Heat, Mass and Momentum

Question 1

What is the equation for Fourier’s law, and what does it refer to?

Answer 1

The rate of heat transfer.

Question 2

What is the equation for Fick’s law, and what does it refer to?

Answer 2

The rate of mass transfer.

Question 3

What is the equation for Newton’s law, and what does it refer to?

Answer 3

The rate of momentum transfer.

Question 4

Name three purposes of mathematical modelling.

Answer 4

1) description and prediction: what will the effect of making a certain change be on another parameter? describing how a piece of equipment works or its temperature profile
2) design and control: what will be the output concentration? Is it within the specification? How will changing the parameters change it?
3) understanding: what is the flow structure? does is change at all by altering the inlet conditions?

Question 5

Show how fluxes act on a control volume

Answer 5

Question 6

How does heat travel in the following situation? What is the equation for this?

Answer 6

From the hot end to the cold end.

Question 7

Give the typical heat transfer conductivity values for water, aluminium, concrete, glass and Earth and W/m²

Answer 7

water 0.61

aluminium 206

concrete 0.92

glass 0.71

earth 1.7

Question 8

What happens when we ‘shrink’ the control volume that the conservation laws are applied to when we model them?

Answer 8

You get a partial differential equation, with two spatial boundary conditions and a time boundary condition. This means it is an equation that is 2nd order wrt space and 1st order wrt time