A plane wall has a thermal conductivity of $$1.15$$ $$W/m.K.$$ If the inner surface is at $${1100^ \circ }C$$ and the outer surface is at $${350^ \circ }C$$, then the design thickness (in meter) of the wall to maintain a steady heat flux of $$2500\,\,W/{m^2}$$ should be ____________.

A material $$P$$ of thickness $$1$$ $$mm$$ is sandwiched between two steel slabs, as shown in the figure below. $$A$$ heat flux $$10\,kW/{m^2}$$ is supplied to one of the steel slabs as shown. The boundary temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is $$10W/m.K.$$. Considering one-dimensional steady state heat conduction for the configuration, the thermal conductivity ($$k$$, in $$W/m.K$$) of material $$P$$ is _____________

Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $$\left( \ell \right)$$. The conductivity of one section is $$k$$ and that of the other is $$2k.$$ The left face of the wall is at $$600$$ $$K$$ and the right face is at $$300$$ $$K.$$

The interface temperature $${T_i}$$ (in $$K$$) of the composite wall is ___________

Consider steady-state heat conduction across the thickness in a plane composite wall as shown in fig exposed to convection conditions on both sides.

Assuming negligible contact resistance between the wall surfaces, the interface temp $$T(C)$$ of the two walls will be