🎬Steady-State Heat Transfer-Comparison of Dirichlet and Robin (Newton's Cooling) and Neumann Boundary

Steady-State Heat Transfer-Comparison of Dirichlet and Robin (Newton's Cooling) and Neumann Boundary Conditions

The comparison of Dirichlet, Robin, and Neumann boundary conditions for 1D steady-state heat transfer demonstrates how the boundary interaction dictates the entire temperature profile inside the material. With one side held at a fixed $100^{\circ} C$, the temperature at the opposite boundary ( $x=L$ ) determines the heat flow: the Neumann (insulated) condition imposes zero heat flow (zero temperature gradient), resulting in the highest possible temperature-a uniform $100^{\circ} C$ across the wall. The Dirichlet (fixed temperature) condition forces the temperature to a set ambient value( $20^{\circ} C$ ), representing the maximum possible heat transfer and the steepest linear temperature drop. The Robin (Newton's cooling) condition, which models convection, yields a physically realistic intermediate temperature ( $33.33^{\circ} C$ ), where the heat flow is moderate, proportional to the temperature difference between the wall surface and the ambient air.

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Steady-State Heat Transfer-Comparison of Dirichlet and Robin (Newton's Cooling) and Neumann Boundary Conditions | Animated Resultsviadean on Notion