Heat Equation: Modeling and Numerical Methods

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Related lectures (50)

Boundary Conditions - 1D Systems Log in to Mediaspace to watch this video

Covers boundary conditions for heat diffusion in 1D systems.

Heat Equation: Diffusion Log in to Mediaspace to watch this video

Covers the heat equation for diffusion and conservation of thermal energy.

Inverse Monotonicity: Stability and Convergence Log in to Mediaspace to watch this video

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Example: 1D steady diffusion Log in to Mediaspace to watch this video

Explores the numerical simulation of steady convection-diffusion problems, discretization, boundary conditions, and algebraic system assembly.

Heat Transfer Applications Log in to Mediaspace to watch this video

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

Material and Energy Balances Log in to Mediaspace to watch this video

Explores material and energy balances in chemical engineering for process optimization and design.

Heat Equation: Separation of Variables Log in to Mediaspace to watch this video

Covers the application of separation of variables method to solve the heat equation.

Conduction in Solids: Fundamentals and Applications Log in to Mediaspace to watch this video

Explores the basics of heat conduction in solids, covering Fourier's law, thermal conductivity, energy conservation, and practical applications.

Thermal Bridge Analysis: Materials and Conditions Log in to Mediaspace to watch this video

Explores thermal bridge analysis, material properties, and boundary conditions for building insulation.

Stability and Convergence in Numerical Methods Log in to Mediaspace to watch this video

Explores stability, consistency, and convergence in numerical methods, emphasizing the importance of order consistency and boundary conditions.

Snowpack Model: Principles and Applications Log in to Mediaspace to watch this video

Explores the principles and applications of the snowpack model, covering topics such as snow compaction, settling, heat transfer, and phase change processes.

Calculus of Variations and Euler's Elastica Log in to Mediaspace to watch this video

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Root Finding Methods: Bisection and Secant Techniques Log in to Mediaspace to watch this video

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Effectiveness-NTU Method Log in to Mediaspace to watch this video

Covers the Effectiveness-NTU method for analyzing heat exchangers and determining the highest heat transfer.

Closed Surfaces and Integrals Log in to Mediaspace to watch this video

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Thermal Effects Log in to Mediaspace to watch this video

Explores thermal effects, including conduction, thin films, nanowires, carbon nanotubes, and heat transfer by convection.

Numerical Root Finding with Scipy Log in to Mediaspace to watch this video

Introduces numerical root finding, differentiation, integration, and ODE solving using Scipy.

Numerical Analysis: Quadrature Formulas Log in to Mediaspace to watch this video

Covers the concept of numerical integration using quadrature formulas.

Eigenvalues and Eigenvectors Log in to Mediaspace to watch this video

Covers eigenvalues and eigenvectors, explaining their importance in linear algebra.

Numerical Integration: Simpson Quadrature Rule Log in to Mediaspace to watch this video

Covers the Simpson quadrature rule for numerical integration, explaining the method to compute integrals using interpolation nodes and weights.

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