A plane, solid slab of thickness L, shown in the figure, has thermal conductivity k that varies with the spatial coordinate x as k = A + Bx, where A and B are positive constants (A > 0, B > 0). The slab walls are maintained at fixed temperatures of T(x = 0) = 0 and T(x = L) = T0 > 0. The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?
![GATE ME 2024 Heat Transfer - Conduction Question 6 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx6qdred/c7507220-9e92-45cf-ba25-a11af501677f/a1664b40-25ec-11ef-aa3a-b50fcd52eab4/file-6y3zli1lx6qdree.png?format=png)
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).
![GATE ME 2024 Heat Transfer - Conduction Question 5 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lx720xpe/5428ef8e-09cd-4937-80bc-70c3d3c47948/2a4d7820-261a-11ef-a279-4f9760cfcb83/file-6y3zli1lx720xpf.png?format=png)