A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m2K. The thermophysical properties of steel are: density ρ = 7800 kg/m3, conductivity k = 40 W/mK and specific heat c = 600 J/kgK. The time required in seconds to cool the steel ball in the air from 1030°C to 430°C is
2144
For the sphere, Lc=V/A=d/6=0.01 m and Bi=hLc/k=0.005, validating the lumped model. Time is (ρcLc/h)ln[(1030−30)/(430−30)]=2340ln2.5=2144 s.
Important Questions from Transient Heat Transfer
Consider the following statements about the thermal diffusivity of a substance:
1. It is directly proportional to density.
2. It is inversely proportional to specific heat.
3. It is inversely proportional to thermal conductivity.
4. It is directly proportional to thermal conductivity.
Which of the given statements are INCORRECT?
Lumped heat transfer analysis of a solid object suddenly exposed to a fluid medium at a different temperature is valid when
- The dimensionless numbers used for analyzing the transient heat conduction problems in a plane wall, cylinder, and sphere is ________.
Choose the correct statement.
The curve for unsteady state heating and cooling of bodies with Bi < 0.1 is
A spherical thermocouple junction of diameter 0.706 mm is to be used for measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is \(400~\frac{W}{{{m^2} - K}}\). The thermo physical properties of thermocouple material are \(k = 20~\frac{W}{{m - K}},\ c = 400\frac{J}{{kg - K}},\ \rho = 8500~\frac{{kg}}{{{m^3}}}\). If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°, is
