In this article, the author has used fractional calculus to explain the wave nature of heat propagation as well as heat conduction at molecular level with dual phase lag; in this row he proposed dual phase lag heat equation of fractional order. Modified Adomian Decomposition Method and New Iterative Method are applied to obtain the approximate analytical solutions of the proposed model. Numeric...

The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the derivation of the Helmholtz term arising in the bio-heat transfer equation is not completely satisfactory. Here we use homogenization techniques to show that this term may be understood as asymptotic result of boundary value problems which provide a microscopic description ...

In the first part, we derive a sharp gradient estimate for the log of Dirichlet heat kernel and Poisson heat kernel on domains, and a sharpened local Li-Yau gradient estimate. In the second part, without explicit curvature assumptions, we prove a global upper bound for the fundamental solution of an equation introduced by G. Perelman, i.e. the heat equation of the conformal Laplacian under back...

Heat propagation in the Guyer–Krumhansl model is studied. The exact analytical solutions for the one-dimensional Guyer–Krumhansl equation are obtained. The operational formalism is employed. Some examples of initial functions are considered, modeling various initial heat pulses and distributions. The effect of the ballistic heat transfer in an over–diffusive regime is elucidated. The behavior o...

Fig. 1. The original purpose of our paper (Wei and Sandwell, 2006) was to provide an estimate of the global Cenozoic heat flow that was largely independent of the sometimesbiased conductive heat flow measurements (Hofmeister and Criss, 2005). The increasing seafloor depth with increasing age is one of the most obvious signals of global plate tectonics. Global mantle convection with thin surface...

Several approaches to numerical modelling of liquid droplet heating and evaporation by convection and radiation from the surrounding hot gas are discussed. The finite thermal conductivity of liquid, recirculation in droplets, and time dependence of gas temperature and the convection heat transfer coefficient are taken into account. For the constant and almost constant convection heat transfer c...

solute transport in unsaturated porous media can be viewed as a coupled phenomenon with waterand heat transport, together with mechanical behaviour of media. in this paper, solute transport is formulatedmathematically considering heat and water flow in deformable porous media. advection, dispersion anddiffusion of chemical species in the liquid phase are considered. convection and conduction fo...

In this short note, we study the gradient estimate of positive solutions to Poisson equation and the non-homogeneous heat equation in a compact Riemannian manifold (Mn, g). Our results extend the gradient estimate for positive harmonic functions and positive solutions to heat equations. Mathematics Subject Classification (2000): 35J60, 53C21, 58J05

Available online xxxx Keywords: Nonlinear heat equation Blow up Sobolev spaces with variable exponents a b s t r a c t In this paper we consider a nonlinear heat equation with nonlinearities of variable-exponent type. We show that any solution with nontrivial initial datum blows up in finite time. We also give a two-dimension numerical example to illustrate our result.

We discuss the phenomenon of Bose-Einstein condensation under general external conditions using connections between partition sums and the heat-equation. Thermodynamical quantities like the critical temperature are given in terms of the heat-kernel coefficients of the associated Schrödinger equation. The general approach is applied to situations where the gas is confined by arbitrary potentials...