We explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. We restrict our consideration to the génoise and obtain a semiempirical relation for the baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The relation, which is based on the diffusion equation, has three parameters whose values are estimated from data obtained by baking cakes in cylindrical pans of various diameters. The relation takes into account the evaporation of moisture at the top surface of the cake, which is the dominant factor affecting the baking time of a cake.
REFERENCES
The baking process involves several stages before the cake is completely baked. The study in Refs. 7 and 8 applies only to the initial stage of the baking process.
A comprehensive review of existing research is given in Ref. 8.
The only significant modification to the recipe is that the eggs have not been warmed over boiling water prior to mixing.
Reference 4, pp. 151–174, provides an excellent discussion of the physics and chemistry of baking sponge cakes, of which the génoise is an example.
The cake exhibits a slight amount of shrinkage from the sides of the pan, and its top springs back, when lightly pressed.
If the cake is rectangular, the term is replaced by , where and are the length and width of the cake pan.
The reader should be aware that some equations are expressed in terms of diameter rather than radius. The reason is to make transparent the relation between these formulas and those applicable to rectangular cake pans.
Standard cake pans are not readily available with these dimensions. This lack has necessitated substituting a coffee can, filled with batter to a depth of for a cake pan. In fact, génoises are commonly not baked greater than in depth.
Temperature display instruments are located outside of the oven, so that temperature data can be collected without opening the oven door.
It has been necessary to truncate the sum at such large values of and (, ) to obtain reasonable estimates of temperatures close to the initial temperature of the cake.
We have observed that typically the mass of a baked cake is less by approximately 10%.
Any time dependence of the thermal diffusivity is assumed to result from that of the thermal conductivity only. We neglect the possible time dependence of the mass density and specific heat. This neglect simplifies the analysis and avoids physically unrealistic, temporal discontinuities in the temperature which result from discontinuous changes in the thermal diffusivity.
The computations were performed using MAPLE software. The optimization of adjustable parameters in the model was achieved by trial and error.
In this section the diameter rather than the radius is used in all formulas.