Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus

Explore the derivation of the heat equation in higher dimensions using Gauss's theorem in this 25-minute video lecture. Delve into the mathematical intricacies as the instructor guides you through the process, starting with an overview and progressing to the heat equation derivation. Learn how to transform surface integrals into volume integrals and ultimately convert volume integrals into partial differential equations. Gain valuable insights into control volumes and vector calculus applications in thermal physics. Follow along with the step-by-step explanation, enhancing your understanding of advanced mathematical concepts in heat transfer and multidimensional analysis.

Deriving the Heat Equation in 2D & 3D (& in N Dimensions!) with Control Volumes and Vector Calculus