In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric...

Convection diffusion equation R-value (insulation) Heat pipe Fick's law of diffusion Relativistic heat conduction Churchill–Bernstein equation Fourier number...

book was Fourier's proposal of his heat equation for conductive diffusion of heat. This partial differential equation is now a common part of mathematical...

Heat equation Wave equation Laplace's equation Helmholtz equation Klein–Gordon equation Poisson's equation Navier-Stokes equation Burgers' equation Types...

diffusion equation is a special case of the convection–diffusion equation when bulk velocity is zero. It is equivalent to the heat equation under some...

Specific heat of melting (Enthalpy of fusion) Specific heat of vaporization (Enthalpy of vaporization) Frenkel line Heat capacity ratio Heat equation Heat transfer...

nonlinear. For example, Fisher's equation is a nonlinear PDE that includes the same diffusion term as the heat equation but incorporates a linear growth...

In fluid dynamics, the general equation of heat transfer is a nonlinear partial differential equation describing specific entropy production in a Newtonian...

In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate...

dynamics. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace's equation describes situations of...

Heat transfer can be modeled in various ways. The heat equation is an important partial differential equation that describes the distribution of heat...

A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when...

mechanics Heat capacity ratio Statistical mechanics Thermodynamic equations Thermodynamic databases for pure substances Heat equation Heat transfer coefficient...

The porous medium equation, also called the nonlinear heat equation, is a nonlinear partial differential equation taking the form: ∂ u ∂ t = Δ ( u m )...

the solutions of the heat equation. Among other results, they showed that if one has a positive solution u of the heat equation on a closed Riemannian...

approach as in the case of the Heat Equation above. We write the wave equation as a first order in time partial differential equation by introducing the following...

Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the...

and spatial modeling. One of the most studied SPDEs is the stochastic heat equation, which may formally be written as ∂ t u = Δ u + ξ , {\displaystyle \partial...

methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial...

difference method used for numerically solving the heat equation and similar parabolic partial differential equations. It is a first-order method in time, explicit...

Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric...

usual heat equation for non-relativistic heat conduction must be modified, as it leads to faster-than-light signal propagation. Relativistic heat conduction...

u=(C_{\text{v}})(\delta T)} Inserting the specific heat equation into the thermal efficiency equation (Equation 2) yields. η = 1 − ( C v ( T 4 − T 1 ) C v (...

Functional equation Functional equation (L-function) Constitutive equation Laws of science Defining equation (physical chemistry) List of equations in classical...

differential equations with boundary and initial conditions, such as the heat equation, wave equation, Laplace equation, Helmholtz equation and biharmonic...

way. Energy portal History of heat Heat equation Heat diffusion Heat transfer coefficient Relativistic heat conduction Heat death of the Universe Effect...

wave equation, and vibrating plate equation. It is named after Jean-Marie Duhamel who first applied the principle to the inhomogeneous heat equation that...

equation Heat equation Laplace's equation Laplace operator Harmonic function Spherical harmonic Poisson integral formula Klein–Gordon equation Korteweg–de...

heat capacity) results in a simple differential equation expressing temperature-difference as a function of time. The solution to that equation describes...

The Fourier number arises naturally in nondimensionalization of the heat equation. The general definition of the Fourier number, Fo, is: F o = time time...