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

For the three dimensional object shown in the fig below. Five faces are insulated. The sixth face $$(PQRS),$$ which is not insulted, interacts thermally with the ambient , with a convective heat transfer coefficient of $$10W/{m^2}K.$$ The ambient temperature is $${30^ \circ }C$$. Heat is uniformly generated inside the object at the rate of $$100W/{m^3}.$$ Assuming the face $$PQRS$$ to be at uniform temperature, its steady state temp is

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