This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

Velocity estimation using tracer conservation or heat flow equation based on infrared image sequence is one of the most challenging inverse problems in geosciences and remote sensing applications. In this paper, a new nonlinear model has been created for estimating top surface velocity from an infrared image sequence. The differential form of tracer conservation or heat flow equation is replace...

Objectives: We propose a parallel hybrid particle swarm optimization (PHPSO) algorithm to reduce the computation cost because solving the one-dimensional (1D) heat conduction equation requires large computational cost which imposes a great challenge to both common hardware and software equipments. Background: Over the past few years, GPUs have quickly emerged as inexpensive parallel processors ...

this paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .the vessels are in spherical shape and fibers are winded in circumferential direction. the analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. the heat transfer equ...

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

Thermo-elastic damping is a significant dissipation mechanism in high quality factor microstructures. In this paper, thermo-elastic damping of the in-plane vibration of fully clamped rectangular micro-plates has been studied. The governing equation of the micro-plate motion and heat conduction equation were derived. Then, The Galerkin method has been used to solve the coupled heat-displacement ...

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...

The sideways heat equation is a one dimensional model of a problem, where one wants to determine the temperature on the surface of a body using interior measurements. More precisely, we consider a heat conduction problem, where temperature and heat–flux data are available along the line x=1 and the solution is sought in the interval 0≤x <1. The problem is ill–posed in the sense that the solutio...

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The interaction of thermal radiation with conduction and laminar natural convection in a vertical circular pin, situated at participating gas, is numerically investigated. An absorbing and emitting gas is considered, and treated to be a gray participating media. Under the idealizing of gray gas, the Rosselan4 approximation is employed to describe the radiative heat flux in the energy equation. ...