Assignment No. - 01

Title: Basic Heat Transfer

 

 

Date of submission:

 

Cross those boxes corresponding to questions that you have not  attempted

 

1.     A woman informs her husband that “hot water will freeze faster than cold water”. He calls this statement nonsense. She answers by saying that she has actually timed the freezing process for ice trays in the home refrigerator and found that hot water does indeed freeze faster. As a friend, you are asked to settle the argument. Is there any logical explanation for the woman’s observation ?

 

2.     A service engineer got a call from a woman ,who says that she frequently feels cooler in the summer when standing in front of an open refrigerator. The engineer tells her that she is only “imagining things” because there is no fan in the refrigerator to blow the cool air over her. A lively argument ensues. Whose side of the argument do you take? Why ?

 

3.     Define thermal conductivity and state the reason why it is important in designing thermal equipments ? Explain why the conductivity of metal decreases and conductivity of insulating materials increases with increase in temperature

 

4.     Describe the mechanism of conduction, convection and radiation ?

 

5.     A square silicon chip (k=150 W/m K) is of width w =5 mm on a side and of thickness t=1 mm. the chip is mounted in a substrate such that its side and back surfaces are insulated, while the front surface is exposed to a coolant. If 4 W are being dissipated in circuits mounted to the back surface of the chip, what is the steady- state temperature difference between back and front surfaces ?

 

6.     Sketch the steady state one dimensional temperature variation in the cone with constant properties having no heat generation noting t1 > t2, t1 and t2 being surface temperatures.

 

7.     Sketch the steady state one dimensional temperature distribution in the square slab with uniform heat generation when the two surfaces are at the same temperature Ts.

 

8.     Sketch the steady state one dimensional temperature variation in the cylinder made of iron, copper and silver. There is no heat source and properties are constant. The end of iron cylinder is at T1 and that of silver at T2 where T1> T2.

 

9.     A current of 200 A is passed through a stainless steel wire ( k =19 W/m °C ) 3 mm in diameter. The resistively of the steel may be taken as 70 μ ohm.cm, and the length of the wire is 1 m. The wire is submerged in a liquid at 110 °C and experiences heat transfer coefficient of 4 kW/m². °C .Calculate the center temperature of the wire in degree Celsius, Kelvin and Fahrenheit.

 

10. Prove that the heat flow through a hollow cylinder is given by

Q=2*Pi*L*(T1 – T2)*k / ln(R2/R1)

 

11. A composite wall is made up of an external thickness of brick work 110 mm thick and inside layer of fibre-glass of 75 mm thick. The fibre glass is faced internally by an insulating board 25 mm thick. The coefficient of thermal conductivity for the three materials are as follows:

Brick work=1.15 W/ m-K

Fibre-glass=0.04 W/m-K

Insulating board=0.06 W/m-K

The surface heat transfer coefficient of the inside wall is 25 W/m²-K while that of the outer wall is 3.1 W/m²-K. Determine the overall heat transfer coefficient for the wall and using the same determining the heat lost per hour through such a wall of 4m high and 10 m long. Take the inside wall temperature as 27°C and external ambient temperature as 10°C.

 

12. Define thermal diffusivity, Fourier conduction equation and logmean area.

 

13. A  wall thickness L is made of materials whose thermal conductivity varies with the temperature as follows:

k=k₀T²

Find the expression for the steady state heat conduction through a wall per unit area if two surfaces are maintained at temperatures T1 and T2. If one want to write q as the product of temperature difference and mean thermal conductivity divided by L, at what temperature must this conductivity be calculated so that such equation gives the right result ?

 

14. Find the expression for temperature distribution and heat flow for homogenous sphere for steady state conduction when

k= k₀ (1+T)  is given.

 

15. A  reinforced concrete smoke stack with an inner diameter 80 cm and outer diameter 130 cm must be lined with refractory on the inside. Determine the thickness of the refractory lining and the temperature of the outer surface of the smoke stack under the conditions that the heat loss must not exceed 2000 W per metre height. The temperature of the inner surface of the refractory lining is 425°C and the temperature of the inner surface of the reinforced concrete should not exceed 200°C.

k₁(lining material)=0.5 W/m °C.

k₂(concrete)=1.1 W/m °C.

If the lining is made of fire clay, find the thickness required considering all conditions same except

k₁(fire clay)=0.84 (1+0.00075 T )W/m °C.

 

16. The temperature distribution at an instant in a slab with no source and with constant properties is shown in the given below figure. Determine whether the slab is being heated or cooled. Justify your answer.

 

 

 

 

 

 

 

 

 

 

 

17. Compute the heat flux through the furnace wall, 30 cm thick, if the inside and outside surfaces are at 320°C and 38°C and the thermal conductivity is k=0.003 T - 10^-6 T² W/m-K, where T is in °C

 

18. Describe non-Fourier model of heat conduction ?

 

19. Explain the physical mechanism of thermal contact resistance ?

 

20. Derive a relation for the critical radius of insulation for a sphere ?