This article deals with the determination of temperature distribution, displacement and thermal stresses of a rectangular plate having nonhomogeneous material properties with internal heat generation. The plate is subjected to sectional heating. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law along x direction. Solution of the two-dim...

An analytical characterization of forced convective ~ow through a channel _lled with a porous medium is presented in this work[ Based on a two!equation model\ including transverse conduction contributions\ exact solutions are obtained for both ~uid and solid phase temperature _elds[ The Nusselt number is also obtained in terms of the pertinent physical parameters\ namely the Biot number for the...

The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirichlet problem for Laplace’s equation, its implementation is rather easy. The definition of the random walk is based on a new mean value formula for...

Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By making use of Pontryagin’s maximum principle and a special kind of property for nontrivial solutions of the heat equation, we derive a bangbang property for time optimal control. Using the bang-bang property and establishing certain connections between timeand norm optimal...

In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-time scaling of the potential’s oscillations is not given by the diffusion scaling that leaves the heat equation invariant. Instead, we treat the case where spatial oscillations are much faster than temporal oscillations...

As one of the most important mathematics-physics equations, heat equation has been widely used in engineering area and computing science research. Large-scale heat problems are difficult to solve due to computational intractability. The parallelization of heat equation is available to improve the simulation model efficiency. In order to solve the three-dimensional heat problems more rapidly, th...

The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...

The effect of time-periodic oscillations of the RayleighBénard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real GinzburgLandau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection a...

In this paper, we develop new methods of solving the Poincaré-Lelong equation. It is mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is shown to be effective through obtaining better, sometimes optimal, existence results for the Poincaré-Lelong equation.