Why the heat flux vector at a point must be perpendicular to the temperature isothermal surface? Is it a definition or a deduction?
Before the question: I am working on numerical calculation of three dimension parabolic equation that based on Fourier's Law of which I am a little confused. Here comes the law in modern mathematics ...
Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector ...