Lectures related to Fourier Analysis and PDEs

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Heat Transfer Applications

Explores the applications of the Fourier equation in heat transfer phenomena.

Applications of Fourier Equation

Explores applications of the Fourier equation in different heat transfer scenarios.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Heat Transfer Phenomena

Explores the applications of the Fourier equation in heat transfer phenomena, covering conduction, convection, and radiation.

Fourier Equation in 2D: Stationary Regime

Explores the Fourier equation in 2D for a stationary regime without heat production in a semi-infinite wall.

Fourier Equation in 2D

Explores the Fourier equation in 2D for heat conduction in various scenarios, using the separation of variables method.

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Heat Equation: Modeling and Numerical Methods

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Transient Heat Transfer: Spatial Effects

Explores transient heat transfer with spatial effects, including Bi number and convective cooling.

Transient Heat Transfer: Analytical Solutions

Explores transient heat transfer, analytical solutions, boundary conditions, and heat flux density in various geometries and materials.

Heat Exchangers: Fundamentals and Applications

Explores the fundamentals of heat exchangers, including conduction, convection, and temperature profiles, with practical examples.

Complex Analysis: Laplace and Fourier Transforms

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.

Diffusion: Macroscopic View

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Fourier Transform and Partial Differential Equations

Explores the application of Fourier transform to PDEs and boundary conditions.

Unbounded and Bounded Systems: Fourier Methods

Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.

Heat Recovery in Process Units

Explores heat recovery, heat exchanger calculation, and pinch analysis for energy optimization.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Boundary Conditions - 1D Systems

Covers boundary conditions for heat diffusion in 1D systems.

Thermal Circuits: Overall Heat Transfer Coefficient

Explores thermal circuits and the overall heat transfer coefficient in the context of heat conduction.