Wrapping a hot dish of food in shiny aluminium foil seems to keep the dish warm longer than wrapping it in clear plastic film. aluminium is much better conductor of heat than plastics, so why does it impede the flow of heat so well?

There are three different mechanisms for heat to transfer. Let's take a look at them to see if any of them explain the cause.

1. Conduction - This is the transfer of heat from one object to another via physical contact. And in the question, aluminium is a far better conductor of heat than plastic, so aluminum would transfer heat faster via conduction than plastic. So the cause for the observed phenomena has to be one of the other 2 mechanisms.

2. Convection - This mechanism relies upon the fact that for fluids (both gasses and liquids) change their volume and therefore their density with changes in temperature. This means that you can have a fluid get warmed up by something that's hot, expand to decrease it's density and then get pushed away from the warm surface by colder, denser fluid. The warmed fluid then gets cooled off when it contacts a colder surface, it's density increases, and then flows back replacing the newly warmed fluid. For both aluminum and plastic, there is likely to be equivalent convection effects in the air gap between the hot food and the substance being used to cover the food. And once again, since aluminum is a better conductor of heat, it would be more effective in cooling the warmed air, making convection work faster. So this mechanism doesn't work either. So let's look at the 3rd method of transferring heat.

3. Radiation - This is the process by which heat is radiated out from a warmer body in all directions via photons traveling through either vacuum or a transparent medium. An example would be the heat you feel from an electric stove. In this case, the photons carrying energy will go right through the clear plastic wrap unimpeded, while they would be reflected back to the food with the aluminum foil. So of the 3 mechanisms, the aluminum foil impedes the flow of heat via radiation far better than the clear plastic film. And in fact, it does that so much better than even with the disadvantage the foil has via conduction, it's more than out weighed by the better performance against radiation.