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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

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

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

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.

Open access

K.V. Prasad, H. Vaidya, K. Vajravelu, P.S. Datti and V. Umesh

Abstract

The present analysis is focused on the study of the magnetic effect on coupled heat and mass transfer by mixed convection boundary layer flow over a slender cylinder in the presence of a chemical reaction. The buoyancy effect due to thermal diffusion and species diffusion is investigated. Employing suitable similarity transformations, the governing equations are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically via the implicit, iterative, second order finite difference method. The numerical results obtained are compared with the available results in the literature for some special cases and the results are found to be in excellent agreement. The velocity, temperature, and the concentration profiles are presented graphically and analyzed for several sets of the pertinent parameters. The pooled effect of the thermal and mass Grashof number is to enhance the velocity and is quite the opposite for temperature and the concentration fields.

Open access

K.V. Prasad, K. Vajravelu and I. Pop

Abstract

The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

Open access

P. Devaki, S. Sreenadh, K. Vajravelu, K. V. Prasad and Hanumesh Vaidya

Abstract

In this paper, the peristaltic wave propagation of a Non-Newtonian Casson liquid in a non-uniform (flexible)channel with wall properties and heat transfer is analyzed. Long wavelength and low Reynolds number approximations are considered. Analytical solution for velocity, stream function and temperature in terms of various physical parameters is obtained. The impact of yield stress, elasticity, slip and non-uniformity parameters on the peristaltic flow of Casson liquidare observed through graphs and discussed. The important outcome is that an increase in rigidity, stiffness and viscous damping force of the wall results in the enhancement of the size and number of bolus formed in the flow pattern.

Open access

K. V. Prasad, Hanumesh Vaidya and K. Vajravelu

Abstract

An analysis is presented for mixed convection and heat transfer in a viscous electrically conducting fluid flow at an impermeable stretching vertical sheet with variable thickness. The nonlinear equations that describe the fluid flow, and heat transfer processes have been solved using the Keller-box method. A limited parametric study is undertaken to determine the sensitivity and changes in the flow and temperature fields with respect to variations in the buoyancy parameter, the temperature dependent viscosity and thermal conductivity parameters, the plate velocity power index, and the Prandtl number which are presented in graphical and tabulated formats. To validate the results, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The effects of embedded parameters on the dimensionless velocity profiles and temperature are examined through graphs. The variation of Local Nusselt number is also analysed. One of the important findings of our study is that the velocity distribution at a point near the plate decreases as the wall thickness parameter increases and hence the thickness of the boundary layer becomes thinner when m < 1. Further, the effect of the magnetic field is to reduce the fluid velocity and to increase the temperature field.

Open access

K.V. Prasad, H. Vaidya and K. Vajravelu

Abstract

An unsteady boundary layer free convective flow and heat transfer of a viscous incompressible, microploar fluid over a vertical stretching sheet is investigated. The stretching velocity is assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in the micropolar fluid. The transformed highly non-linear boundary layer equations are solved numerically by an implicit finite difference scheme for the transient, state from the initial to the final steady-state. To validate the numerical method, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The obtained numerical results are analyzed graphically for the velocity, the microrotation, and the temperature distribution; whereas the skin friction, the couple stress coefficient and the Nusselt number are tabulated for different values of the pertinent parameters. Results exhibit a drag reduction and an increase in the surface heat transfer rate in the micropolar fluid flow compared to the Newtonian fluid flow.

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.