Related papers: Solving the heat equation with variable thermal co…
In this study, we derive an analytical solution to address the problem of one-dimensional vertical infiltration within bounded profiles. We consider the Richards equation together with various boundary conditions, simulating different…
In this paper, we study the Cauchy problem for a heat equation governed by a mixed local--nonlocal diffusion operator with spatially irregular coefficients. We first establish classical well-posedness in an energy framework for bounded,…
We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…
In this work we find a solution to problem of the heat equation which is annihiliated at a cubic boundary $f$. The solution turns out to be the convolution between the fundamental solution of the heat equation and a function $\phi$ which…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient $q$ depending on $x$ is constructed. The solutions represent the images of the heat polynomials…
Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain $D=\mathbb{R}^{n-1}\times\br^{+}$ for which the internal energy supply depends on an average in the…
In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations,…
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards' equation reduces to Burgers'…
We use the nonstandard Fourier transform method, along with an established nonstandard approach to ODE's, to find a solution to the heat equation, on $(0,\infty)\times\mathcal{R}$, with a given boundary condition $g$ at $t=0$. We use this…
The heat-balance integral method of Goodman has been thoroughly analyzed in the case of a parabolic profile with unspecified exponent depending on the boundary condition imposed. That the classical Good man's boundary conditions defining…
By a probabilistic method we provide an explicit fundamental solution of the Cauchy problem associated to the heat equation on the half-line with constant drift and Dirichlet boundary condition at zero.
We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
The flexible profile approach proposed earlier to create CTM (compact or reduced order thermal models) is extended to cover the area of conjugate heat transfer. The flexible profile approach is a methodology that allows building a highly…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…