Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

“…The HAM always provides us with a family of solution expressions in the auxiliary parameter the convergence region and rate of each solution might be determined conveniently by the auxiliary parameter Furthermore, the HAM is rather general and contains the homotopy perturbation method (HPM) [12], the Adomian decomposition method (ADM) [14] and δ-expansion method. In recent years, the HAM has been successfully employed to solve many types of nonlinear problems such as the nonlinear equations arising in heat transfer [15], the nonlinear model of diffusion and reaction in porous catalysts [16], the chaotic dynamical systems [17], the non-homogeneous Blasius problem [18], the generalized three-dimensional MHD flow over a porous stretching sheet [19], the wire coating analysis using MHD Oldroyd 8-constant fluid [20], the axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet [21], the MHD flow of a second grade fluid in a porous channel [22], the generalized Couette flow [23], the Glauert-jet problem [24], the Burger and regularized long wave equations [25], the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field [26], the nano boundary layer flows [27], the twodimensional steady slip flow in microchannels [28], and other problems. All of these successful applications verified the validity, effectiveness and flexibility of the HAM.…”

Hydromagnetic Viscous Fluid Over a Non-Linear Stretching and Shrinking Sheet in the Presence of Thermal Radiation

“…If this parameter is properly chosen, the given solution is valid, as verified in previous works , Hang et al (2007), Zhu (2009), Ali et al (2008) and Ziabakhsh (2009). Since the interval for the admissible values of corresponds to the line segments nearly parallel to the horizontal axis.…”

“…Also, Mehmood et al (2006) and(2008). Then, Liao (2009), Fakhari et al (2007 and Domairry et al (2008), Domairry et al (2009 Tan et al (2008), Ali et al (2008) and Ziabakhsh et al (2009) in a wide variety of scientific and engineering applications to solve different types of governing differential equations: linear and non-linear, homogeneous and non-homogeneous, and coupled and decoupled as well. This method offers highly accurate successive approximations of the solution.…”

Determination of temperature distribution for annular fins with temperature‐dependent thermal conductivity

“…In the works of Hayat et al [7][8][9][10] and Liao [11][12][13][14], it is also shown that the HAM method logically contains some previous techniques such as Adomian's decomposition method, Lyapunov's artificial small parameter method, and the δ-expansion method. Many authors (Abbasbandy [15], Ali et al [16,17], and Domairry et al [18][19][20][21]) have successfully applied HAM in solving different types of nonlinear problems, i.e., coupled, decoupled, homogeneous, and non-homogeneous equations arising in different physical problems such as heat transfer, fluid flow, oscillatory systems, etc.…”