The Heat Equation

The Heat Equation

Solution for the Heat Equation

Control of the Heat Equation

The 1-D Heat Equation

Rate of heat transfer ∂u = (1) −K0 area ∂x where K0 is the thermal conductivity, units [K0] = MLT U . In other words, heat is transferred from areas of high temp to low temp. 3. Conservation of energy. Consider a uniform rod of length l with non-uniform temperature lying on the x-axis from x = 0 to x = l. By uniform rod, we mean the density ρ, specific heat c, thermal conductivity K0, cross-sec...

Geometric Heat Equation and

We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reaction-diiusion framework proposed by 28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with a renormalization by arc-length at each innnitesimal step. For images, the smoothing is similar to ...