Volume 6, Issue 3

This communication presents the transportation of third order hydromagnetic fluid with thermal radiation by peristalsis through an irregular channel configuration filled a porous medium under the low Reynolds number and large wavelength approximations. Joule heating, Hall current and homogeneous-heterogeneous reactions effects are considered in the energy and species equations. The Second-order velocity and energy slip restrictions are invoked. Final dimensionless governing transport equations along the boundary restrictions are resolved numerically with the help of NDsolve in Mathematica package. Impact of involved sundry parameters on the non-dimensional axial velocity, fluid temperature and concentration characteristics have been analyzed via plots and tables. It is manifest that an increasing porosity parameter leads to maximum velocity in the core part of the channel. Fluid velocity boosts near the walls of the channel where as the reverse effect in the central part of the channel for higher values of first order slip. Larger values of thermal radiation parameter R reduce the fluid temperature field. Also, an increase in heterogeneous reaction parameter K s magnifies the concentration profile. The present study has the crucial application of thermal therapy in biomedical engineering.

An analysis has been carried out to study the effect of nonlinear thermal radiation on slip flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet immersed in a porous medium. Water is considered as a base fluid with dust particles along with suspended Aluminum Oxide (Al 2 O 3 ) nanoparticles. Using appropriate similarity transformations, the coupled nonlinear partial differential equations are reduced into a set of coupled nonlinear ordinary differential equations. The reduced equations are then solved numerically using Runge-Kutta-Fehlberg45 order method with the help of shooting technique to investigate the impact of various pertinent parameters for the velocity and temperature fields. The obtained results are presented in tabular form as well as graphically and discussed in detail. Effect of different parameters on skin friction coefficient and Nusselt number are also discussed.

In this paper, we consider a Roseland approximation to radiate heat transfer, Darcy’s model to simulate the flow in porous media and finite-length fin with insulated tip to study the thermal performance and to predict the temperature distribution in a vertical isothermal surface. The energy balance equations of the porous fin with several temperature dependent properties are solved using the Adomian Decomposition Sumudu Transform Method (ADSTM). The effects of various thermophysical parameters, such as the convection-conduction parameter, Surface-ambient radiation parameter, Rayleigh numbers and Hartman number are determined. The results obtained from the ADSTM are further compared with the fourth-fifth order Runge-Kutta-Fehlberg method and Least Square Method(LSM) (Hoshyar et al. 2016 [1])) to determine the accuracy of the solution.

In this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space E17 $\text{E}^7_1$ . We express the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh m ϕ , sinh m ϕ }, and we derive the necessary and sufficient conditions for the coefficients to vanishes identically. Finally, an example is given to show two dimensional kinematic surfaces with zero scalar curvature.

Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

A nonlinear singularly perturbed boundary value problem depending on a parameter is considered. First, we solve the problem using the backward Euler finite difference scheme on an adaptive grid. The adaptive grid is a special nonuniform mesh generated through equidistribution principle by a positive monitor function depending on the solution. The behavior of the solution, the stability and the error estimates are discussed. Then, the Richardson extrapolation technique is applied to improve the accuracy of the computed solution associated to the backward Euler scheme. The proofs of the uniform convergence for the backward Euler scheme and the Richardson extrapolation are carried out. Numerical experiments validate the theoretical estimates and indicates that the estimates are sharp.

A new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.

A simple mechanical model is proposed to describe the dynamics system of the taut inclined cable excited by the deck vibration. Using Galerkin method, the dynamics system is simplified into a one-degree of freedom nonlinear system. Average method is used to obtain the average equations and bifurcation equation. Bifurcation maps are obtained and used to reveal the evolution mechanism of period-1 motion to period-2 motion. Several motion forms are discussed and evolution progress between different motions is studied. Several kinds of parametric resonance are revealed in various parameter regions. The conclusions indicate that the parametric resonance excited by the frequency ratio 3:2 is significant should be paid more attention.