Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the in terms explicit functions θ and ϕ are derived subject to certain differential constraints. By restricting flat Friedman case wave presented. Invertible transformations constructed from specific subalgebra these convert with variable coefficients one constant coefficients.

The numerical solution of the Boltzmann equation for thin film applications requires extensive computational power. An analytical to phonon transport is fruitful in order reduce effort and cost. In present study, an radiative carried out. treatment problem reduces two identical equations Fredholm integral second kind. resulting intensity data are presented terms dimensionless temperature across gray films silicon diamond. findings compared with their counterparts predicted from simulations....

Symmetry analysis of wave equation on all static spherically symmetric spacetimes admitting maximal isometry groups G10 or G7 G6 is carried out. algebras the are found and their structural information-in sense Iwasawa decomposition-is obtained. Joint invariants appropriate subalgebras utilized to obtain many exact solutions spacetimes.

A closed-form solution for temperature and stress fields is presented short-pulse laser heating of the metal surface. Thermo-mechanical coupling between heat equations incorporated in analysis. The lattice site equation based on non-equilibrium energy transport used to account thermal field due heating. Lie symmetry method adopted obtain with appropriate boundary conditions. In analysis, wave dissipation omitted space mathematical simplifications. It found that displacement negative early...

Laser short-pulse heating of a nano-size wire is considered and entropy generation rate predicted during the pulse. The analytical solution heat equation obtained using Lie point symmetry for laser heating. assumed to be symmetric along its y-axis. pulse intensity Gaussian at irradiated surface while exponential decay incorporated in time domain. It found that temperature variation lattice subsystem almost follows distribution surface. Entropy attains low values axis it increases...

This paper considers non-equilibrium energy transport in the solid due to short-pulse heating and presents an analytical solution for electron lattice site temperature distributions inside solid. The study is extended include of governing equation volumetric surface heat sources. It found that obtained from source differs considerably corresponding model; which case, higher than at surface, despite fact same value peak intensity used both cases.

We present here, in compact form, the necessary and sufficient conditions for linearization of third-order ordinary differential equations y'''=f (x,y,y', y'') with maximal symmetry group via point transformation. A simple procedure to construct transformation using isomorphism subalgebra sl(2, ℝ) is also presented. This semi-simple part Levi-Decomposition 7-dimensional algebra.

In the present study, analytical solution for nonequilibrium heating of metallic surfaces is presented and closed-form thermal stress distribution obtained in relation to laser short-pulse process. Two boundaries are considered, which include free boundary continuity at surface. One-dimensional situation incorporated formulate temperature stressfields. It found that developed surface region tensile condition it becomes compressive as distance from increases. Thermal remains attains high values

Analytical solution for laser short-pulse heating of a micro-sized metal wire is presented. In the analysis, volumetric and surface heat sources are incorporated same pulse intensity. The source resembles absorption by irradiated field according to Lambert’s Beer law while represents short through high intensity thermal contact at surface. method Lie point symmetries combined with Fourier cosine transformation solve temperature equation appropriate boundary conditions. It found that profiles...

The Cartan equivalence method is applied to provide an invariant characterization of the third-order ordinary differential equation $u'''=f(x,u,u',u'')$ which admits a five-dimensional point symmetry Lie algebra. given in terms function $f$ compact form. A simple procedure construct equivalent canonical form by use obtained constant also presented. We show how one obtains transformation that does reduction linear Moreover, some applications are provided.