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The roles of nanoparticles and geometric effects are incredible in nanotechnology. The significant prospective of nanoparticles can be found in the manufacturing of machineries, heating/cooling of nuclear reactors, chemical and thermal engineering, mechanical and aerodynamics, etc. Thus, the current model study is performed for the heat transport mechanism in a newly engineered ternary nanofluid model for sinusoidal surface. The conventional model was updated via influences of ternary nanoparticles, transient phenomena, radiation and heat generation effects, convective and thermal slip impacts. The primary governing laws are reduced into the desired model form via transient similarity expressions and ternary nanoliquid models. Afterward, the shooting scheme supportive by RK technique is endorsed for physical configuration of the model dynamics under multiple ranges of the parameters. The outcomes revealed that both the components of velocity showed different behaviors for nodal and saddle points against the nodal-saddle parameter $s_1$ that is, in the saddle case the velocity is decreased while in the nodal case its value is boosted when the value of $s_1$ is slightly increased. Further, the temperature of the fluid is increased when $Q_1$ and $\mathrm{\text{Rd}}$ varied from $0.1$ to $0.7$. Further, the skin friction augments from $119.5\%$ to $121.55\%$, $121.54\%$ to $129.15\%$ when $s_1$ and $s_t$ vary from $0.1$ to $0.5$, respectively. The Nusselt number improved from $12.2124\%$ to $12.218\%$ (for nanoparticles concentration), $11.9109\%$ to $11.7996\%$ (for heating source $Q_1$ from $0.2$ to $0.5$) and increased from $22.3815\%$ to $47.5804\%$ (for Biot number variations from $0.2$ to $0.5$). Hence, the Biot number highly contributes to the heat transfer rate than other parameters.

The study of squeezing fluids is considered to be one of the most important areas of scientific research due to its various engineering and bioapplications such as the squeezing processes that occur in the brake mechanisms in trucks and Piston’s systems, liquid metal lubrication systems, polymer processing and compression/injection molding as well as the contraction processes in the arteries and veins. This work deals with the study of one of these applications through modeling using the basic equations governing the squeezing fluids and their boundary conditions, and the presence of some external thermal influences such as the magnetic field and linear/nonlinear thermal radiation in its basic form as a nonlinear partial differential equations system, then converting this system into nonlinear ordinary differential equations that were solved numerically and analytically for special cases. The results focused on showing the thermal and flow behavior of the fluid at different concentrations of nanoparticles, which induce the effect of thermal forces represented by the magnetic field and thermal radiation. These results were demonstrated through a set of graphs and tables and discussed in detail, and in summary, some important results were found from the physical analysis. For some of these results, the use of different types and concentrations of particles increases the viscosity of the fluid, which causes an increase in temperature ranging between 17% and 45%.

Stagnation point flow of viscoelastic second grade fluid over a stretching cylinder under the thermal slip and magnetic hydrodynamics effects are studied. The mathematical model has been developed under the assumption of non-Newtonian viscoelastic fluid flow over a stretching cylinder by means of the boundary layer approximations. The developed model further reduced through the similarity transformations and constructs the model of nonlinear ordinary differential equations. The system of nonlinear differential equations is dimensionless and solved through the numerical technique bvp5c methods. The results of the physical parameters are found and interpreted in the form of tables and graphs. The velocity shows that the graph of curves enhances away from the surface when the values material parameter ${\beta }^{\ast }$ increase, which means the momentum boundary layer increases for enhancing the material parameter ${\beta }^{\ast }$. The temperature gradient reduced due enhancing the values of material parameter ${\beta }^{\ast }$ because thermal boundary layer reduced for higher values of material parameter ${\beta }^{\ast }$.

The progress in new inventions in the modern technological world demands outstanding heat transport. Unfortunately, common solvents are unable to produce such desired amount of heat which compelled the scientists and researchers towards the development of new heat transfer fluids (Nanofluids). Therefore, the study of C₈H${}_{18}$ with hybridization of [(MnZnFe₂O₄–NiZnFe₂O${}_4)$]${}_{\mathrm{\text{hnps}}}$ under novel effects of thermal radiations and convective heat conditions over a slippery permeable surface is organized. The modified thermophysical correlations for hybrid nanofluids were used and successfully achieved the modified heat transfer model. After numerical investigation, the results were plotted under varying parameters and provided for comprehensive discussion. The results revealed faster fluid motion and $G^{\prime }(\eta )$ is dominant. The velocities drop significantly due to the permeability of the surface. Further, thermal radiations potentially boost heat transfer by providing extra energy to fluid particles. The temperature coefficient ${\beta }_w$ due to nonlinear thermal radiations also indicated faster heat transport.

The flow of air containing small particles past a pointed area of an aircraft, bullet and bonnet of vehicles exhibits the flow over paraboloid surface of revolution. Therefore, the study of Al₂O₃-H₂O nanofluid over upper paraboloid horizontal surface of revolution (UPHSR) is organized. The concerned model develops via thermal conductivity dealing with the particles shape factor and similarity transforms. Afterward, numerical analysis is performed and the influences of pertinent parameters on the velocity and temperature $𝜃(\eta )$ in Al₂O₃-H₂O are examined. The deep inspection of the results in the view of physics behind them revealed that Al₂O₃-H₂O drops for the stringer magnetic field. Further, nonlinear thermal radiations and internal heat generation made Al₂O₃-H₂O a better heat conductor which increased its applications in a broad zone.

Development of numerical code for evaluating the solidification of water has been scrutinized in this work. The container has two circular and sinusoidal cold walls at bottom and top surfaces. Galerkin-based code has been employed to model this phenomenon. To elevate the conductivity of phase change material (PCM), alumina particles with nanosized were utilized with incorporating different shapes. The conductivity of nanoencapsulated phase change material (NEPCM) is a function of concentration and shapes of nanoparticles. The freezing process is mainly dominated by conduction and selecting curved shaped and adding nanoparticles can affect this mechanism. Verification test reveals the good accommodation and applying adaptive grids leads to higher accuracy. As shape coefficient increases, the period of process declines around 10.65% owing to stronger conduction. Also, mixing water with alumina nanopowders with blade shape causes decrement in needed time around 32.51%. Besides, outputs reveal that utilizing blade shape of powders has more effect on required time than that of cylindrical shape.

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 enchases the performance of the inertial drag on the Buongirino model nanofluid flow past a curved stretching surface embedding within a permeable medium. The radiating heat transport property for the interaction linear approach of Rosseland thermal radiation vis-à-vis reacting species enriches the flow behavior. Further, this study is novel due to the consideration of convective boundary conditions for both the energy and solutal bounding surface condition in association with the slip velocity condition. In a practical situation, when the fluid and surface temperature are different, it is wise not to neglect the convective boundary conditions. The application of convective conditions is useful for the fabrication of the final product in the manufacturing processes. Further, the renovation of the proposed model is obtained for the suitable assumption of the similarity transformation. Traditional numerical technique, i.e., fourth-order shooting-based Runge–Kutta is the best choice for the solution of the set of the transformed equation for the assumed parameters within their specified range. Velocity contour for different parameters vis-à-vis the parametric behavior is presented graphically. Numerical validation as well as the statistical testing for the rate coefficients are the novel approaches of this study. However, interesting outcomes are deployed as follows: The enhanced Brownian and thermophoresis both encourage the fluid temperature, whereas thermophoresis decelerates the fluid concentration.

The consequence of thermal radiation vis-a-vis external heat generation/absorption on the inertial drag force of a hybrid nanoliquid flow in three-dimensional geometry is investigated. It is proposed that with the symmetric or non-symmetric particle shape, the velocity differs because of the direction of the drag. Furthermore, the conducting fluid for the interaction of the magnetic field through a permeable medium past an expanding surface influences the flow phenomenon. The present analysis is useful for the dialysis of blood in the artificial kidneys, the flow of blood in capillaries as well as the design of filters in engineering problems. However, the formulated problem is transformed into its non-dimensional form for the implementation of particular similarity rules. The set of nonlinear governing equations with specific contributing parameter values is subjected to handle by employing shooting-based Runge–Kutta fourth-order technique. Because of the system’s irreversibility, the simulation of entropy and the Bejan value is the main draw. For each profile, the graphical results of specific parameters such as momentum, temperature, entropy, and the Bejan number are shown. Further, the important outcomes are the axial and the transverse velocity profiles are restricted by the inclusion of volume concentration in association with magnetic field and the enhanced Brinkman number augments the entropy generation significantly. However, the numerical validation shows a good correlation between the earlier investigations in particular cases.

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature.

Variable permeability plays a crucial role in various manufacturing and technical applications such as fixed-bed catalytic reactors, heat exchangers, and dying, among others. The primary focus of this paper is to investigate the impacts of variable permeability on hybrid nanofluid (HNF) flow due to nonlinear sheet stretching with thermal heat flux. The HNF is made up of a mixer of ${\mathrm{\text{TiO}}}_2$ and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ nanoparticles and water serving as the base fluid. Using efficient similarity transformations, the flow-governing equations are converted into a set of ordinary differential equations, and the resulting system is computationally solved by using the MATLAB program (bvp4c). The impact of various physical variables on the fluid velocity and heat transfer characteristics is analyzed via graphs. It is found that as the permeability parameter rises, the velocity of the HNF diminishes while the temperature amplifies. The drag force coefficient declines with an intensification of the volume fraction of the ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$ nanoparticles. The HNF $({\mathrm{\text{TiO}}}_2+{\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕{\mathrm{\text{H}}}_2\mathrm{\text{O}})$ exhibits 0.45–0.75% increase in heat transfer rate when compared to a nanofluid $({\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4∕{\mathrm{\text{H}}}_2\mathrm{\text{O}})$ for different values of heat source parameter. The current investigation is compared to the existing literature, revealing a good level of agreement.

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.