Volume 25 (2020): Issue 1 (March 2020)

In this work, we discuss a fractional model of a flow equation in a simple pipeline. Pipeline narrowing is a crucial aspect in drinking water distribution processes, sewage system and in oil-well schemes. The solution of the mathematical model is determined with the aid of the Sumudu transform and finite Hankel transform. The results derived in the current study are in compact and graceful forms in terms of the Mittag-Leffler type function, which are convenient for numerical and theoretical evaluation.

Failure analysis of a laminated composite beam subjected to uniformly distributed load and thermal load is studied for different boundary conditions and fiber orientation angles, based on first ply failure load. Three different boundary conditions are studied: simply supported, fixed-fixed and fixed-free. The strength ratio is computed and compared for different failure theories. The effect of fiber orientation angle and aspect ratio on the strength ratio based on first ply failure load is presented in the paper. The strength ratio and transverse deflection are determined for Graphite/Epoxy and Glass/Epoxy composite and their hybrid combinations to find out the optimum hybrid composite beam with minimum weight, deflection and cost. The problem is solved in MATLAB platform. The mode of failure of the composite beam is determined by using maximum stress theory.

This work investigates the effects of radiation and Eckert number on an MHD flow with heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the sixth order Runge-Kutta method with shooting technique. Tabular and graphical results are provided to examine the physical nature of the problem. Heat transfer rate at the surface decreases with radiation, Eckert number and as radiation increases, the flow temperature also increases for velocity ratio parameters ɛ <1 and ɛ >1.

This work investigates the mixed convection in a Magnetohydrodynamic (MHD) flow and heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the fourth order Runge-Kutta method with shooting technique. The influence of pertinent flow parameters on velocity, temperature, surface drag force and heat transfer rate are computed and analyzed. Graphical and tabular results are given to examine the nature of the problem. The heat transfer rate at the surface increases with the mixed convection.

The paper presents a comprehensive analysis of the stress field and selected triaxiality parameters near the crack tip for C(T) specimen dominated by the plane strain state using the finite element method. It includes some theoretical information about elastic-plastic fracture mechanics, the basics of the FEM modeling and presentation of the numerical results. The FEM analysis includes calculations with large strain assumptions. The influence of the external load and crack length is discussed. Additional elements of the paper are a qualitative assessment of the size of plastic zones and the crack tip opening displacement.

A weakly nonlinear thermal instability is investigated under rotation speed modulation. Using the perturbation analysis, a nonlinear physical model is simplified to determine the convective amplitude for oscillatory mode. A non-autonomous complex Ginzburg-Landau equation for the finite amplitude of convection is derived based on a small perturbed parameter. The effect of rotation is found either to stabilize or destabilize the system. The Nusselt number is obtained numerically to present the results of heat transfer. It is found that modulation has a significant effect on heat transport for lower values of ω_f while no effect for higher values. It is also found that modulation can be used alternately to control the heat transfer in the system. Further, oscillatory mode enhances heat transfer rather than stationary mode.

The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linear boundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and right-end layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.

In the present study, heat transfer from a small three dimensional rectangular channel due to turbulent jet impinging from a nozzle normal to the main flow at the inlet has been investigated. Hemispherical convex dimples are attached to the bottom plate from where heat transfer calculations are to be performed. Numerical simulations were performed using the finite volume method with SST k– ω turbulence model. The duct and nozzle Reynolds number are varied in the range of 10000 ≤ Re_D ≤ 50000 and 6000 ≤ Re_d ≤ 12000, respectively. Different nozzle positions (X/D = 10.57, 12.88, 15.19) along the axial direction of the rectangular duct have been considered. It has been found that higher heat transfer is observed at X/D = 10.57 as compared to the other positions. The heat transfer enhancements with and without cross-flow effects have also been compared. It has been shown that the heat transfer rate with cross-flow is found to be much higher than that without cross-flow. Also, the effect of dimples on the heated surface on heat transfer was investigated. The heat transfer is found to be greater in the presence of a dimpled surface than a plane surface.

The effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferrofluid layer saturating a sparsely distributed porous medium has been investigated by using the Darcy-Brinkman model in the simultaneous presence of a uniform vertical magnetic field and a uniform vertical rotation. A correction is applied to the study of Vaidyanathan et al. [11] which is very important in order to predict the correct behavior of MFD viscosity. A linear stability analysis has been carried out for stationary modes and oscillatory modes separately. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameter M₁. Numerical results are obtained and are illustrated graphically. It is shown that magnetic field dependent viscosity has a destabilizing effect on the system for the case of stationary mode and a stabilizing effect for the case of oscillatory mode, whereas magnetization has a destabilizing effect.

A computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation Rd, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter M and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.

This article deals with a 2-D problem of quasi-static deformation of a multilayered thermoelastic medium due to surface loads and heat source. The propagator matrix is obtained for the multilayered formalism of thermoelastic layers. Analytical solutions, in terms of the displacements, stresses, heat flux and temperature function, are obtained for normal strip and line loads, shear strip and line loads and strip and line heat sources. Numerical computation of the obtained analytical expressions is also done. The effects of layering have been studied. For the verification of the results, results of earlier studies have been obtained as particular cases of the present study.

A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.

In this paper, a theoretical analysis has been made to study the effect of mixed convection MHD oscillatory Couette flow in a vertical parallel channel walls embedded in a porous medium in the presence of thermal radiation, chemical reaction and viscous dissipation. The channel walls are subjected to a constant suction velocity and free stream velocity is oscillating with time. The channel walls are embedded vertically in a porous medium. A magnetic field of uniform strength is applied normal to the vertical channel walls. The nonlinear and coupled partial differential equations are solved using multi parameter perturbation techniques. The effects of physical parameters, viz., the radiation absorption parameter, Prandtl number, Eckert number, dynamic viscosity, kinematic viscosity, permeability of porous medium, suction velocity, Schmidt number and chemical reaction parameter on flow variables viz., temperature, concentration and velocity profile have been studied. MATLAB code is used to analyze theoretical facts. The important results show that an increment in the radiation absorption parameter and permeability of porous medium results in an increment of the temperature profile. Moreover, an increment in the Prandtl number, Eckert number and dynamic viscosity results in a decrement of the temperature profile. An increment in suction velocity results in a decrement of the velocity profile. An increment in the Schmidt number, chemical reaction parameter and kinematic viscosity results in a decrement of the concentration profile.

The problem of gap estimation for a break of a continuous welded rail is studied. The track is represented as a semi-infinite rod on elastic-based damping. Static and dynamic solutions are obtained. It is shown that during the rail break, the dynamic factor does not exceed 1.5. We derive equations for thermal deformation of the welded rail of jointless track on an elastic foundation in the presence of the insert into the base with another characteristic stiffness. It is shown that the presence of the insertion of up to 20% of the length of the rail, with both large and small stiffness, has a little effect on the stress-strain state (SSS) of the track. The presence of a rigid insert may increase the clearance of an accidental break of the rail, which has a negative effect on traffic safety.