How Is the Steady State Assumed in Solving the Thermal Diffusion Equation?

[bon]

thermal diffusion equation - URGENT

Homework Statement

Please see attached q

Homework Equations

The Attempt at a Solution

Ok so thermal diffusion equation is DT/Dt = D del squared T

apparently this is a steady state problem, so DT/dt = 0, how am i meant to know? any hints on solving please?

 

[bon]

I've done part (a) how do you do (b) though

 

[bon]

is (b) a steady state too? how do we know..?

 

[bon]

Ok i guess it is...

is the equation i have to solve:

del squared T = alpha/k (T(a) - Tair) - I^2 ro/pi^2 a^4?

 

[rwisz]

The thermal diffusion equation is a fundamental equation in thermal physics that describes the transfer of heat in a system. It is a partial differential equation that relates the change in temperature (T) over time (t) to the thermal diffusivity (D) and the Laplacian of the temperature (del squared T). This equation is often used to model heat transfer in various systems, such as conduction, convection, and radiation.

In order to solve the thermal diffusion equation, you will need to have boundary conditions and initial conditions specified. These conditions will determine the specific form of the equation and the appropriate techniques to solve it. In the case of a steady state problem, as mentioned, the time derivative (DT/dt) is equal to zero, meaning that the temperature is not changing over time. This can be determined by looking at the physical system and determining if it is in a state of equilibrium or not.

To solve the thermal diffusion equation, you will need to use techniques from calculus and differential equations, such as separation of variables, Fourier series, or numerical methods. It is important to carefully consider the boundary and initial conditions and choose the appropriate method to solve the equation.

In summary, the thermal diffusion equation is a powerful tool in understanding heat transfer in various systems. To solve it, you will need to have the appropriate boundary and initial conditions and use mathematical techniques to obtain a solution. I hope this helps and good luck with your homework!