Glimpse on the relationship between Feynman integral and integrable system

We briefly review recent attempts to relate the concept of Feynman integral and integrable systems. This constitutes an endeavour on our part in making the Feynman path integral into a mathematically meaningful entity

Comparative study on Maxwell and Navier stokes fluid equations with pressure gradient over a flat plate for convective boundary layer flow and heat transfer

In this article, Maxwell fluid over a flat plate for convective boundary layer flow with pressure gradient parameter is considered. The aim of this study is to compare and analyze the effects of the presence and absence of λ (relaxation time), and also the effects of m (pressure gradient parameter) and Pr (Prandtl number) on the momentum and thermal boundary layer thicknesses. An approximation technique namely Homotopy Perturbation Method (HPM) has been used with an implementation of Adam and Gear Method’s algorithms. The obtained results have been compared for zero relaxation time and also pressure gradient parameter with the published work of Fathizadeh and Rashidi. The current outcomes are found to be in good agreement with the published results. Physical interpretations have been given for the effects of the m, Pr and β (Deborah number) with λ. This study will play an important role in industrial and engineering applications

On the correlation of theory and experiment for transversely isotropic nonlinear incompressible solids

A novel strain energy function for finite strain deformations of transversely isotropic elastic solids which is a function five invariants that have immediate physical interpretation has recently been developed. Three of the five invariants are the principal stretch ratios and the other two are squares of the dot product between the preferred direction and two principal directions of the right stretch tensor. A strain energy function, ex- pressed in terms of these invariants, has a symmetrical property almost similar to that of an isotropic elastic solid written in terms of principal stretches. This constitutive equation is attractive if principal axes techniques are used in solving boundary value problems and experimental advantage is demonstrated by showing a simple triaxial test can vary a single invariant while keeping the remaining invariants fixed. Explicit expressions for the weighted Cauchy response functions are easily obtained since the response function basis is almost mutually orthogonal. In this paper a specific form of the strain energy function for incompressible materials which is linear with respect to its physical parameters is developed. When a curve fitting method is (sensibly) applied on an experimental data, the values of the parameters are obtained uniquely via a linear positive definite system of equations. The theory compares well with experimental data and the performance of the proposed specific form is discussed. A constitutive inequality, which may reasonably be imposed upon the material parameters, is discussed

Polarized seismic and solitary waves run-up at the sea bed

The polarization effects in hydrodynamics are studied. Hydrodynamic equation for the nonlinear wave is used along with the polarized solitary waves and seismic waves act as initial waves. The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. The output demonstrates the inundation behaviors. Consequently, the polarized seismic waves along with the polarized solitary waves tend to generate dissimilar inundation which is more disastrous

Electrical unsteady MHD natural convection flow of nanofluid with thermal stratification and heat generation/absorption

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness

Reactivity Controlled Compression Ignition (RCCI) of Gasoline- CNG Mixtures

Reactivity controlled compression ignition (RCCI) is a dual fuel combustion method that relies on the significant difference in reactivity of the fuels involved. RCCI had a low performance at high engine speed due to its high tendency on knocking and high pressure rise rate. Therefore, this study investigates the effect of the fuel stratification on the RCCI combustion and its extended to the interaction of two low reactive fuels, gasoline and compressed natural gas (CNG), in the RCCI combustion system. The investigation was experimentally performed on a single cylinder engine and constant volume chamber. The stratification was created by varying injection timing in the engine by injecting CNG at 80° and 120° before top dead center (BTDC) and varying injection gap in the constant volume chamber with the gaps between two fuel injection timing were varied between 0 ms to 20 ms. The results in the engine experiment show that proportions of gasoline and CNG and degree of stratification of CNG were found to be effective means of combustion control within certain limits of engine load and HC and CO emissions could be significantly reduced. While in constant volume chamber it has a significant effect on the combustion phasing. Stratified mixture produces shorter combustion duration while homogeneous mixture produces longer duratio