An un-insulated air conditioning duct of rectangular cross section $$1\,\,m \times 0.5\,m,$$ carrying air at $${20^ \circ }C$$ with a velocity of $$10 m/s,$$ is exposed to an ambient of $${30^ \circ }C$$. Neglect the effect of duct construction material. For air in the range of $${20-30^ \circ }C,$$ data are as follows: thermal conductivity $$=0.025 W/m.K;$$ viscosity $$ = 18\mu Pa.s;$$ Prandtl number $$=0.73;$$ density $$= 1.2$$ $$kg/{m^3}.$$. The laminar flow Nusselt number is $$3.4$$ for constant wall temperature conditions and, for turbulent flow, $$Nu = 0.023\,\,R{e^{0.8}}\,{\Pr ^{0.33}}.$$

The heat transfer per meter length of the duct, in watts, is

Consider a laminar boundary layer over a heated flat plate. The free stream velocity is $${U_\infty }.$$ At some distance $$x$$ from the leading edge the velocity boundary layer thickness is $${\delta _v}$$ and the thermal boundary layer is $${\delta _r}.$$ If the Prandtl number is greater than $$1,$$ then

The properties of mercury at $$300K$$ are : density $$ = 13529kg/{m^3},$$ $${C_P} = 0.1393$$ $$kJ/kgK,$$ dynimic viscosity $$ = 0.1523\,\, \times \,\,{10^{ - 2}}\,\,N - s/{m^2}$$ and thermal conductivity $$=8.540$$ $$W/m$$-$$K$$. The Prandtl number of the mercury at $$300K$$ is

Water (Prandtl number $$=6$$ ) flows over a flat plate which is heated over the entire length. Which one of the following relationship between the hydrodynamic boundary layer thickness $$\left( \delta \right)$$ and thermal boundary layer thickness $$\left( {{\delta _t}} \right)$$ is true