## Baking Cake: A Mathematical Model

By Vivien Yeung, University of Wollongong

The phrase, ‘having your cake and eating it’ is quite literal these days, as the cake and pastries industry is worth \$2 bn in Australia alone.

For thousands of years, bakers around the world have slaved over how to create the perfect, fluffy, moist cake. But baking cake requires lots of energy in a complex process involving simultaneous heat and mass transfer. To minimise energy consumption when baking in industry, predictive mathematical models are desired.

The science of baking is an area of increasing interest in food engineering. Engineers have conducted experiments on baking different types of cake and have modeled the heat and mass transfer phenomena inside of it. One such experiment was conducted by (Sakin et al., 2007) where a very thin sample of white cake was baked (3 mm thick and 220 mm in diameter). It’s more of a pancake, really!

A relatively simple model that can model the baking of a thin sample of cake is the lumped reaction engineering approach (LREA), a drying model developed by chemical engineers (Putranto et al., 2011, Chen & Putranto, 2013), and was applied to the experimental data obtained by (Sakin et al., 2007).

What does drying have to do with baking? Well, when heat is applied to the cake, water migrates from wet core of the cake batter up to the surface, where it then evaporates. We can think of this process as ‘drying’. So although the LREA has predominantly been used to model the drying of thin materials (such as drying milk droplets and thin fruit slices (Chen & Putranto, 2013)), the LREA is still appropriate to model baking.

The LREA is a system of differential equations that can be solved to obtain moisture content and temperature profiles. Temperature profiles implicitly measure energy requirements for baking because heat is thermal energy being transferred due to differences in temperature.

But to solve this system in the first place, we need to estimate the parameters of the model. It’s a recipe for disaster that involves lots of chemical engineering knowledge, but I promise that it’s not a dry subject!

References

[1] Chen, X.D., & Putranto, A. (2013). Modeling drying processes: A reaction engineering approach, Cambridge University Press.

[2] Putranto, A., Chen, X.D., & Zhou, W. (2011). Modeling of baking of thin layer of cake using the lumped reaction engineering approach (LREA). Journal of food engineering, 105(2), 306-311.

[3] Sakin, M., Kaymak-Ertekin, F., Ilicali, C., 2007. Modeling the moisture transfer during baking of white cake. Journal of Food Engineering 80, 822–831.

Vivien Yeung was a recipient of a 2018/19 AMSI Vacation Research Scholarship.