How do you determine boundary conditions for heat transfer?
Convection boundary condition can be specified at outward boundary of the region. It describes convective heat transfer and is defined by the following equation: Fn = α(T – T0), where α is a film coefficient, and T0 – temperature of contacting fluid medium.
What is heat equation in PDE?
In mathematics and physics, the heat equation is a certain partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region.
How do you derive the heat equation in one dimension?
u(x,t) = temperature in rod at position x, time t. ∂u ∂t = c2 ∂2u ∂x2 . (the one-dimensional heat equation ) The constant c2 is called the thermal difiusivity of the rod. We now assume the rod has finite length L and lies along the interval [0,L].
What does the second derivative of the heat equation represent?
The second derivative corresponds to the change of the temperature gradient at the considered point. The temporal change of the temperature in a certain point results from the spatial change of the temperature gradient at this point. The heat equation describes for an unsteady state the propagation of the temperature in a material.
What does the heat equation describe?
The heat equation describes for an unsteady state the propagation of the temperature in a material. In general, temperature is not only a function of time, but also of place, because after all the rod has different temperatures along its length.
What is the cause of the heat flow in this equation?
This equation ultimately describes the effect of a heat flow on the temperature, but not the cause of the heat flow itself. The cause of a heat flow is the presence of a temperature gradient dT/dx according to Fourier’s law (λ denotes the thermal conductivity): One can determine the net heat flow of the considered section using the Fourier’s law.
Why is the heat equation also called the diffusion equation?
For this reason, the heat equation is also called diffusion equation. For a three-dimensional case of heat conduction, heat flows no longer have to be considered in one dimensional direction only, but in all three directions (this also applies to the mass flows in the case of diffusion).