Consider steady, 1-D heat conduction problems where we wish to use inverse technique to estimate the unknown thermal conductivity using measured temperatures at few discrete locations. In each of the following cases, formulate the inverse problem, and write the complete algorithm to estimate the unknown thermal conductivity:

1. Thermal conductivity is a second-degree polynomial function of temperature. Assume known temperatures at the boundaries.

2. Thermal conductivity is a unknown function of temperature. Assume known temperatures at the boundaries.

3. Thermal conductivity is a second-degree polynomial function of temperature. Assume known temperature at one boundary and known heat flux at the other.

4. Thermal conductivity is a unknown function of temperature. Assume known temperature at one boundary and known heat flux at the other