A hemispherical furnace of $$1$$ $$m$$ radius has the inner surface (emissivity, $$\varepsilon = 1$$) of its roof maintained at $$800K,$$ while its floor $$\left( {\varepsilon = 0.5} \right)$$ is kept at $$600K$$. Stefan-Boltzmannn constant is $$\,5.668 \times {10^{ - 8}}$$ $$W/{m^2}.{K^4}.$$ The net radiative heat transfer (in $$kW$$) from the roof to the floor is __________.

Water flows through a tube of diameter $$25mm$$ at an average velocity of $$1.0m/s.$$ The properties of water are $$\rho = 1000\,\,kg/{m^3},$$ $$\mu = 7.25 \times {10^{ - 4}}\,\,N.s/{m^2},$$ $$\,K = 0.625W/m.K,$$ $$Pr=4.85.$$ Using $$Nu=0.023$$ $$R{e^{0.8}}\,\,{\Pr ^{0.4}},$$ the convective heat transfer coefficient (in $$W/{m^2}.K$$) is ______________.

In a heat exchanger, it is observed that $$\Delta {T_1} = \Delta {T_2},$$ where $$\Delta {T_1}$$ is the temperature difference between the two single phase fluid streams at one end and $$\Delta {T_2}$$ is the temperature difference at the other end. This heat exchanger is

In a concentric counter flow heat exchanger, water flows through the inner tube at $${25^ \circ }C$$ and leaves at $${42^ \circ }C$$. The engine oil enters at $${100^ \circ }C$$ and flows in the annular flow passage. The exit temperature of the engine oil is $${50^ \circ }C.$$ Mass flow rate of water and the engine oil are $$1.5kg/s$$ and $$1$$ $$kg/s,$$ respectively. The specific heat of water and oil are $$4178$$ $$J/kg.K$$ and $$2130$$ $$J/kg.K,$$ respectively. The effectiveness of this heat exchanger is _________.