Search

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S c ≤ S   and   M c ≤ M ( S c > S   and   M c > M ). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. [ABSTRACT FROM AUTHOR]

In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge–Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when λ1 = 0 where λ1 is a mixed convection parameter and A > 0.1, and a single solution exists when λ1 > 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces. [ABSTRACT FROM AUTHOR]

Fractional differential equations describe nature adequately because of the symmetry properties which describe physical and biological processes. In this article, a fourth-order new implicit difference scheme is formulated and applied to solve the two-dimensional time-fractional modified sub-diffusion equation involving two times Riemann–Liouville fractional derivatives. The stability of the fourth-order implicit difference scheme is investigated using the von Neumann technique. The proposed scheme is shown to be unconditionally stable. Numerical examples are given to illustrate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

A nonlocal fractional model of Brinkman type fluid (BTF) containing a hybrid nanostructure was examined. The magnetohydrodynamic (MHD) flow of the hybrid nanofluid was studied using the fractional calculus approach. Hybridized silver (Ag) and Titanium dioxide (TiO2) nanoparticles were dissolved in base fluid water (H2O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Ag-TiO2-H2O) was considered in a microchannel (flow with a bounded domain). The BTF model was generalized using a nonlocal Caputo-Fabrizio fractional operator (CFFO) without a singular kernel of order α with effective thermophysical properties. The governing equations of the model were subjected to physical initial and boundary conditions. The exact solutions for the nonlocal fractional model without a singular kernel were developed via the fractional Laplace transform technique. The fractional solutions were reduced to local solutions by limiting α → 1 . To understand the rheological behavior of the fluid, the obtained solutions were numerically computed and plotted on various graphs. Finally, the influence of pertinent parameters was physically studied. It was found that the solutions were general, reliable, realistic and fixable. For the fractional parameter, the velocity and temperature profiles showed a decreasing trend for a constant time. By setting the values of the fractional parameter, excellent agreement between the theoretical and experimental results could be attained. [ABSTRACT FROM AUTHOR]

Numerical simulations are performed to examine the effect of size of control rods (d1) and spacing ratio (g) on flow around a square rod with upstream and downstream control rods aligned in-line using the lattice Boltzmann method (LBM). The Reynolds number (Re) is fixed at Re = 160, while the spacing between the main rod and control rods is taken in the range 1 ≤ g ≤ 5 and the size of the control rod is varied between 4 and 20. Seven different types of flow mods are observed in this study at different values of g and d1. Variation in force statistics, like mean drag coefficient (Cdmean), Strouhal number (St), root mean square values of drag (Cdrms) and lift coefficients (Clrms), and percentage reduction in mean drag coefficient is discussed in detail. It was examined that vortex shedding completely suppressed at (g, d1) = (1, 12), (2, 12), and (2, 16) where steady flow mode exists. Moreover, it was found that at large gap spacing, where g = 5, the effect of control rods on the main rod vanishes. Due to this strong vortex shedding produced and as a result, maximum value of Cdmean is found at (g, d1) = (5, 8). The negative values of mean drag force are also observed at some gap spacing and size of control rods are due to the effect of thrust. Furthermore, the maximum percentage reduction in Cdmean is 121%, found at (g, d1) = (2, 20). [ABSTRACT FROM AUTHOR]

Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an efficient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination. [ABSTRACT FROM AUTHOR]

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form A < 0 . However, the unique result is obtained for flow in accelerating form A ≥ 0 . In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result. [ABSTRACT FROM AUTHOR]

A two-dimensional numerical study was conducted for flow past a square rod in the presence of two control rods. One is placed vertically in the upstream direction and the second one is placed horizontally in the downstream direction of the square rod. The influence of gap spacing was studied by taking g1 = 1–5 and g2 = 0.5–5 (where g1 is the gap between the upstream control rod and the main rod, and g2 is the space between the main rod and the downstream control rod) at Re = 160. The simulation results were obtained in the form of vorticity contour, drag and lift coefficients, Strouhal number, and force statistics. Under the effect of gap spacing, three different flow modes were found and named according to their behavior. It was found that the mean drag coefficient showed decreasing behavior by increasing the value of g2 continually at a fixed value of g1. The largest value of C d m e a n was found at (g1, g2) = (1, 1) and the greatest percentage reduction in C d m e a n was obtained at (g1, g2) = (1, 3), which is 139.72%. The effect of thrust was also noticed for all selected values of g1 and g2. Furthermore, it was noticed that the Strouhal number and the root mean square values of the drag and lift coefficients smaller values than the single rod values, except for the Clrms value of (g1, g2) = (1, 3) and (1, 4). [ABSTRACT FROM AUTHOR]

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative). [ABSTRACT FROM AUTHOR]

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization. [ABSTRACT FROM AUTHOR]

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor. [ABSTRACT FROM AUTHOR]

The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and thermal radiations. Nonlinear ordinary differential equations are obtained from governing nonlinear partial differential equations by using compatible similarity transformations. The quantities associated with engineering aspects, such as skin friction, Sherwood number, and heat exchange along with various impacts of material factors on the momentum, temperature, and concentration, are elucidated and clarified with diagrams. The numerical solution of the present study is obtained via the Keller-box technique and in limiting sense are reduced to the published results for accuracy purpose. [ABSTRACT FROM AUTHOR]

The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous dissipation, and heat generation/absorption on flow fields is also investigated. Similarity transformations are employed to convert the nonlinear governing equations to nonlinear ordinary differential equations, and then solved via the Keller box method. Findings demonstrate that the magnitude of the friction factor and mass transfer rate are suppressed with increment in Casson parameter, whereas heat transfer rate is found to be intensified. Increase in the curvature parameter enhanced the flow field distributions. The magnitude of wall shear stress is noticed to be higher with an increase in porosity and suction/blowing parameters. [ABSTRACT FROM AUTHOR]

In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed. [ABSTRACT FROM AUTHOR]

We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p . The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities. [ABSTRACT FROM AUTHOR]

In the article, the authors present several inequalities of the Čebyšev type for conformable k-fractional integral operators. [ABSTRACT FROM AUTHOR]

Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail. [ABSTRACT FROM AUTHOR]