A metal ball of diameter 60 mm is initially at 220°C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coefficient is 200 W/m2K. The specific heat, thermal conductivity and density of the metal ball are 400 J/kg. 400 W/mK and 9000 kg/m3, respectively. The ball temperature (in °C) after 90 seconds will be approximately
141
For the sphere, \(L_c=V/A=D/6=0.01\ \mathrm m\) and Bi = hLc/k = 0.005, so lumped cooling is valid. The time constant is \(\rho cL_c/h=180\ \mathrm s\). Thus \(T=20+200e^{-90/180}=141.3^\circ\mathrm C\approx141^\circ\mathrm C\).
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
