Critical Thickness of Insulation for Cylinder

Q. An absetos insulation having thermal conductivity $0.172W/mK$ surrounding a pipe of 60 mm idameter and exposed to room air at $300K$ with h.t.c fo $2.8W/m^{2}K.$ Calculate the heat loss from the pipe per unit length of pipe if the surface temperature of the pipe is $475K$ when covered with critical radius of insulation

1. 92.46 W/m
2. 50.43 W/m
3. 65.43 W/m
4. 110.16 W/m

Q.

The amount of heat produced in a wire depends on:

1. Material

2. Length

3. Thickness

4. All of These

Q. In order to reduce heat loss, a steam line with a tube diameter of 1.0 cm is insulated with a material having thermal conductivity of 0.108 W/mK. Heat is dissipated from the outer surface of the insulating material by natural convection with a heat transfer coefficient of 12 $W/m^{2}K$ into the ambient at a constant temperature. The heat loss becomes maximum when the critical diameter is

1. 18 mm
2. 4 mm
3. 2 mm
4. 9 mm

Q. Inner and outer radius of the hollow cylinder and hollow sphere are r, 3r, 2r and 3r respectively. Insulation is applied on both hollow cyinder and hollow sphere. Both are made up of same material and have same environmental conditions. Find the difference in the critical thicknesses of insulation. (Notations have their usual meanings).

1. $\frac{2k}{h_0}$
2. $\frac{k}{h_0}-r$
3. $\frac{2k}{h_0}-r$
4. $\frac{k}{h_0}$

Q. On an electrical wire of 1 mm diameter and 1 mm thick plastic sheeting is provided to increase current carrying capacity. The thermal conductivity of plastic is $0.1W/mK$ and heat transfer coefficient of surrounding air is $25W/m^{2}K.$ On further addition of insulation material, the current carrying capacity will

1. Increases
2. Increases and then decreases
3. Decreases
4. Decreases and then increases

Q. An electric cable of aluminium conductor $[K=240W/mK]$ is to be insulated with rubber $[K=0.15W/mK]$. If cable is to be located in air $[h=6W/m^{2}K]$, the critical radius of insulation will be

1. $25mm$
2. $40mm$
3. $80mm$
4. $160mm$

Q. It is planned to insulated the shell of a heat exchanger. The outside diameter of the shell is $30cm,$ its outer surface temperature is at ${280}^{\circ }C$ and it may be assumed to be remains constant even after applying insulation on the shell.

If the air temperature of the outer surface of insulation is must not exceed 30 and the loss of heat form heat exchanger is 200 W/m. What is the thickness of insulation provided

1. 1.43 m
2. 0.71 m
3. 0.55 m
4. 1.25 m

Q. It is planned to insulated the shell of a heat exchanger. The outside diameter of the shell is $30cm,$ its outer surface temperature is at ${280}^{\circ }C$ and it may be assumed to be remains constant even after applying insulation on the shell.

If the outside surface heat transfer coefficient is 2, what is the maximum thermal conductivity of insulating material for effectively reducing heat transfer from shell

1. 0.3
2. 0.24
3. 1.2
4. 2.4