Unsteady State Conduction Questions and Answers

Answer: C

The Biot number is 0.06.

The Biot number compares conduction resistance inside a solid with convection resistance at its surface: \(Bi = hL/k\), where k is the conductivity of the solid. Here the solid is a glass pane, 3 mm thick, with the air film coefficient on its surface:

\[ \begin{aligned} Bi &= \frac{hL}{k_{glass}} \\ &= \frac{10 \times 0.003}{0.5} = 0.06 \end{aligned} \]

Using the conductivity of air in place of glass gives 1.50 with the 3 mm pane, or 1.00 with the 2 mm air layer. Using the 2 mm air gap with the glass conductivity gives 0.04. None of these is a Biot number for the pane.

Answer: B

A transient condition is conduction when temperature at a point varies with time.

In transient (unsteady) conduction the temperature at a point changes with time, \(\partial T/\partial t \neq 0\), as when a hot casting cools or a cold slab is heated. In steady conduction the temperature at every point stays fixed.

The other options describe amounts or durations, not the time-dependence that defines the term. A short period of heat transfer can be steady, and a small heat flow or a small temperature difference can be either steady or transient.

Answer: B

The most unsteady heat flow occurs during annealing of castings.

In annealing, a casting is heated to a set temperature, held there, and then cooled slowly in the furnace. Its temperature changes with time throughout, so the heat flow in it is transient (unsteady).

Heat flow through a refrigerator wall, through the walls of a furnace in continuous operation, or through insulated pipes carrying steam settles to a steady state, with temperatures at each point that do not change with time.

Answer: C

Fourier number is the ratio of heat conduction rate to the rate of thermal energy storage in the solid.

The Fourier number, \(Fo = \frac{\alpha t}{L^{2}}\), appears in transient conduction. It compares how fast heat is conducted through a body with how fast the body stores it, and works as a dimensionless time: a large Fourier number means the heat has had time to penetrate deep into the solid.

The ratio of internal conduction resistance to surface resistance is the Biot number. Buoyancy over viscous force is the Grashof number, and gravitational over surface tension forces is the Bond number. All three appear as options to mislead.