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

Steady two dimensional heat conduction takes place in the body shown in the fig below. The normal temperature gradients over surface $$P$$ and $$Q$$ can be considered to be uniform. The temperature gradient $$\partial T/\partial x = $$ at surface $$Q$$ is equal to $$10$$ $$K/m.$$ surfaces $$P$$ and $$Q$$ are maintained at constant temperatures as shown in the fig. While the remaining part of the boundary is insulated . The body has a constant thermal conductivity of $$0.1$$ $$W/mk$$, the value of $$\partial T/\partial x$$ and $$\partial T/\partial y$$ at surface $$P$$ are