Heat Transfer Questions and Answers

Answer: C

In solids, conduction may be attributed to atomic activity in the form of lattice vibrations, along with the movement of free electrons in metals. This is the statement the key accepts. Conduction is a microscopic mechanism and not a macroscopic form, in fluids it occurs from collisions and diffusion of molecules in their random motion, and the basic equation of conduction is Fourier's law, not Maxwell's law. The second option is also a textbook statement but the key names the third.

Answer: B

The film coefficient is about 16.67 W m^-2 K^-1.

In a thin gap the trapped air hardly moves, so heat crosses it by conduction, and the equivalent film coefficient is the conductivity divided by the gap width:

\[ h = \frac{k}{\delta} = \frac{0.025}{0.0015} = 16.67 \]

3.75, 37.52 and 60.21 do not follow from \(k\) and the 1.5 mm gap; a common slip is to leave the gap in millimetres, which gives 0.0167.

Answer: B

Air has the least thermal conductivity.

Gases conduct heat far less well than liquids or solids because their molecules are widely spaced. Still air has a conductivity of about 0.026 W/m K, which is why trapped air is the working ingredient of most insulators.

Rubber and plastics are around 0.1 to 0.2 W/m K, and water about 0.6 W/m K, all several times higher than air. That is why foamed plastics and wool insulate better than the solid material: they trap air.

Answer: C

The analogue of conductivity is the viscosity of the fluid.

Fourier's law of conduction, \(q = -k\,dT/dy\), and Newton's law of viscosity, \(\tau = \mu\,du/dy\), have the same form. Thermal conductivity relates the flux of heat to a temperature gradient, just as viscosity relates the flux of momentum (shear stress) to a velocity gradient.

Velocity is the quantity whose gradient drives the momentum flux, so it corresponds to temperature, not to conductivity. Density and dielectric constant have no role in this analogy.

Answer: C

The correct matching is (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii).

• Stanton number, \(St = Nu/(Re\,Pr)\), is used in forced convection (a-iii).
• Grashof number, buoyancy over viscous force, governs natural convection (b-i).
• Peclet number, \(Pe = Re\,Pr\), is used in forced convection where Pr is small, as in liquid metals (c-iv).
• Schmidt number, momentum diffusivity over mass diffusivity, belongs to mass transfer (d-ii).

Two pairs are enough: Grashof with natural convection and Schmidt with mass transfer appear together only in this option. The options starting (a)-(ii) give Stanton to mass transfer, which is wrong.

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.