-1
votes
1answer
34 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
1
vote
1answer
115 views

Temperature rate of change inside a cylinder

I was wondering about this today, mainly for baking a cylindrical cake. Say you have a solid cylinder which is at temperature T0 inside. Say you then move the ...
3
votes
1answer
337 views

Diffusion of gas in a liquid with changing pressure and solubility (chemical potential)

Modelling the diffusion of a gas dissolved in water in a vertical column of water, several meters deep. Also assuming the water is completely still, so only diffusion plays a role. (Actually a model ...
2
votes
1answer
170 views

What is the physical basis behind thermal diffusion in a Clusius-Dickel column?

A Clusius-Dickel column allows separation of two species by the application of a thermal gradient. In its simplest form, two bulbs are maintained at two different temperatures $T_1$ and $T_2$ and ...
2
votes
0answers
71 views

Why does the water diffuse at right angles in my coffee? [closed]

I purchase an espresso shot each morning at my local coffee shop, and I usually water it down slightly to take the edge off as well as to cool it. Recently, I have noticed that when I pour the cold ...
0
votes
1answer
58 views

heat spread from hot coil: diffusion, radiation?

When modeling the heat spread from a hot object through a vacuum (or a gas), what is the dominant physical process for heat energy transportation? Thermal diffusion, thermal radiation, a mix of the ...
1
vote
2answers
223 views

Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
3
votes
1answer
493 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE{*} and the Mass/Material Balance PDE have a similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive ...
2
votes
1answer
1k views

How does smoke move in the air and how can I direct it so it will go to a place I want it to go?

Let's assume a close room with 1-2 people who only one of them smoking cigarette. What is the equation describe the smoking spreading? is it diffusion? what are the parameters is so? Is there a ...
0
votes
1answer
1k views

What's the temperature distribution of a plane wall insulated on one side with no internal heat gen.?

Let's say we have a plane wall that is insulated on one side, exposed to a fluid on the other side, and has no internal heat generation. Would the shape of the temperature distribution be a constant? ...
1
vote
1answer
107 views

What are the patterns appear after kernel averaging?

Having a 2D map filled uniformly by random values (Figure:top-left) to demonstrate a disordered phenomena, the next maps are ...
2
votes
3answers
447 views

Finite difference formulation of the heat equation with thermal conductivity in 1D

This may seem trivial, but I'm having some trouble deriving the finite difference form of the heat equation with a thermal conductivity function $a(x)$ depending on $x$: $$\frac{\partial u(x, ...