This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method HAM is employed for the presentation of series solutions. The HAM is accepted as an elegant tool f...

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which converted into fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on HAM are guaranteed to be more accurate than exact solutions, relative errors between 0.0089% and 2.64%. When λ = 0, pressure drop of Da...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on duffing equation. analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. in this paper, the general form of duffing equation with cubic nonlinearity as well as paramet...

Squeezing flow of a Casson fluid is considered between two parallel disks. Upper disk is taken to be impermeable but capable of moving towards or away from the lower fixed and porous disk. Governing equations are derived with the help of conservation laws combined with suitable similarity transforms. Homotopy analysis method (HAM) is then been employed to determine the solution to resulting ord...

In this paper, we have tried to find a solution for quick transfer of nuclear wastes from pools of cool water to dry stores to reduce the environmental concerns and financial cost of burying atomic waste. Therefore, the rate of heat transfer from atomic waste materials to the outer surface of the container should be increased. This can be achieved by covering the bottom of the pool space with c...

in the age of technology, it is vital to cool down different parts of a device to use it more beneficially. using nanofluids is one of the most common methods which has shown very effective results. in this paper, we have rephrased a classic equation in fluid mechanics, i.e. the falkner-skan boundary layer equation, in order to be used for nanofluid. this nonlinear equation, which was presented...

In this paper, we investigate the accuracy of the Homotopy Analysis Method (HAM) for solving the problem of the spread of a non-fatal disease in a population. The advantage of this method is that it provides a direct scheme for solving the problem, i.e., without the need for linearization, perturbation, massive computation and any transformation. Mathematical modeling of the problem leads to a ...

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method HAM . Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The...

An analysis has been carried out to study the flowandheat transfer in a liquid filmover a permeable stretching sheet.Using similarity transformations, the time-dependent boundary layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting parameter problem and velocity as well as temperature fields are solved using the homotopy analysis method (HAM). Analyti...