Semi-infinite slab Flashcards
In the model for a semi-infinite slab, which scale disappears?
The characteristic length scale
Draw the system and state the boundary conditions for a semi-infinite slab.
See footnote 8.
Draw the control volume and indicate the in and out fluxes for a semi-infinite slab.
See footnote 9.
Construct the energy balance for heat transfer through a control volume of a semi-infinite slab.
See footnote 10.
Simplify the heat balance for the heat transfer through a semi-infinite slab by constructing a length scale and give the new boundary conditions.
See footnote 11.
What is the purpose of a similarity solution?
It replaces the independent coordinates that would otherwise be treated separately.
What is the assumption for the similarity solution used for the solution for heat transfer in a semi-infinite slab?
Boundary conditions are consistent with the introduction of the similarity solution.
Solve the simplified differential equation for the heat transfer through a semi-infinite slab.
See footnote 12.
Apply the boundary conditions to the simplified differential equation for heat transfer through a semi-infinite slab.
See footnote 13.
Simplify the final equation back to the original variables for heat transfer through a semi-infinite slab.
See footnote 14.
What is the Gaussian function?
What is the error function?
Derive the equation for calcualting the surface heat flux on a semi-infinte slab.
See footnote 15.
Derive the equation for the total heat transferred from the surface of a semi-infinite slab from the equation for surface heat flux.
See footnote 16.
Draw two graphs to show what happens when you plot the space time curves for heat transfer through a semi-infinite slab in terms of the original variables and in terms of the similarity variable.
