Lumped Heat Analysis

Q. An average human body is modeled as a 30 cm diameter, 170 cm long cylinder having $72\%$ water by mass taking thermal conductivity of body as $7\text{W/mK}$. A person was found dead today at 6 am in a room temperature of which was maintained at $20{}^{\circ }C$. The temperature of the body is measured to be $26{}^{\circ }C$. Assuming human body properties as that of water, and convective heat transfer coefficient as $8{\text{W/m}}^2\text{K}$ at what time man died ? (Take body temperature of living man as $37{}^{\circ }C$)

1. 7 : 35 pm yesterday
2. 8 : 00 pm yesterday
3. 10 : 24 pm yesterday
4. 10 : 40 pm yesterday

Q. A 2 cm thick steel slab heated to ${525}^{\circ }C$ is held in air stream having a mean temperature of ${25}^{\circ }C.$ Determine the time interval when the slab temperature would not depart from the mean value of ${25}^{\circ }C$ by more than ${0.5}^{\circ }C$ at any point in the slab when Boit Number$=Bi=0.0078,$ Fourier number $=F_0=\mathrm{0.127.}\tau$

1. 9573 sec
2. 6907 sec
3. 885 sec
4. 6973 sec

Q. A steel casting cools to 90% of the original temperature difference in 30 min in still air. The same casting is cooled to 90% of the original temperature difference in a moving air stream. The convective heat transfer coefficient in moving air is 5 times that of still air. The time (in minutes) to cool the casting in moving air is__________.

1. 10 min
2. 16 min
3. 6 min
4. 5 min

Q. A metallic ball $(\rho =2700kg/m^{3}and{C}_p=0.9kJ/kg.K)$ of diameter 7.5cm is allowed to cool in air at 25°C. When the temperature of the ball is 125°C, it is found to cool at the rate of 4°C per minute. If thermal gradients inside the ball are neglected, the heat transfer coefficient ($inW/m^2.K)$ is

1. 20.34
2. 81.36
3. 2.034
4. 203.4

Q. Large brass plate of 40 mm thickness having temperature of ${20}^{\circ }C,\rho =8530kg/m^3,Cp=380K/kgK$ and $K=110W/mK$ are heated in a furnace, maintained at ${500}^{\circ }C.$ Taking the combined convection and radiation coefficient as $120W/m^{2}K,$ the surface temperature of plate after 7 min with a Fourier number of 35.6 is

1. ${280}^{\circ }C$
2. ${500}^{\circ }C$
3. ${420}^{\circ }C$
4. ${210}^{\circ }C$

Q. The total heat transfer from a spherical copper ball of diameter 15 cm initially at 220 °C, and its environment at a constant temperature of 25°C and convection coefficient h = 100 W/$m^2$K, during the first 20 min of cooling is calculated to be 2400 kJ. Assuming the properties of the copper to be k = 400 W/mK, $\rho$ = 8933 kg/$m^3$ and $c_p$ = 385 J/kgK. This result is

Q. When Biot number tends to zero in the unsteady heat conduction, which one of the following is correct?

1. Convection resistance is very small compared to conduction resistance in this problem.
2. Internal temperature of solid will not be uniform in this problem.
3. Lumped capacity analysis can be used
4. Heisler chart is required for analysis of such problem.

Q. In transient heat conduction, if Biot number $\left(Bi\right)<<<0.1,$ then what will be the temperature profile for a solid being cooled?

1. 
2. 
3. 
4. 

Q. Lumped heat capacity in a solid body is used when,

1. when internal resistance is more than 10% of surface resistance
2. when internal resistance is 63.2% of surface
3. when external resistance is equal to 10% of surface resistance
4. when internal resistance is less than 10% of surface resistance

Q. In non periodic transient heat conduction problem, the lumped heat parameters analysis is used when

1. Temp gradients within the body are negligible
2. Boit number is less than 0.1
3. Fourier number is less than 0.1
4. Boit number is greater than 0.1

1. 2 & 3
2. 1 & 2
3. 1, 2, & 3
4. 3 & 4

Q.

An ideal refrigerator has a freezer at a temperature of $-13°\mathrm{C}$, The coefficient of performance of the engine is $5$. The temperature of the air to which heat is rejected will be

1. $325°\mathrm{C}$

2. $39°\mathrm{C}$

3. $325\mathrm{K}$

4. $320°\mathrm{C}$

Q. A small body (Biot number < 0.1) has temperature variation as $T=A+B{e}^{C\tau },\tau =$ time in seconds
Where A, B, and C are constants.
If that small body is used as thermocouple its time constant is given by

1. -1/C
2. 1/C
3. -C
4. C

Q. Which of the following electrical circuit can represent the lumped heat capacity method, Where

1. 
2. 
3. 
4.