**Department of Aeronautical Engineering**

**AE 2024: Heat Transfer - Question Bank**

__PART A - (2 marks____)__

- State and explain the Fourier's law of heat conduction.
- Define the efficiency and effectiveness of a fin.
- Distinguish the heat transfer by conduction and convection.
- What is the role of extended surfaces in heat transfer applications?
- What do you understand by Log Mean Area? State its significance.
- What is lumped heat analysis?
- Write about transient heat conduction.
- Write expression for variation of thermal conductivity with temperature.
- What is an error function?
- What is the difference between the free convection and forced convection?
- Define heat flux and thermal diffusivity.
- Distinguish between Grashoff number and Nussetl's number.
- What are the types of fins? Which one is more effective'?
- A thin plate 1 meter long and 1 meter wide is placed in an air stream moving with velocity of 0.25 m/s. Determine the type of flow over the plate.
- Distinguish between natural and forced convection.
- Give the physical significance of Nusselt number and Prandtl number.
- Define the Nusselt number and Prandtl number.
- Illustrate the hydrodynamic boundary layer thickness for the flow over the flat plate in the forced convection.
- “A turbulent flow over a solid surface facilitates more heat transfer when compared to a laminar flow.” Comment on the statement.
- Give at least two practical examples for free convective heat transfer.
- Explain Reynolds Analogy for laminar flow.
- Define intensity of radiation.
- Define radiation intensity and radiation shape factor.
- Define irradiation and radiosity.
- Define the terms absorptivity and transmittivity of radiation.
- State the reciprocity theorem of the radiation shape factors.
- Define radiation shape factor.
- Define black body in radiative heat transfer.
- What is Fouling factor'?
- Define effectiveness as a function of NTU of heat exchanger for counter flow type.
- Define overall heat transfer coefficient.
- Define "LMTD".
- Define the effectiveness of the heat exchanger.
- What is ablative heat transfer?
- Draw the temperature profile across a cooled rocket combustion chamber wall.
- Why does an aerospace vehicle flying at high supersonic Mach number experience aerodynamic heating in atmosphere?
- What is meant by recuperator?
- What is shape resistance .How it influences on over all heat transfer coefficient?
- How is ablation used for high speed cooling?
- Define Transpiration Cooling?

__PART B - (16marks)__- A steel pipe (K = 45.0 W/m.K) having a 0.05 m O.D is covered with a 0.042 m thick layer of magnesia (K = 0.07 W/m.K) which in turn covered with a 0.024 m layer of fiberglass insulation (K = 0.048 W/m.K). The pipe wall outside temperature is 370 K and the outside surface temperature of the fiberglass is 305 K. What is the interfacial temperature between the magnesia and fiberglass? Also calculate the steady state heat transfer.
- i) One end of a long rod, 35 mm in diameter, is inserted into a furnace with the other end projecting in the outside air. After the steady state is reached the temperature of the rod is measured at two points 180 mm apart and found to be 180° C and 145°C. The atmospheric air temperature is 25°C. If the heat transfer coefficient is 65 W/m
^{2}C, calculate the thermal conductivity of the rod. (Assume the end of the fin is insulated).^{0}

ii) Determine the time required for a 1.25 cm diameter Carbon Steel (K = 40.0 W/m

**K) sphere to cool from 500 °C to 100 °C if exposed to a cooling air flow at 25°C resulting in the convective coefficient 110 W/m**^{O}^{2}K.- i) Explain the following terms of the forced convection:

(a) Displacement thickness, b) Momentum thickness and c) Energy thickness.

ii) For heating water from 20°C to 60 °C an electrically heated tube resulting in a constant heat flux of 10 KW/m

^{2}is proposed. The mass flow rate is to be such that Re_{D}= 2000, and consequently the flow must remain laminar. The tube inside diameter is 25 mm. The flow is fully developed (Velocity profile). Determine the length of the tube required.- i) In a certain glass making process, a square plate of glass 1 m
^{2}area and 3 mm thick heated uniformly to 90°C is cooled by air at 20°C flowing over both sides parallel to the plate at 2 m/s. Calculate the heat transfer rate from the plate. Neglect the temperature gradient in the glass plate and consider only forced convection.

ii) Water is heated by a 15 cm by 15 cm vertical flat plate which is maintained at 52°C. Find the heat transfer rate by free convection when the water is at 20 DC.

- i) Assuming the sun to be a black body emitting radiation with maximum intensity at Î». = 0.49 Âµm, calculate the surface temperature of the sun and also heat flux at the surface of the sun.

ii) Derive an expression for the shape factor to the radiation heat exchange between two surfaces.

- i) Derive the expression for the heat exchange between two black surfaces by radiation.

ii) Consider the two large parallel plates one at 1000 K with the emissivity 0.8 and the other is at 300 K having an emissivity of 0.6. A radiation shield is place between them. The shield has emissivity as 0.1 on the side facing hot plate and 0.3 on the side facing the cold plate. Calculate the percentage reduction in radiation heat transfer as a result of radiation shield.

- i) Derive an expression for logarithmic mean temperature difference of the parallel flow heat exchanger.

ii) Hot oil is used to heat water, flowing at the rate of 0.1 kg/s, from 40 °C to 80 °C in a counter flow double-pipe beat exchanger. For an overall heat transfer coefficient of 300 W/m

^{2}**K find the heat transfer area, if the oil enters at 105°C and leaves at 70°C.**^{O}- i) Draw the temperature distribution curve of the fluids in the single pass parallel flow heat exchanger and single pass counter flow heat exchanger.

ii) The overall temperature rise of the cold fluid in a cross flow beat exchanger is 20°C and overall temperature drop of hot fluid is 30 °C. The effectiveness of heat exchanger is 0.6. The heat exchanger area is1 m

^{2}and overall heat transfer coefficient is 60 W/m^{2}^{0}C. Find out the rate of heat transfer. Assume both fluids are unmixed.- i) Describe the working principle of the Gas turbine combustion chamber.

ii) How are the rocket thrust chambers classified, and explain anyone of the thrust chamber?

- i) Explain how the high speed flow heat transfer differs from normal heat transfer.

ii) Write short notes on the aerodynamic heating.

- i) Explain the concept 'internal thermal resistance' in heat transfer.

ii) Determine the thermal conductivity of a test panel 0.15 m by 0.16 m and 0.0125 m thick, if during a two hour test 8.35 kJ of heat are conducted through the panel against temperature gradient of 35°C at 25°C between two faces.

iii) Differentiate between conductivity and conductance. What are their units?

- i) Carry out the dimensional analysis for the forced convection obtain the following relationship through a long tube and Nu = f(NRe, Pr).

ii) A 60 watt lamp is buried in soil (whose thermal conductivity is 0.0084 J/s cm

^{O}C) at 0°C and burned until steady state is reached. Find the temperature 30 cm away if the lamp produces 60 J/s.- i) A hollow cone of metal with thermal conductivity 0.15 J/cm
^{o}C and thickness 1 mm connects a pipe of 6 cm diameter with exterior metal sheath of an insulated vessel. The base of the cone is 20, cm in diameter and its length measured along the cone is 24 cm. If the pipe is at 200°C and the base of the cone at 0°C, calculate the rate of heat loss through the cone.

ii) How is cup mixing temperature defined for laminar flows in tubes? What is Gratez number?

- i) A flat plate heated to 80
^{0}c is cooled by an air stream at 20°C flowing at 10 m/s. Calculate the value of local heat transfer coefficient at X = 30 cm. Assume that the boundary layer on the plate is laminar.

ii) Bring out the essential differences between forced convection and free convection heat' transfer. Give four examples of forced convective heat transfer in engineering industry.

- i) A fluid flows through a 10 cm ID pipe. Assume that the velocity is uniform over the cross section of the pipe but the temperature varies linearly from 100°C at the pipe wall to 0°C at the centre line. Calculate the heat transfer co-efficient based on the mean fluid temperature if the heat flow rate from the pipe wall is 117600 w/m
^{2}K

(ii) Define the following with neat sketches: Thermal boundary layer thickness, skin friction coefficient and Stanton number.

16. i) Explain the salient features of ablative heat transfer with a neat sketch. Give at least one practical application of ablative heat transfer. (ii) What are the heat transfer problems faced by rocket thrust chambers? Sketch wall heat flux distribution of a rocket nozzle along the length.

17. i) a)Write short notes on cooling of gas turbine combustion chambers. b) Mention any two types of cooling methods with neat sketches.

(ii) How are the mechanical properties affected by high temperature for aerospace materials?' How does this aspect affect the design of aerospace vehicles? Give your answer citing one example.

18. i) Air at 25°C at the atmospheric pressure is flowing over a flat plate at 3 m/s. If the plate is 1 m wide and the wall temperature is 75°C, calculate (a) Hydrodynamic boundary layer thickness, (b) Local friction coefficient, (c) Thermal boundary layer thickness and (d) Local heat transfer co-efficient at 1 m from the leading edge of the plate. (ii) Show that the energy density in an isothermal enclosure will be twice that in front of a black surface from radiation emitted by that surface.

19. i) What is radiation pressure? Define monochromatic emissivity, total emissivity and normal total emissivity.

(ii) A vertical plate is heated from one side and maintained at 96 C. On the other side is air at atmospheric pressure and 20°C. Calculate the local heat transfer coefficient at a distance 20 em from the lower edge and the average value over the 20 cm length.

20. Explain boundary layer similarity parameters and obtain dimensionless forms of velocity and thermal boundary layer equations.

21. A round copper bus bar of 15 mm diameter is cooled by an air stream at 200 C moving across it at a velocity of 1 m/ s. If the surface temperature of the bus bar is not allowed to exceed 80° C. Calculate the heat transfer coefficient between the bus bar and the cooling air. Also eliminate the maximum admissible current intensity for the bus bar under these conditions. The resistivity of copper is 0.0175 ohm m

^{2}/m.23. i). Obtain an expression for temperature distribution in a hollow cylinder with internal heat generation.

ii). A thin hollow tube with 6 mm outer diameter and 4 mm inner diameter carries a current of 1000 A. Water at 30° C is circulated in side the tube for cooling the tube. Taking the heat transfer coefficient of the water side as 35000 W/m2 K and K for the tube material 18 W /m K. Estimate the surface temperature of the tube if its outer surface is insulated .The electrical resistivity of the material is 0.1lohmm m2 1m.

25. i). State any three laws of Black body radiation.

ii). Estimate the rate of solar radiation on a place normal to sun rays. Assume the sun to be a black body at a temperature of 5527

^{0}C .The diameter of the sun is 1.39 * 10^{6 }km and its distance from the earth is 1.5 * 10^{8}km.26. The surface of double walled spherical vessel used for storing liquid oxygen are covered with a layer of silver having an emissivity of 0.03.The temperature of the outer surface of the inner wall is -153 ° C and the temperature of the inner surface of the outer wall is 27°C. The spheres are 21 cm and 30 cm in diameter, with a spacing between them evacuated. Calculate the radiation heat transfer through the walls into the vessel and the rate of evaporation of liquid oxygen if its rate of vaporization in 220 KJ /Kg.

27. i) Obtain an expression for effectiveness in terms of NTU counter flow heat exchangers.

ii) Water heated to 80 ° C.f1ows through 2.54 cm I.D and 2.88 cm O.D Steel tube with K is 50 W/m.K. The tube is exposed to an environment which is known to provide an average convection coefficient of ho = 30800 W/m

^{2}K on the outside of the tube. The water velocity is 50 cm/s. Calculate the overall heat transfer coefficient based on the outer- area of the pipe.28. i. Derive an expression for LMTD for counter flow heat exchanger?

ii. Water heated to 80 ° C. flows through 2.54 cm I.D and 2.88 cm O.D Steel tube with K is 50 W/m.K. The tube is exposed to an environment which is known to provide an average convection coefficient of h

_{0}= 30800 w/ m2 K on the outside of the tube. The water velocity is 50 cm/s. Calculate the overall heat transfer coefficient based on the outer area of the pipe.29. (i) Derive the expression of heat loss from the composite spherical wall surrounded by air on both sides.

(ii) A copper slab (K = 372 w/m.

**C) in 3 mm thick. It is protected from corrosion by 2 mm thick layer of stainless steel (K = 17 w/m.**^{0}**C) on both sides. The temperatures of the two outer surface of steel are 400°C and 100°C. What is the temperature of the two interfaces?**^{0}30. (i) What is meant by thermal contact resistance? Upon what parameters does this resistance depend?

(ii) A wall 2 cm thick is to be constructed from material which has an average thermal conductivity of 1.3 W/m.K. The wall is to be insulated with material having an average thermal conductivity of 0.35 W/m.K, so that the heat loss per square meter will not exceed 1830 W. Assuming that the inner and outer surface temperatures of the insulated wall are 1300°C and 30°C, calculate the thickness of insulation required.

31. (i) Carry out the dimensional analysis for the forced convection obtain the following relationship through a long tube and Nu = f(NRe, Pr).

(ii) Water flows over a flat heater 0.06 m in length at 300°C under high pressure. The free stream velocity is 2 m/s and the heater is held at 315°C. What is the average heat transfer coefficient and average heat flux? Given: K = 0.520 W/m.

^{o}C , Kinematic viscosity = 0.124 * 10^{-6}m^{2}/s, Local Nusselt number,*Nux*= 0.332 (NRex)^{0.5}32. (i) What is the physical significance of Grashoff number? How is a modified Grashof number defined for a constant- heat flux condition on a vertical plate? (ii) A hot vertical plate is placed in a stagnant air inside a room. Draw the temperature and velocity profile in the thermal boundary layer generated due to heat transfer from the plate to the surrounding air.

33. Derive an expression for the heat transfer between two very large flat parallel plates.

34. (i) What is Kirchoff's law identity? When does it apply?

(ii) Two parallel plates 0.5 by 1.0 m are spaced 0.5 apart. One plate is measured at 1000

^{0}c and the other at 500^{0}c. The emissivities of the plates are 0.2 and 0.5, respectively. The plates are located in a very large room, the walls of which are maintained at 27°c. The plates exchange heat with each other and with the room, but only the plate surfaces racing each other are to be considered in the analysis. Find the net transfer to each plate and to the room.35. (i) Define overall heat transfer coefficient? Write down the expression of overall heat transfer coefficient by including all the resistance involved in case of heat transfer through the tubes of an exchanger.

(ii) Derive an expression for log mean temperature difference for a counter current flow double pipe heat exchanger.

36. (i) Define heat exchanger effectiveness. (ii) A shell and tube heat exchanger is to be constructed with 2.54 cm LD tube. The cold fluid is flowing through the tubes at the rate of 18,000 Kg/hr. the inlet temperature is 35°c while outlet temperature of cold water is 65°C. The hot water flows outside the tube at the rate of 12,800 kg/hr and entering at 100°C. The average velocity of the cold water through the tube is 0.3 m/s and overall heat transfer coefficient is 1600 w/m

^{2}DC. Specific heat for both the water is 4.18 KJ/Kg^{o}C. Determine the number of tubes and required length of the tubes for 1--1 shell and tube heat exchanger. Given: Density of water at 50°C = 988 kg /m^{3}, Surface area/unit length = 0.0798 m^{2}/m per tube, Cross sectional area = 0.0003098 m^{2}per tube.37. i) What is the main purpose of a gas turbine combustion chamber? Why the design of combustion chamber is rather difficult? ii) What are the main requirements of a gas turbine combustion chamber? Are these requirements mutually compatible? (iii) Enumerate the various methods of fuel injection in combustion chamber of a gas turbine and discuss their advantages and disadvantages.