Search results with tag "Dimensional heat equation"
The One-Dimensional Heat Equation - Trinity University
ramanujan.math.trinity.eduThe heat equation Homogeneous Dirichlet conditions Inhomogeneous Dirichlet conditions TheHeatEquation One can show that u satisfies the one-dimensional heat equation u t = c2u xx. Remarks: This can be derived via conservation of energy and Fourier’s law of heat conduction (see textbook pp. 143-144). The constant c2 is the thermal diffusivity: K
1 Two-dimensional heat equation with FD
geodynamics.usc.eduExcerpt from GEOL557 Numerical Modeling of Earth Systems by Becker and Kaus (2016) x z Dx Dz i,j i-1,j i+1,j i,j-1 i,j+1 L H Figure 1: Finite difference discretization of the 2D heat problem. 1 Two-dimensional heat equation with FD We now revisit the transient heat equation, this time with sources/sinks, as an example for two-dimensional FD ...
The one dimensional heat equation: Neumann and Robin ...
ramanujan.math.trinity.eduNeumann Boundary Conditions Robin Boundary Conditions Remarks At any given time, the average temperature in the bar is u(t) = 1 L Z L 0 u(x,t)dx. In the case of Neumann boundary conditions, one has u(t) = a 0 = f. That is, the average temperature is constant and is equal to the initial average temperature.