Related papers: Mathematical Modeling of Heat Conduction
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
A simple vibrational model of heat transfer in two-dimensional (2D) fluids relates the heat conductivity coefficient to the longitudinal and transverse sound velocities, specific heat, and the mean interatomic separation. This model is…
This paper investigates an induction heating problem in a multi-component system containing a moving non-magnetic conductor. The electromagnetic process is described by the eddy current model, and the heat transfer process is governed by…
This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem,…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
Heat conduction and radiation are two of the three fundamental modes of heat transfer, playing a critical role in a wide range of scientific and engineering applications ranging from energy systems to materials science. However, traditional…
The thermo-electrical properties of a complex silicon cantilever structure used in thermal scanning probe lithography are modeled based on well established empirical laws for the thermal conductivity in silicon, the electrical conductivity…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
A differential-difference operator is used to model the heat equation on a finite graph analogue of Poincar\'e's upper half-plane. Finite analogues of the classical theta functions are shown to be solutions to the heat equation in this…
This paper modifies a n-dimensional Hopf-Cole transformation to the n-dimensional Burgers' system. We obtain the n-dimensional heat conduction equation through the modification of the Hopf-Cole transformation. Then the fourth-order precise…
Using molecular dynamics simulations, we study supercritical fluids near the gas-liquid critical point under heat flow in two dimensions. We calculate the steady-state temperature and density profiles. The resultant thermal conductivity…
Using previous results and general thermodynamical formalism,an expression is obtained for the specific heat per particle under constant volume of a degenerate non-relativistic electron gas on a 1D lattice.The result is a non-linear…
Quantum heat transfer through a generic superconducting set-up consisting of a tunable transmon qubit placed between resonators that are termined by thermal reservoirs is explored. Two types of architectures are considered, a sequential and…
A shell and tube heat exchanger design with respect to the total heat transfer rate and temperature profile has been invstigated by numerical modelling. The HE comprises of a single tube and has been resolved by the two equation models…
In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there…
In this work, a thermal energy transfer problem in a one-dimensional multilayer body is theoretically analyzed, considering diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, as well as…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as…
Projectile like fragments emerging from heavy ion collision have an excitation energy which is often labeled by a temperature. This temperature was recently calculated using a geometric model. We expand the geometric model to include also…