Explore the vast range of titles available.

The main objective of the present investigation is to examine the couple stress fluid flow occurring as a result of rotation of a disk. On implementing a suitable transformation, the governing system of partial differential equations (PDEs) is converted into nonlinear differential equations of a single independent variable. These equations are solved analytically by virtue of the Homotopy Analysis Method (HAM) which gives solutions in the form of a series. The solution of most of the governing problems is determined in terms of the absolute exponential and decaying functions by means of this powerful technique. To support analytic results, some graphs are plotted for determining the convergence of the solution. Also the graphical interpretation of velocity profiles corresponding to the effects of pertinent parameters are shown and discussed in detail. The numerical results are calculated for evaluation of the influence of fluid parameter. It can also be anticipated that the radial and axial velocity components show decreasing behavior due to rise in the values of couple stress parameter which conflict the behavior of the tangential component of velocity.

This paper provides analytical solution of the non-aligned stagnation point flow of second grade fluid over a porous rotating disk in the presence of a magnetic field and suction/injection at the disk surface. The mathematical formulation of the fluid model is obtained in terms of partial differential equations (PDEs). The PDEs governing the motion are transformed into a system of ordinary differential equations (ODEs) by means of a similarity transformation and these corresponding nonlinear ODEs are solved by employing the homotopy analysis method (HAM) and the convergence analysis of the presented method is also performed graphically. An inclusion of the influences of various admissible parameters has been shown numerically and graphically on the flow field. Furthermore, comparison is made and it concedes that the obtained results are found to be in good agreement with results existing in literature.

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail.

The convection differential models play an essential role in studying different chemical process and effects of the diffusion process. This paper intends to provide optimized numerical results of such equations based on the conformable fractional derivative. Subsequently, a well-known heuristic optimization technique, differential evolution algorithm, is worked out together with the Taylor?s series expansion, to attain the optimized results. In the scheme of the Taylor optimization method (TOM), after expanding the functions with the Taylor?s series, the unknown terms of the series are then globally optimized using differential evolution. Moreover, to illustrate the applicability of TOM, some examples of linear and non-linear fractional convection diffusion equations are exemplified graphically. The obtained assessments and comparative demonstrations divulged the rapid convergence of the estimated solutions towards the exact solutions. Comprising with an effective expander and efficient optimizer, TOM reveals to be an appropriate approach to solve different fractional differential equations modeling various problems of engineering. nema

This article is concerned with the study of free convective unsteady magnetohydrodynamic flow of the incompressible Oldroyd-B fluid along with chemical reaction. The fluid flows on a vertical plate that is impulsively brought in motion in the presence of a constant magnetic field which is applied transversely on the fluid. The structure has been modeled in the form of governing differential equations, which are then nondimensionalized and solved using a numerical technique, that is, Crank–Nicolson’s scheme to obtain solutions for velocity field, temperature distribution, and concentration profile. These solutions satisfy the governing equations as well as all initial and boundary conditions. The obtained solutions are new, and previous literature lacks such derivations. Some previous solutions can be recovered as limiting cases of our general solutions. The effects of thermophysical parameters, such as Reynolds number, Prandtl number, thermal Grashof number, modified Grashof number, Darcy number, Schmidt number, dissipation function, magnetic field, radiation–conduction, chemical reaction parameter, relaxation and retardation times on the velocity field, temperature, and concentration of fluid, are also examined and discussed graphically.

This investigation is concerned with the study of thin film flow of a generalized Maxwell fluid along with slip conditions, confronting withdrawal and drainage on non-isothermal cylindrical surfaces. The governing equations have been formulated from the continuity equation, momentum equation, and energy equation. Analytical solutions for the velocity field, volume flow rate, average film velocity, tangential stress, and temperature are obtained in series form through the Binomial expansion technique in both withdrawal and drainage cases. The well-known solutions for a Newtonian fluid are regained as a particular case of our acquired general solutions in all flow cases. In addition, solutions for the power-law fluid model, executing alike motion, can be recovered as a limiting case of our acquired general solutions. The influence of different dimensionless parameters on all physical quantities (i.e. velocity, volume flow rate, average film velocity, tangential stress, and temperature profile) is examined and discussed graphically for both generalized Maxwell and Newtonian fluids.

The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has a great perfection in the Adomian decomposition method (ADM) truncated series solution which diverges promptly as the applicable domain increases. The approximate solutions are obtained in a broad range of the problem domain and are compared with the generalized Euler method (GEM). The comparison shows a precise agreement between the results, the applicable one of which needs fewer computations.

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u ¨ + u + α 3 u 3 + α 5 u 5 + α 7 u 7 + ⋯ + α n u n = 0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u ¨ + α u | u | n − 1 = 0 . This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n , the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.

In this article, an effort has been made to compute and inspect the rotational flow of Oldroyd-B fluid between two co-axial circular cylinders. As novelty, the rotation of both cylinders produces motion of the fluid. The velocity field and tangential stress corresponding to the motion of an Oldroyd-B fluid with fractional derivatives have been obtained using Laplace and Hankel integral transforms. The velocity profiles of the respective model are graphically presented and deliberated for the pertinent parameters. Corresponding solutions are also obtained for ordinary Oldroyd-B fluid, ordinary and fractional Maxwell fluids, ordinary and fractional second-grade fluids, and Newtonian fluid as limiting cases of our general solutions.

Understanding and accurately modeling the dynamics of climate-related processes is essential for predicting and mitigating the effects of global warming. This study introduces a fractional order atmospheric model that simultaneously captures the interactions among three key variables: permafrost thaw, atmospheric temperature, and greenhouse gas concentration. The model was formulated using the Atangana-Baleanu-Caputo fractional derivative, allowing for the inclusion of memory effects that are critical in climate dynamics. To solve the resulting nonlinear fractional differential equations, we constructed an operational matrix of the Atangana-Baleanu fractional integral operator based on Haar wavelets. Using Haar series expansions and operational matrices, the system was transformed into an objective function. This objective function was then minimized using differential evolution optimization to determine unknown Haar coefficients. The proposed method was validated against traditional numerical and predictor-corrector methods, with theoretical analysis confirming existence, uniqueness, and a provable upper bound for the approximation error. Numerical experiments under various parameter settings demonstrated the high accuracy, efficiency, and flexibility of the method. These results highlight the potential of fractional order modeling as a powerful framework for analyzing complex environmental systems and improving climate prediction