Explain using equations from the data sheet how the Grashof number is used to estimate heat transfer and to which mode of heat transfer it is relevant.

A closed rectangular metal tank resting on a perfectly insulating floor and completely filled with cooling oil is to have its heat dissipation rate by convection increased by a factor of 2 by the addition of fins to the side walls and the top surface. The surface temperature of the tank without fins is $105^\circ\mathrm{C}$ and the ambient air temperature is $25^\circ\mathrm{C}$. The heat transfer coefficient $h = 13\ \mathrm{W\,m^{-2}\,K^{-1}}$ for all surfaces and at all temperatures. (This value applies to the tank and the fin surfaces both on the sides and the top.) Calculate the heat loss per square metre from the tank before the fins are added and also the heat loss per square metre of tank after the fins are added (i.e. multiply by 2).

For the tank described in part (b) the fins are to be 6 mm thick with a pitch of 100 mm (the pitch is the centre to centre spacing). The thermal conductivity $k$ for the metal of the fins will be $56\ \mathrm{W\,m^{-1}\,K^{-1}}$. Assuming that when the fins are added, the surface temperature of the tank (i.e. the fin base temperature) drops to $90^\circ\mathrm{C}$ and neglecting radiation losses, estimate the length of the fins.

With respect to part (c) estimate the temperature of the fin tips.

The tank is located in a building such that the walls which surround it are at $25^\circ\mathrm{C}$. If, before the fins are attached, the tank was painted with a paint whose emittance was 0.7 what would have been the net radiant heat loss per square metre from the tank's walls (or top)?

Now suppose that the tank's length, width and height, before the fins are added, are all one metre exactly. Place limits on the amount by which radiative loss from the tank changes (expressed as a fraction or a percentage) when the fins are added assuming they also are painted with the same paint as used in part (e).