Numerical explorations of cake baking using the nonlinear heat equation

UNCW Author/Contributor (non-UNCW co-authors, if there are any, appear on document)
Rebecca Wilkinson (Creator)
Institution
The University of North Carolina Wilmington (UNCW )
Web Site: http://library.uncw.edu/
Advisor
Russell Herman

Abstract: Much can be said about the culinary aspects of cake baking. How much of and which types of ingredients are used to determine the flavor of the cake. However, is flavor the only ingredient for taste? Does a dry, crumbling cake still satisfy the pallet? One can control the flavor of the batter, but once it is placed in the oven for baking, what determines the consistency of the finished dessert? We consider a simple model of the actual baking process which is based on the diffusion equation @T @t = r · (DrT) , (1) where D is the heat diffusivity of the batter and T is the temperature of the cake at time t. We begin with this model and numerically investigate solutions for various cake geometries while also looking at the effects of varying the heat diffusivity over space and time.

Additional Information

Publication
Thesis
A Thesis Submitted to the University of North Carolina Wilmington in Partial Fulfillment of the Requirements for the Degree of Master of Science
Language: English
Date: 2009
Keywords
Baking--Mathematical models, Baking--Mathematics, Cake--Mathematics, Heat equation, Nonlinear functional analysis
Subjects
Nonlinear functional analysis
Heat equation
Baking -- Mathematics
Baking -- Mathematical models
Cake -- Mathematics