From baking a cake to solving the diffusion equation

American Journal of Physics

Volumn 74, Issue 6, 2006, Pages 502-509

  Olszewski, Edward A ^a  

^a UNIVERSITY OF NORTH CAROLINA WILMINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745116570     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2186330     Document Type: Article

References (25)

1. Alton Brown, I'm Just Here for More Food: Food×Mixing+Heat =Baking (Stewart, Tabori & Chang, New York, 2004).
2. Harold McGee, On Food and Cooking: The Science and Lore of the Kitchen (Scribner, New York, 2004).
3. Robert L. Wolke, What Einstein Told His Cook: Kitchen Science Explained (Norton, New York, 2002).
4. P. Barham, The Science of Cooking (Springer-Verlag, Berlin, 2001).
5. B. Zanoni and C. Peri, "Study of the bread baking process," J. Food. Eng. 19, 389-398 (1993).
6. K. Thorvaldasson and C. Skjöldebrand, "Water diffusion in bread," Lebensm.-Wiss. Technol. 31, 658-663 (1998).
7. M. Lostie, R. Peczalski, J. Andrieu, and M. Laurent, "Study of sponge cake batter baking process. I. Experimental data," J. Food. Eng. 51, 131-137 (2002).
8. M. Lostie, R. Peczalski, J. Andrieu, and M. Laurent, "Study of sponge cake batter baking process. II. Modeling and parameter estimation," J. Food. Eng. 55, 349-357 (2002).
9. 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.
10. A comprehensive review of existing research is given in Ref. 8.
11. The only significant modification to the recipe is that the eggs have not been warmed over boiling water prior to mixing.
12. J. Pépin, La Technique (Times Books, New York, 1976), pp. 356-358.
13. 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.
14. The cake exhibits a slight amount of shrinkage from the sides of the pan, and its top springs back, when lightly pressed.
15. Klamkin has considered such a model for estimating the scaling behavior in the cooking time of a roast. See M. S. Klamkin, "On cooking a roast," SIAM Rev. 3, 167-169 (1961).
16. C. Kittel, Thermal Physics (Freeman, New York, 1980), pp. 424-425.
17. George B. Arfken and Hans J. Weber, Mathematical Methods for Physicists (Academic, New York, 1995), 4th ed., pp. 473, 664.
18. 2, where X and Y are the length and width of the cake pan.
19. 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.
20. 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 4.0 in. for a cake pan. In fact, génoises are commonly not baked greater than 2 in. in depth.
21. Temperature display instruments are located outside of the oven, so that temperature data can be collected without opening the oven door.
22. It has been necessary to truncate the sum at such large values of m and n (m= 17, n= 17) to obtain reasonable estimates of temperatures close to the initial temperature of the cake.
23. We have observed that typically the mass of a baked cake is less by approximately 10%.
24. 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.
25. The computations were performed using MAPLE software. The optimization of adjustable parameters in the model was achieved by trial and error. 26 In this section the diameter rather than the radius is used in all formulas.