## Heat Transfer - Jun 19

### Mechanical Engineering (Semester 5)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**Solve any FOUR**

**1.a.**A refrigerator stands in a room where the air temperature is 30 °C. The surface temperature on the outside of the refrigerator is 25 °C. The sides are 30 mm thick and have an equivalent thermal conductivity of 0.1 W/m K. The heat transfer coefficient on the outside is 10 W/m²K. Assuming one dimensional conduction through the sides, calculate the net heat flow per m² and the surface temperature on the inside.

**1.b.**Define and explain physical significance of Reynolds and Nusselt number.

**1.c.**Explain Fin efficiency and Fin effectiveness. Explain in brief factors affecting fin effectiveness.

**1.d.**Exhaust gases $\left(C_{p}=1.12 \mathrm{kJ} / \mathrm{kg}^{0} \mathrm{C}\right)$ flowing through a tubular heat exchanger at the rate of 1000 Kg/hr are cooled from 300 °C to 120 °C. The cooling is affected by water $\left(C_{p}=4.18 k J / K g^{0} C\right)$ that enters the system at 20 °C at the rate of 1200 Kg/hr. If the overall heat transfer coefficient is $140 \mathrm{W} / \mathrm{m}^{2} \mathrm{K}$,

**1.e.**Define intensity of radiation. What is solid angle? Explain.

**2.a.**Derive general equation of heat conduction in Cartesian coordinate system and reduce it to all three forms

**2.b.**Air at atmospheric pressure and 20 °C flows with 5 m/s velocity through main duct of an air conditioning system. The duct is rectangular in cross-section and measures 40 cm x 80 cm. Determine heat loss per meter length of duct corresponding to unit temperature difference. The relevant thermo-physical properties of air are

$v=15 \times 10^{-6} \mathrm{m}^{2} / \mathrm{s}$, $\alpha=7.7 \times 10^{-6} \mathrm{m}^{2} / \mathrm{hr}$, $\mathrm{k}=0.026 \mathrm{W} / \mathrm{m} / \mathrm{m} \mathrm{K}$

Use Dittus Boelter correlation : $\mathrm{Nu}=0.023 \mathrm{x}(\mathrm{Re})^{0.8} \mathrm{x}(\mathrm{Pr})^{0.4}$

**3.a.**Water flows at the rate of 65 kg/min through a double pipe counter flow heat exchanger. Water is heated from 50°C to 75°C by oil flowing through the tube. The specific heat of oil is 1.780 kJ/kg K. The oil enters at 115°C and leaves at 70°C. The overall heat transfer co-efficient is 340 W/m² K. Calculate the following

i. Heat exchanger area

ii. Rate of heat transfer

Use LMTD method

**3.b.**The following data pertains to the junction of a thermocouple wire used to measure the temperature of a gas stream :

$\rho=8500 \mathrm{Kg} / \mathrm{m}^{3}$ ; $C_{p}=325 \mathrm{J} / \mathrm{kg} \mathrm{K}$ ; $\mathrm{k}=40 \mathrm{W} / \mathrm{m} \mathrm{K}$ and the heat transfer coefficient between the junction and gas h = 215 W/m² K

If thermocouple junction can be approximated as 1 mm diameter sphere, determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference?

**3.c.**Define the following terms:

i. Absorptivity

ii. Reflectivity

iii. Transmissivity

iv. Emissivity

Explain Kirchoff's law.

**4.a.**A rod of 10 mm diameter and 70 mm length with thermal conductivity 15 W/m K protrudes from a surface at 180 °C. The rod is exposed to air at 30 °C with a convection coefficient of 25 W/m² K. How does the heat flow from this rod get affected if the same material volume is used for two fins of the same length? Assume short fin with end insulated.

**4.b.**In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?

**4.c.**Derive an expression for LMTD for parallel flow type heat exchanger.

**5.a.**Determine the radiant heat exchange in W/m² between two large parallel steel plates of emissivities 0.8 and 0.5 held at temperatures of 1000 K and 500 K respectively, if a thin copper plate of emissivity 0.1 is introduced as a radiation shield between the two plates

Take $\sigma=5.67 \times 10^{-8} \mathrm{W} / \mathrm{m}^{2} \mathrm{K}^{4}$

**5.b.**What do you mean by critical thickness of insulation? State its importance. Derive an expression for critical radius of insulation for sphere of thermal conductivity k and outside film coefficient h₀

**6.a.**Draw a neat boiling curve for water showing different regions of boiling. Explain each regime in brief.

**6.b.**Estimate the heat transfer from a 40W incandescent bulb at 125 °C to 25 °C in quiescent air. Approximate the bulb as a 50 mm diameter sphere. What percent of power is lost by free convection? The appropriate correlation for the convection coefficient is

$\mathrm{Nu}=0.60 \mathrm{x}(\mathrm{Gr} \mathrm{Pr})^{0.25}$

The thermo-physical properties of air at mean film temperature are : $v=20.55 \times 10^{-6} \mathrm{m}^{2} / \mathrm{s}$, $\mathrm{k}=0.03 \mathrm{W} / \mathrm{m} \mathrm{K}, \mathrm{Pr}=0.693$

**6.c.**A 250 x 250 mm ingot casting, 1.5 m high and at 1025 K temperature, is stripped from its mold. The casting is made to stand on end on the floor of a large foundry whose wall, floor and roof can be assumed to be at 300 K temperature. Make calculation for the rate of radiant heat interchange between the casting and the room. The casting material has an emissivity of 0.85.

Take Take $\sigma=5.67 \times 10^{-8} \mathrm{W} / \mathrm{m}^{2} \mathrm{K}^{4}$