Two streams of fluid of unit constant specific heats and unit mass flow rate exchange thermal energy in an adiabatic heat exchanger. The inlet temps of hot and cold streams are $${300^ \circ }C$$ and $${30^ \circ }C$$ respectively. Calculate the $$LMTD$$ and effectiveness of the heat exchanger if the hot fluid is cooled to zero entropy condition.

Two insulting materials of thermal conductivity $$K$$ and $$2K$$ are available for lagging a pipe carrying a hot fluid. If the radial thickness of each material is same

Two shafts $$A$$ and $$B$$ are made of the same material. The diameter of shaft $$B$$ is twice that of shaft $$A.$$ The ratio of power which can be transmitted by shaft $$A$$ to that of shaft $$B$$ is

Only $$4$$ pairs can be matched :