When using a kitchen oven, I am always perplexed by the time it takes to cook food, whether a chicken, a goose, or even a turkey. Despite their all being poultry, these birds come in different sizes and have different tissue compositions. The packages provided by large food suppliers typically come with helpful instructions that typically read: cook the bird at a given temperature (say around 180°C) for a time that depends on the weight.

For instance, we are advised to cook a 5 kg turkey for image hours and a 10 kg turkey for 4 hours. Where do these numbers come from? How does the cooking time depend on the bird weight? Maybe there are secret warehouses with rows of well‐calibrated ovens and an army of testers with chef’s hats, large aprons, and industrial size thermometers trying various combinations of weight and poultry for the good of public safety. What if I want to cook an ostrich, with a typical weight varying between 60 kg and 150 kg? How about finding a cooking time estimate for the Bedouin delicacy consisting of a whole camel stuffed with a few sheep that are in turn stuffed with about twenty chickens themselves stuffed with fish? Clearly the problem of cooking poultry could be solved by empirical testing, but this practical solution will never satisfy my curiosity.

4. Cooking time versus mass of various poultry in a log‐log plot (the star between the Duck and the Guinea Fowl is a Free‐range Chicken). Data obtained from commercially available sources. The line indicates the theoretical prediction of a 2/3 scaling law (that is, the cooking time increases as tM = CM2/3 and appears on a log‐log plot as a line of slope 2/3).

The modelling process often starts with simple questions. In this case: how does the cooking time, at a given fixed temperature, depend on the weight? Or consider an even simpler question. If I know the cooking time for a 5 kg turkey, what would be the cooking time for a 10 kg or 100 kg bird? The next step is to simplify the problem by stating a number of assumptions about the system.

This is where we first encounter the art and craft of modelling. We have to decide what are the relevant quantities affecting our problem. We could consider among others: the age of the bird, its shape and size, whether it was corn‐fed or free range, the size and type of oven, the cooking cycle, the basting method and type of stuffing, and so on.

While all these effects may be important, if there is any hope of progress, we will need to make stringent simplifications. The key is to make these simplifications completely explicit so that they can be challenged and modified when considering more realistic situations. Therefore, as a starting point for our first model, we will make the following assumptions:
• The bird is a sphere of radius R with mass M and uniform constant density ρ (its weight per unit volume).

• The bird has an initial temperature Ti, and is cooked at a constant oven temperature To. That is, I assume that the temperature at the surface of the sphere is maintained at a constant To.

• The transfer of heat in the bird is described by a unique constant coefficient of thermal diffusivity k. This coefficient describes the ability of a material to conduct heat. A larger value of k means that the bird cooks faster compared to a bird with a smaller value. Importantly, the thermal diffusivity k has dimensions of length squared divided by time.

Since heating is a physical process, these assumptions are based on the physical theory of heat transfer. In the process of writing our assumptions we have identified the key variables, namely the radius R, the mass M, the temperatures Ti and To, and the thermal diffusivity k. Essentially, we have replaced our bird by a sphere of homogeneous material subject to a constant temperature at the surface.

Mathematicians jokingly refer to this type of assumption as the spherical‐cow assumption,a drastic assumption that transforms a problem into a much simpler one for the convenience of mathematical analysis. Remarkably, in many contexts, these simplifications provide excellent results, even for the unfortunate cows that are not perfectly spherical.

Next, we want to know the mathematical relationship that relates the cooking time tM, defined as the earliest time at which a safe temperature is reached at all points of the mass M, as a function of all the variables:

Note that we do not list the density ρ or the mass M as variables. We assume that the density is the same for all birds. Therefore, the mass is M = ρ × 4π R3/3 (mass is density times volume).

Quite remarkably, within this set of assumptions and without writing any further equations for the physical process taking place, we can already extract some useful information and answer some of our questions. To do so, we will use the method of dimensional analysis, which consists in finding relationships between different quantities with the same physical dimensions.