Natural convection enhanced by a "chimney effect"

[gnurf]

It has been suggested to me that the ability of the heatsink shown below to remove heat from its base (orange) by natural convection could be enhanced by closing the open side (pink) shown in the figure below. Assume a lid (pink) of non-conductive/isolating material. I think the idea is that this would induce a "chimney" effect that would increase the pressure gradient along the fin lengths and thus increase the rate at which warm air is removed.

To me, the idea that artificially limiting the system's access to cold air would somehow have a net cooling effect seems, at the very least, counter-intuitive and although there are some google-hits that sort-of suggest that this is a thing, I've never seen a closed fin design like that and I suspect that is for a reason.

Comments or pointers to fundamental principles are appreciated.

 

[Lnewqban]

I believe that would be the third case discussed in this article (tips at same temperature):
https://en.wikipedia.org/wiki/Fin_(extended_surface)

For a difference made by chimney effect, a sustancial height difference is preferred.

 

[256bits]

I've never seen a closed fin design

You have to look around.
The heat exchanger for the magnetron of your microwave oven has such a system, although modified somewhat, The 'curvy' ends could be considered as such a tip design. Note that there is a directionality involved - the air flow is forced through the more open tip ends, with the curved part adding extra surface area to the perpendicular tips. Reason for the curves rather than a flat piece welded or an extrusion has to due with the lower cost factor of manufacture of stamped aluminium.

Your baseboard heater might have similar stamped aluminium square sheets along the length of the pipe, with the top and bottom open, and the sides closed by a bend in the metal edge, adding again more surface area and heat transfer from those bent tips.

Both would fall under the tip end at constant temperature category,

Assume a lid (pink) of non-conductive/isolating material

Not sure why you would want to insulate and loose any heat transfer from the tip area. ( Although in special cases that could apply )

Fins can be of any thickness t, giving a tip area A_p, having a particular heat conduction along its length k, exhibiting a convection coefficient h, and a length L. One would have to take into account such variables when designing a fin to handle a heat load.

Cost is a factor.
"Best" design might be the infinite length design, but since most of the heat is transferred from the base, and from the base along the fin exponentially, fins become much much shorter, loosing only perhaps 1% to 5% performance of the infinite length fin.

 

[hutchphd]

Isn't there a fan in a microwave for force cooling the magnetron?
I think the convection chimney idea runs afoul of viscosity issues even for air at this scale. I wonder what is the conduction vs radiation number is for a heat sink. Why are only some of them black?

 

[256bits]

Isn't there a fan in a microwave for force cooling the magnetron?
I think the convection chimney idea runs afoul of viscosity issues even for air at this scale. I wonder what is the conduction vs radiation number is for a heat sink. Why are only some of them black?

the air flow is forced through the more open tip ends

Radiation - temperature differential would be a criteria, plus why blacken the fins ( cost again ) if just adding a few additional cheaply solves the problem. Any radiation would then be a bonus.
For more critical designs, the cost of additional calculations and manufacture might be worth it to choose a best profile and surface - all fins are not flat shaped - tapered cross section, circular, etc. Perhaps NASA has special considerations for radiation into space ( not much convection in space ), where weight of the unit is also a design criteria.

If a fin radiates, where does it radiate to if in a series of flat ones close together - to the ones next right to it, and vice versa. Surface conditioning doesn't change anything ( much ) except near the tip ( where by the way the temperature differential would negate a large radiation effect to ambient ).
Spacing between fins - large spacing and short fins - maybe one would consider a blackened surface of the fins and base.

 

[gnurf]

I believe that would be the third case discussed in this article (tips at same temperature):
https://en.wikipedia.org/wiki/Fin_(extended_surface)

Why do you believe that? I stated as a premise that the tips were covered with an insulating material, so surely the tip condition here corresponds to the adiabatic case from your wiki link, and not the constant temperature?

 

[gnurf]

You have to look around.
The heat exchanger for the magnetron of your microwave oven has such a system, although modified somewhat, The 'curvy' ends could be considered as such a tip design. Note that there is a directionality involved - the air flow is forced through the more open tip ends, with the curved part adding extra surface area to the perpendicular tips. Reason for the curves rather than a flat piece welded or an extrusion has to due with the lower cost factor of manufacture of stamped aluminium.

View attachment 264509

Your baseboard heater might have similar stamped aluminium square sheets along the length of the pipe, with the top and bottom open, and the sides closed by a bend in the metal edge, adding again more surface area and heat transfer from those bent tips.

Both would fall under the tip end at constant temperature category,Not sure why you would want to insulate and loose any heat transfer from the tip area. ( Although in special cases that could apply )

Fins can be of any thickness t, giving a tip area A_p, having a particular heat conduction along its length k, exhibiting a convection coefficient h, and a length L. One would have to take into account such variables when designing a fin to handle a heat load.

Cost is a factor.
"Best" design might be the infinite length design, but since most of the heat is transferred from the base, and from the base along the fin exponentially, fins become much much shorter, loosing only perhaps 1% to 5% performance of the infinite length fin.

While an interesting design, I fail to see how the magnetron cooling system you describe is relevant to the OP. My specific question was what happens to a vertical oriented heatsink's ability (by natural convection) to rid itself of heat if you cover the fin tip face with an insulating material, e.g. if the heatsink was placed against an insulating material (shown in pink in the OP).

 

[256bits]

While an interesting design, I fail to see how the magnetron cooling system you describe is relevant to the OP. My specific question was what happens to a vertical oriented heatsink's ability (by natural convection) to rid itself of heat if you cover the fin tip face with an insulating material, e.g. if the heatsink was placed against an insulating material (shown in pink in the OP).

Magnetron is an example of a closed fin.
But, I suppose you did say

I've never seen a closed fin design like that

meaning a ( vertical ) closed fin with insulated tips.

 

[gnurf]

Magnetron is an example of a closed fin.
But, I suppose you did say

meaning a ( vertical ) closed fin with insulated tips.

What's your gut feeling re the OP then, if I may ask? None of the books I've seen that go through the process of fin length optimization etc on simple fin structures such as the one in the OP, indicate or mention that covering the finned face with an insulator is a good idea. My hope here was that someone would immediately see the flaw in that idea and point it out to me, but maybe it's more complicated than my intuition leads me to believe. I should probably just do the experiment (carefully) and convince myself one way or another that way.

 

[Lnewqban]

Why do you believe that? I stated as a premise that the tips were covered with an insulating material, so surely the tip condition here corresponds to the adiabatic case from your wiki link, and not the constant temperature?

You are correct, I was not.
Sorry about the late response; I have been away from this site for several days.