GTU Mechanical Engineering (Semester 5)
Heat Transfer
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


1(10) Define volumetric expansion coefficient.
1 M
1(11) Write Momentum equation and Energy equation for laminar boundary layer.
1 M
1(12) What is a black body? What are its properties?
1 M
1(13) What do you mean by spectral and total emissivity?
1 M
1(14) Define the effectiveness and NTU of heat exchanger.
1 M
1(2) What is physical significance of thermal diffusivity?
1 M
1(3) Define critical radius of insulation.
1 M
1(4) Explain the situation when the addition of fins to a surface is not useful.
1 M
1(5) Under what situations does the fin efficiency becomes 100%
1 M
1(6) How does transient heat conduction differ from steady state heat conduction
1 M
1(7) What is Fourier number? What is its physical significance?
1 M
1(8) Define critical Reynolds number in case of flow over flat plate. What is its numerical value?
1 M
1(9) Define thermal entry length for flow in circular tube.
1 M
1(a) How does that heat transfer differ from thermodynamics?
1 M

2(a) What is grey body approximation? Explain how the average emissivity of a grey surface can be determined?
3 M
2(b) What is Radiosity (J)? Show that the net radiant energy leaving the surface \[Q=\frac{A\varepsilon (E_b-J)}{1-\varepsilon }\]
4 M
Solve any one question.Q2(c) &Q2(d)
2(c) A spherical liquid oxygen bank 0.3 m in diameter is enclosed concentrically in a spherical container of 0.4 m diameter and the space in betwwen is evacuated. The bank surface is at -183°C and has an emissivity 0.2. The container surface is at 15°C and has an emissivity of 0.25. Determine the net radiant heat transfer rate and rate of evaporation of liquid oxygen it its latent heat is 220kJ/kg.
7 M
2(d) (a) Explain Wien's displacement law of radiation.
(b) Explain Kirchoff's law of radiation.
7 M

solve any one question Q.3(a,b,c) &Q4(a,b,c)
3(a) Differentiate mean flim temperature and bulk mean temperature.
3 M
3(b) Explain the physical significance of following numbers
a) Nusselt number
b) Grashof number
4 M
3(c) Air 27°C is flowing across a tube with a velocity of 25m/s. The tube could be either a square od 5 cm side or circular cylinder of 5 cm diameter. Compare the rate of heat transfer in each case if the tube surface is at 127°C. Use the correlation: Nu=CRen Pr C=0.027,
n=0.805 for cylinder
C=0.102,
n=0.675 for square tube Use following properties of air
ρ=0.955kg/m3,
kf=0.634 W/mk,
υ= 20.92×10-6 m2s,
Cp=1.009kJ/kgK,
Pr=0.7
7 M

4(a) What do you mean by hydrodynamically developed flow?
3 M
4(b) Explain Chilton Colburn analogy for turbulent flow inside a smooth tube.
4 M
4(c) Water at 20°C enters a 2 cm diameter tube with a velocity of 1.5m/s. The tube is maintained at 100°C. Find the tube length required to heat the water to a temperature of 60°C. Use following properties of water ρ=992.2kg/m3,
kf=0.634 W/mK,
υ = 0.659×10-6 m2s,
Cp= 4174 J/kgK, Pr = 4.31
7 M

solve any one question Q.5(a,b,c) &Q6(a,b,c)
5(a) A plane wall of thickness L is subjected to a heat flux q0 at its left surface, while its right surface dissipates heat by convection with a heat transfer coefficient h in to an ambient at T∞. Write the boundary conditions at the two surfaces of the wall.
3 M
5(b) Explain shortly
a) efficiency and effectiveness of fin
b) time constant and response of thermocouple
4 M
5(c) Write the governing differential equation for conduction heat transfer in spherical coordinate. Show that the resistance offered by it is given as
\[R_sph=\frac{r_2-r_1}{4\pi kr_1r_2}\]
7 M

6(a) What is lumped system analysis? What are the assumption made in the lumped system analysis and when it is applicable?
3 M
6(b) If the general solution for temperature distribution in fin is given by
T-T=C1e-mx+C2emx where C1 and C2 are constant, show that the temperature distribution in infinite long fin is \[\frac{T-T_\infty }{T_0-T\infty }=e^{-mx}\]
4 M
6(c) A steam pipe covered with two layered of insulation, first layer being 3 cm thick and second 5 cm. The pipe is made of steel (k=58W/mk) having ID 0f 160 mm and OD of 170 mm. The inside and outside flim coefficients are 30 and 5.8 W/m2K respectively. Calculate the heat loss per meter of pipe if the steam temperature is 300°C and air temperature 50°C. The thermal conductivity of two insulating materials are 0.17 and 0.093 W/mK respectively.
7 M

solve any one question Q.7(a,b,c) &Q8(a,b,c)
7(a) Explain multi pass that heat exchanger including correction factor. Where it is used.
3 M
7(b) Explain working of storage type heat exchanger and direct contact type heat exchanger with example.
4 M
7(c) prove that the effectiveness of parallel flow heat exchanger is given by
\[\varepsilon \frac{1-exp[-NTU(1+C)]}{1+C}\]
7 M

8(a) Discuss the conditions under which the drop wise condensation can take place. Why the rate of heat transfer in drop wise condensation is many time that of flim condensation.
3 M
8(b) a) What is critical heat flux? How it is useful to designers of heat exchangers?
b) Calculate the critical heat flux of mercury at 1 atm. Use the following properties of mercury hfg = 301kJ/kg,
ρv = 3.90 kg/m 3,
ρt = 12740kg/m3, σ = 417×10-3Nm Use modified Zuber-Kutateladze correlation \[q_{max}=0.149 {\rho_{v}}^{\frac{1}{2}} h_{fg}\left [ \sigma g\left ( \rho _t-\rho _v \right ) \right ]^\frac{1}{4}\] A vertical plate 0.4 m high and 0.41 m wide at 50°C is exposed to steam at 100°C. Calculate the following
a) Film thickness at bottom of the plate
b) Maximum velocity at the bottom of the plate
c) Total heat transfer rate and heat flux Assume at mean temperature of 75°C
ρ=976 kg/m3, kf = 0.668 W/mK,
μ = 405×10-6 kg/ms
hfg = 2258kJ/kg
7 M



More question papers from Heat Transfer
SPONSORED ADVERTISEMENTS