GATE 2021 ME (ME2) – Question 55
Ambient air flows over a heated slab having flat, top surface at $y=0$. The local temperature (in Kelvin) profile within the thermal boundary layer is given by $T(y)=300+200\exp(-5y)$, where $y$ is the distance measured from the slab surface in meter. If the thermal conductivity of air is 1.0 W/m.K and that of the slab is 100 W/m.K, then the magnitude of temperature gradient $|dT/dy|$ within the slab at $y=0$ is _____ K/m (round off to the nearest integer).
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Correct answer: 10
Explanation
The air-side derivative is $dT/dy=-1000e^{-5y}$, giving magnitude 1000 K/m at the wall. Heat-flux continuity requires $k_{air}|T_{air}^{\prime}|=k_{slab}|T_{slab}^{\prime}|$.
Therefore slab gradient is 1×1000/100=**10 K/m**. Temperature gradients differ because conductivities differ.