Heat equation governs the temperature 'u' in a body in space. The following physical assumptions are to considered - 1. The specific heat 𝛔 and the density ρ of the material of the body are constant. No heat is produced or disappears in the body. 2. Heat flows in the direction of decreasing temperature and the rate of flow is proportional to the gradient of 'u'. 3. The thermal conductivity k is constant. The boundary conditions i.e conditions on two ends of a thin bar can be different. For different boundary conditions, solution of heat equation is also different. In the following video, solution of heat equation is discussed where both the ends are kept at temperature 0. These boundary conditions are known as homogeneous boundary conditions. The details of solution are - In the following video, the solution of one dimensional heat equation where both the ends are insulated is discussed. Det...
