Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $Nu_1$. If the freestream velocity is doubled, the Nusselt number changes to $Nu_2$. Choose the correct option for $Nu_{2}/Nu_{1}$.

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, $T$ is the temperature of the fluid, $T_w$ is the wall temperature and $T_m$ is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?

Consider a slab of 20 mm thickness. There is a uniform heat generation of $ \dot{q} = 100 \text{ MW/m}^3 $ inside the slab. The left and right faces of the slab are maintained at 150 °C and 110 °C, respectively. The plate has a constant thermal conductivity of 200 W/(m.K). Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at ______mm (answer in integer).

A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1 kg/s with an inlet temperature of 30 °C. The steam in the condenser shell condenses at the rate of 430 kg/s at a temperature of 50 °C. If the heat of vaporization is 2.326 MJ/kg and specific heat of water is 4 kJ/(kg.K), the effectiveness of the heat exchanger is _______ (rounded off to 3 decimal places).