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Mangalagama Dewasurendra and Kuppalapalle Vajravelu

Abstract

Very recently, Liao has invented a Directly Defining Inverse Mapping Method (MDDiM) for nonlinear differential equations. Liao’s method is novel and can be used for solving several problems arising in science and engineering, if we can extend it to nonlinear systems. Hence, in this paper, we extend Liao’s method to nonlinear-coupled systems of three differential equations. Our extension is not limited to single, double or triple equations, but can be applied to systems of any number of equations.

Open access

K. Vajravelu, S. Sreenadh and R. Saravana

Abstract

In this paper, we investigate the peristaltic transport of a two layered fluid model consisting of a Jeffrey fluid in the core region and a Newtonian fluid in the peripheral region. The channel is bounded by permeable heat conducting walls. The analysis is carried out in the wave reference frame under the assumptions of long wave length and low Reynolds number. The analytical expressions for stream function, temperature field, pressure-rise and the frictional force per wavelength in both the regions are obtained. The effects of the physical parameters associated with the flow and heat transfer are presented graphically and analyzed. It is noticed that the pressure rise decrease with increasing slip parameter β in the pumping region (ΔP > 0). The temperature field decreases with increasing Jeffrey number and the velocity slip parameter; whereas the temperature field increases with increasing thermal slip parameter. Furthermore, the size of the trapped bolus increases with increasing Jeffrey number and decreases with increasing slip parameter. We believe that this model can help in understanding the behavior of two immiscible physiological fluids in living objects.

Open access

F. Talay Akyildiz and K. Vajravelu

Abstract

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

Open access

P. Lakshminarayana, K. Vajravelu, G. Sucharitha and S. Sreenadh

Abstract

The present study deals with simultaneous effects of Joule heating and slip on peristaltic flow of a Bingham fluid in an inclined tapered porous channel with elastic walls. The closed form solutions for the stream function, the velocity and the temperature fields are obtained. The effects of the physical parameters on the flow characteristics are presented through graphs for both slip and no-slip cases. In addition, the performance of the temperature is studied with and without Joule heating effects. Moreover, the trapping phenomenon is analysed. The size of the trapped bolus increases with increasing values of the slip parameter and decreasing values of the magnetic, the permeability and the yield stress parameters. The present results are compared with the available results in the literature and our results agree well with the available results for some special cases.

Open access

Kuppalapalle Vajravelu, Ronald Li, Mangalagama Dewasurendra, Joseph Benarroch, Nicholas Ossi, Ying Zhang, Michael Sammarco and K.V. Prasad

Abstract

In this paper, boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is analyzed. The governing partial differential equations are converted in to a nonlinear ordinary differential equation through an appropriate similarity transformation. The resulting nonlinear equation is solved via homotopy analysis method (HAM). Errors ranging from 10–7 to 10–10 are reported for a relatively few terms. The effects of the pertinent parameters on the velocity and the shear stress are presented graphically and discussed. In the absence of magnetic field and the two slip parameters, the results are found to be in excellent agreement with the available results in the literature. It is expected that the results obtained will not only provide useful information for industrial applications but also complement the earlier works.

Open access

K. Vajravelu, S. Sreenadh, S. Dhananjaya and P. Lakshminarayana

Abstract

In this paper, the influence of heat transfer on the peristaltic flow of a conducting Phan-Thien-Tanner fluid in an asymmetric channel with porous medium is studied. The coupled nonlinear governing differential equations are solved by a perturbation technique. The expressions for the temperature field, the stream function, the axial velocity, and the pressure gradient are obtained. The effects of the various physical parameters such as the magnetic parameter M, the permeability parameter σ, the Brinkman number Br and the Weissenberg number We on the pumping phenomenon are analyzed through graphs and the results are discussed in detail. It is observed that the velocity and the pressure are decreased with increasing the magnetic parameter M whereas the effect of the parameter M on the temperature field is quite the opposite.