I am an EE in need of help with a topic I do not even know where to start looking for answers; given a vertically oriented hollow tube filled with fluid of known qantity and property and heat applied to the bottom of the tube - the heated fluid will travel towards the top of the tube with a certain speed. In its most basic form, how do I compute the speed of the body fluid that rizes upwards? Any pointers to math/physics to study for me?
Tuva
My first guess would be to start solving using the laws of conservation of energy. This type of problem could be found in any good thermodynamics or heat transfer book depending on the types of assumptions you're making.
Being entirely innocent of any analytical approaches to this issue, I would punt: starting like this. Suppose the fluid were solid, with the same specific heat and thermal conductivity: I could certainly work out the rate of change of temperature with time and height - after thrashing around in the books somewhat. So I have a lower limit on the rate of energy transfer.
Then I might work some sums for a central column of rising fluid of 1/3 the column cross section area, flowing to a decending annulus also occupying one third of the cross section area , and opposed by a sandwiched annulus which applies viscous shear to the ascending column and descending annulus, so that the sandwiched "brake" stays still. That would be a rising column diameter of 58% of total column diam, a decending annulus at 82% plus of total column diameter What is the buoyant force? The sinking force would be the same. What is the area of the cylinder at (say )
70% of the column diameter? What is the thickness of the annulus applying viscous shear? (82% - 58% = 24% of the column diameter) What is the viscosity of the fluid? You know it. What is the viscous force resisting the motion? That ought to get me close to a number for the rising column's speed. Maybe.That model is rather artificial, but I think I could shake some numbers out of it. Then I might actually try a fluid column and check the speed of suspended particles, review the temperature profile etc., etc.
Or if this is all too much? - talk to a mech eng who works in the area
- or a physics whiz.
Brian Whatcott Altus OK
A better source would be a transport phenomena book such as Bir, Stewart, & Lightfoot. This problem has already been solved.
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