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

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

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatures of $${160^0}C$$ and $${120^0}C$$ respectively. The plate has a constant thermal conductivity of $$200W/mK.$$

The location of maximum temp within the plate from left face is

Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp under these conditions is $${10.17^0}C$$. The outside temp is $$ - {23^0}C$$ (dry bulb) and internal and external surface heat transfer coefficients are $$8\,\,W/{m^2}K$$ and $$23$$ $$W/{m^2}K$$ respectively. If the building wall has a thermal conductivity of $$1.2$$ $$W/mK,$$ the minimum thickness (m) of wall required to prevent condensation is