Fourier Law of Conduction . P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi. More Inventions through Mathematical Modeling…. Statement of Fourier’s Law.
P M V Subbarao
Mechanical Engineering Department
More Inventions through Mathematical Modeling…
The (mod of) heat flux, q’’, (the flow of heat per unit area and per unit time), at a point in a medium is directly proportional to the temperature gradient at the point.
Temperature gradient across the slab of thickness Dx:
The heat flux across the slab
Global heat transfer rate:
Using the principles of vector calculus:
Will mathematics approve this ?
What could be the most general acceptable behavior of k, approved by both physics and mathematics?
k can be a vector !!!!
We are at cross roads !!!!!
Thermal conductivity of a general material is a tensor.
Salt through cheese.
Smoke through meat.
Curing solution through meat
Not mass transfer:
Moving a fluid from one place to another