Search Results (10)

The fluid flow through blunt bodies that are yawed and un-yawed frequently happens in many engineering applications. The practical significance of deep-water applications such as propagation control, splitting the boundary layer over submerged blocks, and preventing recirculation bubbles is explained by the fluid flow across a yawed cylinder. The current work examined the mixed convective flow and convective heat transfer by incorporating water-based graphene oxide nanofluid around a yawed cylinder with viscous dissipation and irregular heat source/sink. To investigate the heat diffusion across the system of buoyancy effects, the mathematical formulation of the problem was modeled in terms of coupled, nonlinear partial differential equations. The boundary value problem of the fourth-order (bvp4c) solver was operated to find the non-similarity solution. The outcomes indicated that the velocity in both directions enlarged owing to the higher impacts of yaw angle for the phenomenon of assisting flow but decreased for the instance of opposing flow, while the temperature of nanofluid increased because of heightened estimations of yaw angle for both assisting and opposing flows. In addition, with larger impacts of nanoparticle volume fraction, the shear stresses were enhanced by about 0.76% and 0.93% for the case of assisting flow, while for the case of opposing flow, they improved by almost 0.65% and 1.38%, respectively. Full article

The need for effective heating and cooling systems in the automotive, chemical, and aerospace industries is driving a rapid proliferation of heat-transfer technology. In recent times, GO (Graphene Oxide) has been emerging as one of the most promising nanoparticles because of its uninterrupted behavior of electrical conductivity even at a minimum carrier concentration. Due to this incentive, the behavior of jet flow with heat and mass transfer features of electrically conducting based kerosene oil (KO) fluid dispensed by graphene nanoparticles was studied. In addition, the activation energy, irregular heat source/sink, thermophoretic particle deposition, and chemical reaction are also provoked. In order to provide numerical results, the boundary value problem of fourth-order (bvp4c) solver was used. The graphs were used to illustrate the effects of relevant parameters on the fluid flow, heat, and mass transfer rates. The incorporation of graphene nanoparticles significantly improves heat conductivity. Additionally, the nanoparticle volume fraction augments the temperature and concentration profile while the velocity profile declines. Moreover, the temperature enhances due to the heat source, whilst the contrary behavior is observed in the presence of the heat sink. Furthermore, the shear stress increases up to 12.3%, the Nusselt number increases up to 0.119%, and the Sherwood number increases up to 0.006% due to the presence of nanofluid. Finally, we can conclude that the latest work will be useful for thermal cooling systems, including cooling for engines and generators, nuclear systems, aviation refrigeration systems, and other systems. Full article

The present study reveals the behavior of shear-thickening and shear-thinning fluids in magnetohydrodynamic flow comprising the significant impact of a hybrid nanofluid over a porous radially shrinking/stretching disc. The features of physical properties of water-based Ag/TiO₂ hybrid nanofluid are examined. The leading flow problem is formulated initially in the requisite form of PDEs (partial differential equations) and then altered into a system of dimensionless ODEs (ordinary differential equations) by employing suitable variables. The renovated dimensionless ODEs are numerically resolved using the package of boundary value problem of fourth-order (bvp4c) available in the MATLAB software. The non-uniqueness of the results for the various pertaining parameters is discussed. There is a significant enhancement in the rate of heat transfer, approximately 13.2%, when the impact of suction governs about 10% in the boundary layer. Therefore, the heat transport rate and the thermal conductivity are greater for the new type of hybrid nanofluid compared with ordinary fluid. The bifurcation of the solutions takes place in the problem only for the shrinking case. Moreover, the sketches show that the nanoparticle volume fractions and the magnetic field delay the separation of the boundarylayer. Full article

Nanofluids offer the potential to improve heat transport performance. In light of this, the current exploration gives a numerical simulation of mixed convection flow (MCF) using an effective Prandtl model and comprising water- and ethylene-based γ${\mathsf{\gamma }-\mathrm{Al}}_2{\mathrm{O}}_3$ particles over a stretched vertical sheet. The impacts of entropy along with non-linear radiation and viscous dissipation are analyzed. Experimentally based expressions of thermal conductivity as well as viscosity are utilized for γ${\mathsf{\gamma }-\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles. The governing boundary-layer equations are stimulated numerically utilizing bvp4c (boundary-value problem of fourth order). The outcomes involving flow parameter found for the temperature, velocity, heat transfer and drag force are conferred via graphs. It is determined from the obtained results that the temperature and velocity increase the function of the nanoparticle volume fraction for ${\mathrm{H}}_2{\mathrm{O}\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ based γ${\mathsf{\gamma }-\mathrm{Al}}_2{\mathrm{O}}_3$ nanofluids. In addition, it is noted that the larger unsteady parameter results in a significant advancement in the heat transport and friction factor. Heat transfer performance in the fluid flow is also augmented with an upsurge in radiation. Full article

In this paper, we prove the existence and uniqueness of solution for some Riemann–Liouville fractional nonlinear boundary value problems. The positivity of the solution and the monotony of iterations are also considered. Some examples are presented to illustrate the main results. Our results generalize those obtained by Wei et al., (Existence and iterative method for some fourth order nonlinear boundary value problems. Appl. Math. Lett. 2019, 87, 101–107.) to the fractional setting. Full article

In this paper, we find the solutions of fourth order fractional boundary value problems by using the reproducing kernel Hilbert space method. Firstly, the reproducing kernel Hilbert space method is introduced and then the method is applied to this kind problems. The experiments are discussed and the approximate solutions are obtained to be more correct compared to the other obtained results in the literature. Full article

The present study emphasizes the combined effects of double stratification and buoyancy forces on nanofluid flow past a shrinking/stretching surface. A permeable sheet is used to give way for possible wall fluid suction while the magnetic field is imposed normal to the sheet. The governing boundary layer with non-Fourier energy equations (partial differential equations (PDEs)) are converted into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. The approximate relative error between present results (using the boundary value problem with fourth order accuracy (bvp4c) function) and previous studies in few limiting cases is sufficiently small (0% to 0.3694%). Numerical solutions are graphically displayed for several physical parameters namely suction, magnetic, thermal relaxation, thermal and solutal stratifications on the velocity, temperature and nanoparticles volume fraction profiles. The non-Fourier energy equation gives a different estimation of heat and mass transfer rates as compared to the classical energy equation. The heat transfer rate approximately elevates 5.83% to 12.13% when the thermal relaxation parameter is added for both shrinking and stretching cases. Adversely, the mass transfer rate declines within the range of 1.02% to 2.42%. It is also evident in the present work that the augmentation of suitable wall mass suction will generate dual solutions. The existence of two solutions (first and second) are noticed in all the profiles as well as the local skin friction, Nusselt number and Sherwood number graphs within the considerable range of parameters. The implementation of stability analysis asserts that the first solution is the real solution. Full article

In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature. Full article

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution. Full article

A study on mixed convection boundary layer flow with thermal radiation and nanofluid over a permeable vertical cylinder lodged in a porous medium is performed in this current research by considering groupings of a variety nanoparticles, consisting of copper (Cu), aluminium (Al₂O₃) and titanium (TiO₂). By using a method of similarity transformation, a governing set of ordinary differential equations has been reduced from the governing system of nonlinear partial differential equations, which are the values of selected parameters such as mixed convection parameter $\lambda$ , nanoparticle volume fraction $\phi$ , radiation parameter Rd, suction parameter S, and curvature parameter $\xi$ are solved numerically. From the numerical results, we observed that the involving of certain parameters ranges lead to the two different branches of solutions. We then performed a stability analysis by a bvp4c function (boundary value problem with fourth-order accuracy) to determine the most stable solution between these dual branches and the respective solutions. The features have been discussed in detail. Full article