6.1 Short-time: exercises (examples)

Course subject(s) 6. Unsteady conduction and diffusion

Exercise 1

A very flat sheet of oak has temperature T0. A layer of steel, temperature T1 (which is higher than T0), is put together with the oak sheet. Calculations are not needed in this exercise.

Exercise 2


Remember the blue mozzarella exercise from module 5? There was a landfill site contaminated with garbage. The groundwater used in the production of mozzarella turned the cheese blue, because it was inherently contaminated as well.

After 10 years, the penetration depth was 0.45 m. The concentration profile was assumed to be linear in depth. Now, with penetration theory, we can do a more realistic calculation.

It is known that the diffusion constant D = 2.0 • 10-10 m²/s and the solubility is constant: c*=2.0 kg/m³at the surface at all times.


We wonder how much contamination is contained in the ground after 18 years, in other words, how much garbage (in kg/m2) has entered the landfill from the moment the garbage is put on top of it (t =0) .

There are several ways to calculate this. In this exercise, you will use the method of integrating the mass flux Φm” over time . The graph below will help you understand this method. It presents the mass flux over time at the surface (depth = 0 m).

Exercise 3


Remember Max burning his hand while cooking the union soup in the spark? This mistake can be partly understood by using penetration theory.

Solving the complete problem involves some knowledge about long-term heating, which will be addressed in the in the next chapter. For now, we will only use penetration theory.

The effective length between the soup and the top of the ladle is 20 cm, the effective length between the soup and the point where Max grabs the ladle is 10 cm. The ladle is made of stainless steel (a = 1.172 • 10-5 m2/s).

Creative Commons License
The Basics of transport phenomena by TU Delft OpenCourseWare is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://ocw.tudelft.nl/courses/basics-transport-phenomena/.
Back to top