- #1

manderson99

- 22

- 0

## Homework Statement

It is often stated that heat sinks, radiators, and the like require proper spacing of fins/pins/etc., especially when relying on natural convection. There is a formula from Rohsenow and Bar-Cohen that allows one to calculate the proper spacing between rectangular fins in a vertical arrangement when natural convection prevails; however, the formula makes reference to the Ra

_{L}, which makes me wonder how useful it is when Gr

_{L}and, consequently, Ra

_{L}are so low that conductive heat transfer (that is, Nu

_{L}= 1) is indicated.

Does this formula apply when conductive heat transfer is in effect due to low Gr

_{L}values? If not, is there an alternative?

## Homework Equations

S

_{opt}= 2.714L/Ra

_{L}

^{1/4}

## The Attempt at a Solution

The only attempt to a solution to this problem that I have made thus far is to mostly ignore this formula and instead examine mass flow as calculated at the end of any given plate, using a y-direction velocity equation and using half the distance between plates as the maximum possible value for δ (I noticed that the heat transfer lessons from my book on pipe flow indicate that the maximum boundary layer thickness is half the interior diameter of a pipe when fully developed, so I figured it would work about the same way between two vertical rectangular fins). Examining the expected amount of heat flow from any given fin, I use C

_{p}values taken at the relevant fluid temperature used elsewhere in evaluating heat flow from the fin(s) to calculate approximately what mass flow would be required to convect the calculated amount of heat away per fin. If the mass flow value derived from using V and δ above does not equal the estimated required mass flow value, then I know my fins are spaced too closely to accommodate the expected/given base temperature (typically, the mass flow value increases as δ increases, though the thermal boundary layer equation taken from the same section of my book as the y-direction velocity equation for vertical flat plates tells me how high δ could ever become). This approach seems logical until one takes conductive (Nu

_{b}) heat transfer situations into account. Even under these circumstances, the velocity formula seems to indicate that there is still movement of air, but the velocity and mass flow numbers are quite low.