In the kitchen we are generally interested in heat flowing from fluids (oven air or boiling water) to solid (meat or vegetables). Heat moves between fluids and solids following the equation below.
Q - rate of heat transfer (how quickly the heat is moving)
h - heat transfer coefficient of the fluid
A - area of contact
ΔT - the difference in temperature between the fluid and solid
This is a simple equation that provides us with some very useful information that we can apply in the kitchen. The rate of heat transfer is proportional to the heat transfer coefficient of the fluid, the area over which the fluid and solid are touching and the temperature difference between the fluid and the solid, increasing any of these will increase the rate of heat transfer which means our food will cook faster.
Step 1: Increase the Heat Transfer Coefficient
Olive Oil 0.17
With a thermal conductivity of 0.58, water is 24 times better at conducting heat than air. You already know this, because you know that boiling potatoes is faster than baking them. And you know that you can go outside in the winter without gloves even if it's well below 0, but you wouldn't stick your hands in a bowl of ice water.
How can we use this knowledge to our advantage?
Water transfers heat much faster than air, while oil is somewhere in between. If you want to heat something up quickly you are much better off boiling or frying it than you are baking it. Similarly, if you need to cool something down quickly running it under cold water will cool it down much faster than blowing on it.
Fast heat isn't always a good thing. Meat heated past 77°C is tough and dry so adding meat to boiling water will bring it up to 100°C quickly and give an unpleasant result. Meat is better cooked very quickly so that the internal temperature remains below 77°C when the outside is cooked or in an environment where the rate of heat transfer is slower.
If you need to thaw meat for dinner the natural thing to do is to leave it out on a warm counter. But air is a great insulator and thawing chicken this way can take hours. In the mean time parts of the chicken can warm to room temperature and allow harmful bacteria to grow. A safer, and faster, way to thaw chicken is to place it in ice water. Even though the ice water is colder than room temperature (23°C) it is warmer than your freezer (-15°C) and because water is such a great conductor it can do more with a 15 degree difference than air can do with a difference of almost 40 degrees.
Hack your Kitchen
Solids in general, but metals especially, are much better conductors that fluids. To defrost something in a real hurry put it on a large metal baking sheet or frying pan. Aluminum has a thermal conductivity of 250W/mK! Think of it as a reverse heat sink.
Step 2: Increase Surface Area
When cooking vegetables cut them in half length-ways to nearly double the surface area and therefore the rate of heat transfer with only one cut.
Cooking vegetable quickly keeps more of their flavour, texture and colour intact. Cut up your vegetables so that they cook evenly and you aren't stuck overcooking the outside waiting for the inside to soften up.
I love making a huge vat of chili or tomato sauce so I can freeze it for later use. Putting a huge container of hot food in the freezer can take a long time to freeze through and in the mean time harmful bacteria can grow in the still warm core. When freezing large batched of food divide it up into serving sized container and spread them around to allow good air flow.
Step 3: Temperature Difference
The temperature difference will change over time and will decrease as the food warms up. To keep the rate of heat transfer relatively quick a large temperature difference is generally used.
Oil has a lower heat transfer coefficient than water but it has the advantage of being able to be heated to a much higher temperature (175°C-190°C verses 100°C) which is what makes french fries fast food.
When cooking a roast chicken the oven is generally set to around 230°C even though cooked chicken is between only 74-85°C. This is to keep the temperature difference large enough that heat will continue to be transferred relatively quickly. For this reason meat that is left in the oven too long can easily become overcooked. Check meat regularly with a thermometer and remove it as soon as a safe temperature is reached. Keep in mind that residual heat will continue to cook the bird even once it is removed from the oven as heat from the surface and the cooking vessel move inwards and equalize.
Hack you kitchen
As the temperature of the food approaches the temperature of its environment the temperature difference decreases and the rate of heat transfer slows to zero. If the temperature of the environment is set to the desired final temperature of the food then perfectly cooked food will result every time. This is the principle behind sous vide cooking. For sous vide cooking at home check out this or this.