In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted
to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find
the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition
method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the
proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method
via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.
The linear stability theory is applied to investigate the effects of rotation and feedback control on the onset of steady and oscillatory thermocapillary convection in a horizontal fluid layer heated from below with a free-slip bottom. The thresholds and codimension-2 points for the onset of steady and oscillatory convection are determined. The effect of feedback control on the parameter space dividing the steady and oscillatory convection regions is demonstrated.
In this work we use an analytical technique to analyse the effect of a vertical uniform magnetic field on the onset of steady Benard-Marangoni convection in a horizontal layer of electrically conducting fluid subject to a uniform vertical temperature gradient in the asymptotic limit short waves. We found that in the limit of short waves, the leading order expression for the marginal curve is not affected by the magnetic field.
Dalam makalah ini kesan medan magnet menegak seragam ke atas lengkung sut permulaan olakan mantap Benard-Marangoni dalam lapisan bendalir mengufuk berpengalir elektrik dikaji tertakluk kepada kecerunan suhu yang seragam dalam had asimptot gelombang pendek. Kami dapati medan magnet tidak memberi kesan kepada sebutan utama lengkung sut dalam had gelombang pendek.
The magnetohydrodynamic (MHD) boundary-layer flow and heat transfer due to a shrinking sheet in a porous medium is considered for the first time. The Navier-Stokes equations and the heat equation are reduced to two nonlinear ordinary differential equations via similarity transformations. The transformed equations are solved by a semi-analytic method. The effects of the suction and porosity parameters, the Prandtl and Hartmann numbers on the skin friction, heat transfer rate, velocity and temperature profiles are discussed and presented, respectively.
In this paper, the problem of laminar viscous flow in a semi-porous channel in the presence of transverse magnetic field is studied. The Optimal Homotopy Asymptotic Method (OHAM) is employed to approximate the solution of the system of nonlinear differential equations governing the problem. The influence of the Hartmann number (Ha) and the Reynolds number (Re) on the flow was investigated. The results of the OHAM were compared with homotopy analysis method (HAM) and variation iteration method (VIM) results.
In this paper, the optimal homotopy asymptotic method (OHAM) is applied to obtain an approximate solution of the nonlinear Riccati differential equation. The method is tested on several types of Riccati differential equations and comparisons that were made with numerical results showed the effectiveness and accuracy of this method.