Heat Transfer Demonstration

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In this video we demonstrate heat transfer through a metal bar. By heating one side of the bar we can impose a non-uniform temperature distribution across the bar. This thermal gradient will then encourage heat transfer to other regions of the bar. We visualize this heat transfer by melting sticks of butter placed along the bar. • This physical phenomenon can be modeled using a partial differential equation (the heat equation). Links to this video as well as others related to partial differential equations are included below. • Additional videos in this series: • -Introduction to Partial Differential Equations ( • Introduction to Partial Differential ... ) • -Standing Waves Demonstration ( • Standing Waves Demonstration ) • -Derivation of the 1D Wave Equation ( • Derivation of the 1D Wave Equation ) • -Solving the 1D Wave Equation ( • Solving the 1D Wave Equation ) • -Heat Transfer Demonstration ( • Heat Transfer Demonstration ) • -Derivation of the Heat Equation ( • Derivation of the Heat Equation ) • -Solving the 1D Heat Equation ( • Solving the 1D Heat Equation ) • -Derivation and Solution of Laplace’s Equation ( • Derivation and Solution of Laplace’s ... ) • -Derivation of the 2D Wave Equation ( • Derivation of the 2D Wave Equation ) • -Solving the 2D Wave Equation ( • Solving the 2D Wave Equation ) • Associated videos on software tools relevant to PDEs include: • -Creating Movies and Animations in Mathematica ( • Creating Movies and Animations in Mat... ) • -Creating Movies and Animations in Matlab ( • Creating Movies and Animations in Matlab )

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