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 _____________

Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.

The free stream velocity is $${U_\infty }$$ and the free stream temperature $${T_\infty }$$ is lower than the cylinder surface temperature $${T_s}.$$ The local heat transfer coefficient is minimum at point

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

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 ______________.