature irrespective of the presence of heat generation or absorption. This can be attributed to the dominating effect of stretching/shrinking of the surface. The first solution provides stability of the flow with an increase in velocity in the presence of heat sink that is commensurate with the strength.

Nanofluid and magnetic field impacts are significant in bioengineering and medical treatment. The effectiveness of gold particles in blood flow (Sisko fluid flow) with nonlinear thermal radiation and heat source over a curved surface is investigated in this work. The partial slip influence is utilized to explore the characteristics of nanofluid flow in depth. The Sisko model’s first-order partial differential equations (PDEs) are simplified to ordinary differential equations (ODEs) by employing suitable variables. The findings are displayed by using the bvp4c (shooting approach) in MATLAB. When compared to earlier reports, the accuracy is found to be satisfactory. In addition to the influence of a magnetic field and radiation, although both are useful in therapeutic hyperthermia, the magnetic field reduces the velocity distribution. The velocity profile is boomed for the estimations of slip parameter while declined for the suction parameter. The thermal profile is boosted up for the higher magnitude of temperature ratio parameter and Biot number. The thermal profile is decreased for the greater values of the suction parameter while increases for the heat source parameter.

The extension of nanoliquid obtained by adding nano-powder composite or various nanoparticles in regular liquid is term as hybrid nanofluid. Hybrid nanofluids are more potential materials that significantly uplift the thermophysical feature and capacity of heat transportation instead of single nanoparticle nanoliquid. Hence, the paramount interest of this paper is to model theoretically the flow of aqueous alumina–titania hybrid nanoliquid across a rotating channel. Temperature-based viscosity is addressed. This analysis further contributes the impact of heat source and dissipation phenomena. Additionally, two different shapes of nanoparticles, namely, bricks- and needle-shaped are included. Similarity variables dimensionless the governing problem. The obtained system is solved by employing Mathematica-based NDSolve approach. The impact of various embedded variables is elucidated graphically. The presence of hybrid nanocomposite greatly affects the temperature and Nusselt number than nanoparticles. Further outcomes declared that rotation and heat source variables significantly increase the thermal field for hybrid nanophase when compared with nanophase.

This paper studies the recent flow phenomena based upon the kerosene-based nanofluid through vertical parallel channel for the consideration of the variable thermal conductivity. The free convection of electrically conducting MHD fluid due to the interaction of inertial drag along with thermal radiation, heat source and the dissipative heat enriches the study as well. The structural behavior of the physical quantities is useful in recent applications like the cooling processes in refrigerators, semi-cryogenic rocket engine, etc. because of the practical application of the kerosene-based nanofluid. Also, the models associated with the thermophysical properties such as viscosity and thermal conductivity for the choice of volume concentration are favorable for the thermal enhancement. The designed model for the transport phenomena is transformed to its non-dimensional form for the suitable choice of similarity variables and the set of equations are handled by traditional numerical technique. Further, the involvement of the physical parameters and their physical significance is described briefly for the appropriate values within the specified range. Finally, the important outcomes of the study are that nanoparticle concentration has vital role in decelerating the fluid velocity and the fact is due to the heavier density and the inclusion of porous matrix is useful to retard the wall thickness at both the ends. Moreover, the increasing concentration favors in enhancing shear rate at the first wall whereas near the second wall, the impact is opposite.

This paper presents an investigation of magnetohydrodynamics (MHD) Casson nanofluid flow along a stretchable surface through a permeable medium. The modeling of the physical phenomena is considered with impact of thermal radiation, heat generation, slip conditions and suction. Transformations of the governing set of mathematical equations for the physical model are carried out into nonlinear ordinary differential equations (ODEs) with appropriate similarity variables. The nonlinear ODE solutions are carried out using the optimal homotopy analysis technique (OHAM), and the findings are presented for determining the influences of the emerging important parameters. The results indicate that velocity field increases in respect of porosity parameter, Casson fluid parameter and magnetic parameter while it declines for enhancing velocity slip and suction parameters. The temperature profile shows rising behavior for heat source, Prandtl number, thermophoresis, radiation and Brownian motion parameters while it declines for enhancing thermal slip parameter. Moreover, the concentration profile enhances for rise in Brownian motion parameter while it reduces for Schmidt number and nanoparticle parameter. We also showed the accuracy of the present results by indicating that skin friction values for varied magnetic parameters agree with earlier findings in the literature.

This paper analyzes the heat transport phenomena of two-phase nanofluid within a permeable circular segment with an interaction of Arrhenius activation energy and, examines the interaction of convective boundary conditions affecting the flow characteristics. The pre-exponential factor of the Arrhenius equation deals with the collision between molecules, and it has significant applications for getting the rate of a chemical reaction and is used to estimate material properties with changes in temperature and energy. To a greater extent, the external uniform heat source encourages thermal properties on account of the behavior of Brownian and thermophoresis parameters. The transformation of the standard nondimensional form of the governing equations is obtained for the assumption of appropriate similarity variables and stream function. The set of these transformed equations is tackled numerically with the shooting technique. The characteristics of physical parameters on the flow phenomena are presented graphically and the validation with earlier research displays a strong correlation for the specific case. The special attraction of the present investigation is the regression analysis for the simulated results of heat and solutal transfer rates using Response Surface Methodology considering various characterizing parameters like heat source, thermal radiation, curvature, activation energy, thermal and solutal Biot numbers within certain range.

We intend to analyze the influences of heat dissipation and heat generation on steady nanofluid stagnated flow along an extending surface along with thermal boundary layers. Water-based Cu and Al₂O₃ nanoparticles are considered. Moreover, the mechanism of injection/suction has been analyzed for such flows. Fundamental governing equations for the flow of an isotropic in-compressible thermally radiative single-phase nanofluid are defined by the set of nonlinear Partial Differential Equations (PDEs) which are transmuted to Ordinary Differential Equation (ODEs) and dealt with numerically by using Runge–Kutta (RK) fourth-order adopting shooting technique that gives approximate simulations. The numerical findings are illustrated as graphical and tabular representations after a careful parametric examination of determined parameters is carried out. The current outcomes specify that the velocity profiles decrease under the influence of magnetic strength while heat distribution positively changes under the effect of magnetic strength, heat source, radiative term and Biot number quantity. The temperature profiles behave negatively with the thermal Grashof number and Prandtl number. Moreover, the comparative simulations of the ongoing study with existing the literature for ensuing the obtained simulations have been worked out.

This paper considers two-dimensional electrically conducting and incompressible ternary hybrid nanofluid flow on a stretching sheet with the convective boundary condition and heat source effect. Relevant similarity formulas are effectuated in converting the governing equations into a system of ordinary differential equations (ODEs) and are further treated numerically using the spectral quasilinearization method (SQLM), with error analysis. The prominent dimensionless parameters controlling the flow, and heat transfer characteristics are discussed. The results of this study show that Eckert number, heat source parameter, and magnetic effect boost the temperature profile. This work expected significant information for the future applications of innovative heat transfer devices, as well as a valuable reference for researchers to study flow behavior under various assumptions.

This study emphasizes the dual exposition of the impact of convective condition and the significant effects of magnetic field, heat source and velocity slip on hybrid nanofluid flow over the exponentially shrinking sheet. The hybrid nanofluid is regarded as a contemporary variety of nanofluid; consequently, it is utilized to enhance the efficiency of heat transfer. By applying the Tiwari–Das model, the key objective of the current research is to investigate the impact of involving factors Biot number, Eckert number, volume fraction, magnetohydrodynamic (MHD), slip and suction on the temperature and velocity profiles. In addition, the Nusselt number and skin friction variations have been explored against the suction effect on the solid volume fraction of copper ${\varphi }_2\in$ [1–3%] and the Biot number $\mathrm{\text{Bi}}\in$ [1–3%]. The nonlinear partial differential equations are converted to a set of an ordinary differential equations by incorporating exponential similarity vectors. Eventually, ordinary differential equations are rectified utilizing MATLAB bvp4c solver. The results demonstrate the presence of dual exposition for suction with varying values of copper volume fraction and the Biot number. The heat transmission rate is observed to escalate in both cases as the strength of the Biot and Eckert numbers intensifies in the range of 1–3%. In summary, the results show that duality and non-unique solutions occur in the aiding flow situation when the suction $S\ge S_{\mathrm{\text{ci}}}$, while there is no flow and unique solutions of hybrid nanofluid feasible when $S<S_{\mathrm{\text{ci}}}$.

In recent days, entropy generation has attracted the attention of several researchers due to its applications in manufacturing electronic devices, heat exchangers, conservation of energy, and generation of power. Further, activation energy is an essential requirement in automobile and chemical industries, nuclear reactors, and so on. This paper investigation aims to examine the entropy generation and the mass and energy transfer in the magneto-hydro dynamic movement of convective Carreau-Yasuda nano liquid past a porous stretching sheet with the consequences of activation energy, energy source, and binary chemical reaction. Also, the analysis of the impact of viscous and Joule dissipation in the presence of suction/injection into the Buongiorno model is an essential objective of this study. By introducing a similarity variable, the partial differential equations are altered into a system of ordinary differential equations. Numerical solutions to the modified equations are determined by utilizing a BVP5C MATLAB package. The findings are presented visually for several relevant flow characteristics and explained carefully. The thermophoresis parameter and activation energy parameter optimize the concentration of nanoparticles. These outcomes further indicate that as the larger Brinkmann and permeability parameters the entropy generation is broadened. It is discovered that an augmentation in thermal and solutal Grashof numbers is associated with greater velocity distribution.

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution.

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno’s relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile $\phi (\eta )$. Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number.

The temperature field due to laser-induced discharge surface strengthening (LIDSS) has significant influence on the microstructure transformation and also the formation quality of discharge pit. A transient axisymmetric thermal model is developed to estimate the temperature distribution during LIDSS based on Fourier heat conduction equation. In the model, a Gaussian heat input distribution is assumed; temperature-dependent material properties are applied and the latent heat of fusion and vaporization is calculated on an enthalpy method. As an application, we use this model to compute the temperature field during the process of tungsten tool electrode machining 1045 steel workpiece and find that the computational results are well consistent with the experimental data.

In this paper, an innovative form of nanofluids is identified as tri-hybrid nanofluid, which is synthesized by dispersing three or more varieties of nanomaterials in the considered base fluid. So, in this study, we comparatively examined SiO₂/H₂O nanofluid, TiO₂+Al₂O₃/H₂O hybrid nanofluid and SiO${}_{2+}$TiO₂+Al₂O₃/H₂O ternary hybrid nanofluid. Stretching of the flat surface enables us to develop the nanofluids flow. Additional considerations include the impacts of MHD, viscid dissipation, nonlinear thermal convection and radiation, joule heating and the presence of a heat source. For transforming PDEs (continuity, motion, heat equation and boundary constraints) into ODEs, an appropriate transformation procedure is used. HAM technique is used to solve these nonlinear coupled ODEs. Graphs are used to evaluate and examine the effect of numerous describing variables on nano, hybrid and tri-hybrid nanofluids speed and heat distribution. Furthermore, the computed values of engineering-relevant parameters ($C_f$ and Nu) are tabulated and analyzed. The velocity of nanofluids acquires enhancing tendency for nonlinear thermal and mix convection parameter, but reverse upshot is assured due to nanoparticle volume fraction, Weissenberg number and magnetic parameters. Thermal field gets intensified in nature for magnetic and Eckert number, heat generation, thermal radiation and nanoparticles volume fractions. The ternary hybrid nanofluid has the most efficient behavior according to the comparative examination of ternary, hybrid and nanofluids.

A numerical model based on the dual reciprocity boundary element method (DRBEM) for studying the transient magneto-thermo-viscoelastic stresses in a nonhomogeneous anisotropic solid subjected to a heat source is presented. The formulation is tested through its application to the problem of a solid placed in a constant primary magnetic field acting in the direction of the z-axis and rotating about this axis with a constant angular velocity. In the case of plane deformation, a numerical scheme for the implementation of the method is presented and the numerical computations are carried out for the temperature, displacement components and stress components. The validity of DRBEM is examined by considering a magneto-thermo-viscoelastic solid occupies a rectangular region and good agreement is obtained with existent results. The results obtained are presented graphically to show the effects of inhomogeneity and heat source on the temperature, displacement components and thermal stress components.