List of top Fluid Mechanics and Thermal Sciences Questions on One dimensional heat conduction asked in GATE ME

Consider incompressible laminar flow over a flat plate with freestream velocity of u_∞. The Nusselt number corresponding to this flow velocity is Nu₁. If the freestream velocity is doubled, the Nusselt number changes to Nu₂. Choose the correct option for Nu₂/Nu₁.

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?

Consider steady one-dimensional heat conduction in a slab of thickness $2L$ (with $L=1$ m). Thermal conductivity varies as $k = C T$, with $C = 2$ W·m$^{-1}$·K$^{-2}$, and the slab generates heat at $1280$ kW/m$^3$. Both faces are held at 600 K. The temperature at $x=0$ is __________ K (in integer).