Discussion
Match List - I and List - II :
| List - I | List - II |
|---|---|
| (a) Free convection | (i) \(\frac{hD}{K}\) |
| (b) Nusselt number | (ii) \(\frac{K}{h_{0}}\) |
| (c) Thermal diffusivity | (iii) \(\frac{K}{\rho Cp}\) |
| (d) Critical radius of insulation in case of cylinder | (iv) Grashof number |
Choose the most appropriate answer from the options given below :
Answer: C
The correct matching is (a)-(iv), (b)-(i), (c)-(iii), (d)-(ii).
- Free (natural) convection is characterised by the Grashof number (a-iv).
- Nusselt number is \(\frac{hD}{K}\), convective over conductive heat transfer (b-i).
- Thermal diffusivity is \(\alpha = \frac{K}{\rho C_{p}}\) (c-iii).
- The critical radius of insulation for a cylinder is \(r_{c} = \frac{K}{h_{0}}\), with K the conductivity of the insulation and \(h_{0}\) the outside film coefficient (d-ii).
Option A gives Nusselt and the critical radius each other's expressions; option B pairs free convection with the Nusselt formula. For a sphere the critical radius would be \(2K/h_{0}\), but the question specifies a cylinder.
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