Hot filament aerosol generator. We covered the basic heat transfer characteristics of a hot filament generator in class. A hot filament is a piece of metal through which current runs, generating heat. We showed that for low temperature operation, radiation heat losses are weak when compared to convection. Retaining only the conduction and convection terms in the 1D balance equation results in the following linear equation. kdx2d2Td2h(TT)+d2w2I2=0 a. In class, we mentioned that the filament is connected to clamps at both ends. These clamps have a temperature of T0. The length of the filament is L. That is, T=T0 at x=0 and at x=L. Thinking about the symmetry, develop an alternative boundary condition at the center of the filament. b. Solve the ODE with the alternative boundary condition 4 and show that the maximum temperature can be given by 5 : Tmax=T+2hdw2I2+(T0T2hdw2I2)cosh(mL/2)1