Heat and Mass TransferUnit –I 1. Discuss about a. Modes of heat transfer b. Mechanism of heat transfer by conduction. 2. Explain about thermal conductivity of materials and its effect with temperature? 3. Derive the heat conduction in a thick wall with variable thermal conductivity. 4. A plane wall is 15cm thick of surface area 4.5m2.Thermal conductivity of the wall is 9.5w/mk. The inner and 0 0 outer surface temperatures of the wall are maintained at 150 c and 45 c respectively. Determine, i) Heat flow rate across the wall ii)Temperature gradient in the heat flow direction and iii) Temperature of surface at 5 cm and 10 cm away from the inner surface. [Ans: Q=29925W, dt/dx = -7000c/m , T(5cm) =150c , T(10cm)=800c] 5. A wire 2.0 mm in diameter and 18 cm long is submerged in water at atm. Pressure. An electric current is passed through the wire until the water boils at 1000c. In case the wire surface temperature is needed to be maintained at 1250c , determine the electric power supplied to the wire . Assume, convective heat transfer coefficient as 4000w/m2 k. [Ans:Q=113.1 w] 6. Air at 270c blows over a hot plate of 0.5 m x 1m surface which is maintained at 2270c. The film conductance is 25w/m2 k. There is a heat loss of 280 w by radiation from surface of the plate. The plate is 2cm thick. Calculate :i) Heat transfer rate ii)The temperature of the other side of the plate. Assume thermal conductivity of plate material as 43w/mk. [ Ans:Q =2780w, T=229.5860c ] 7.A horizontal plate (k=30 w/mk) 600mm x900mm x 30mm is maintained at 3000c. The air at 300c flows over the plate .If the convective co-efficient of air over the plate is 22 w/m2k and 250 w heat is lost from the plate by radiation , Calculate the bottom surface temperature of the plate. 0 [ Ans: T=306.403 c] 8.Consider a slab of 1 cm thickness with constant conductivity of 20w/mk. Uniform rate of internal heat generation is 8x107w/m3.One face of this slab is insulated and the other face dissipates heat 0 2 byconvection to a fluid at a temperature of 100 c with heat transfer coefficient of 4000w/m k .Calculate the temperature of both the surfaces. [ Ans: T(x=0) =5000c, T(x=1cm) =3000c] 9. Rate of heat generation in a plane wall of thickness 10 cm is 1.5 x105 w/m3. One side of the wall is insulated while the other is exposed to a fluid of temperature 1000c where heat transfer coefficient is 500 w/m2k. Thermal conductivity of wall is 15 w/mk. Determine: Derive the equation for critical radius of insulation in case of cylinders and Spheres. The top cover of the box is 1 cm thick and is made up of a material with k=0. A furnace wall lining is made up of material with k=2. A 8 mm thick metal plate. drop in temperature of each side of plate. parallel and in combination of both series and parallel. T=130 c ] 10. This cover is exposed to ambient air at 250c with h=10w/m2k.207 hrs] . [Ans: time=70. Assume the latent heat of ice =330 kJ/kg.6 w/mk) is exposed to vapour at 1000c on one side and cooling water at 300c on opposite side. 5 0 0 [Ans: Q= 1. The temperature of the inner and outer surface of this plane wall lining are 8100c and 3300c respectively. ii) In a compound cylinder 13.dt (coding water side)=51. having thermal conductivity (k=98. An ice box (20 cm x 20 cm x 10 cm height) is filled with 3 kg of ice at 00c.ii)Thickness =40 cm . 0 0 [ Ans: Tmax =180 c . Derive the equations for resistance in a heat transfer problem with an example in case of series.i) Temperature of the surface exposed to fluid assuming that entire generated heat is to dissipated to the fluid.76 c ] 16.5 w/mk.33 w/mk. Determine the rate of heat transfer.dt(Vapour side) =8. All vertical sides and bottom of the box are well insulated. 11. Derive the equations for total resistance offered during heat transfer by conduction and convection in the following cases: i) In a compound spheres. Derive the equations for heat transfer in the following cases when heat transfer is purely by conduction in radial direction.2034x 10 w.05m ] 15. The outer surface is exposed to ambient air at 300c with convective heat transfer coefficient=10 w/m2k. Calculate the time required to melt the ice in the box completely.iii) Thickness = 1. 14. Heat transfer coefficient between inner surface of cover and air inside the box is h=8 w/m2k. i) Through a long hallow cylinder ii) Through a hallow sphere 12. Calculate: i) The rate of heat flow per unit area ii) Thickness of lining in given situation iii) Thickness of lining if the heat flow rate is to be reduced by 50% [ Ans :i) Q=3000w/m2 .47 c . The heat transfer coefficients are hi=14200w/m2k on 2 vapour side and h0 =2325w/m k on the water side. Find: i) Total heat dissipated by rod ii) Temperature of rod at 4 cm from the wall.0 cm diameter and 10 cm long protrudes from the wall maintained at 3000 C. Derive One dimensional (Radial) Steady State Heat Conduction through Hollow Sphere without Heat Generation.T=177. (ii) x=0.8m has the surface temperature as 250 c and 100 c on its two sides. Q(Right side)=50833. The rod is exposed to surroundings at 150 C. A furnace wall of thickness 0. 0 [Ans: Q=22851.k=50 W/mK [Ans : (i)T=-500x2 +183. (ii) Position and magnitude of maximum temperature. The surface area is 2 m2. 4. Determine a) the finefficiency for long fin with insulated tip b) for rectangular fin of infinite length. (iii) Q(Left side)=-9166. 3. An aluminium rod 2.Tmax=201.6W. iv) Fin efficiency Assume that the rod end is insulated. A plane metal plate 12cm thick generates heat at the rate of 5 x 105 W/m3 when an electrical current is passed through it. The thermal conductivity of the wall is given as : 0 0 K=50(1+T/800)W/m C. 19. 20.9 C] 18.5 W] Unit – II 1. Define fin efficiency. State and derive the condition for an infinitely long fin. c ) Overall fin effectiveness. Derive an expression for heat transfer for an adequately long fin with insulated tip. (iii) Heat flow rate from each surface of the plate. find : (i) Temperature distribution across the plate section. . Derive One dimensional (Radial) Steady State Heat Conduction through Hollow Cylinder without Heat Generation and Logarithmic Mean Area.7 W.01833 m.0 0 17. What do you understand by short fins? Derive the temperature distribution and heat flow rate in short fin.where T is in C Determine the heat flow rate and the temperature at the centre of the wall.33x+200. 5. Heat transfer coefficient between rod surface and 2 environment is 20 w/m k . iii) Temperature at the end of rod. 2.680 C. Assume. If the surface temperatures on left and right side to be maintained at 2000 C and 1500 C respectively. Considering rods to be very long fins.Under steady state heat flow. 320 C for ‘B’ . The temperatures at the other ends are 26. h=15w/m k . [ Ans: k=350. Kc=238.83%] 0 6. If the midpoint temperature of the 0 other rod is measured to be 75 C . Derive the error in temperature measurement. One end of a rod is inserted inside the furnace while the other end projects into surrounding air at 0 30 C.B and C protrude from a furnace at 1000 C .70 C iv) Fin efficiency =93. What does it signify? 15.70w/mk.5mm] 11. i) Heat transfer rate before putting the fins. A Centrifugal pump which circulates hot liquid metal at 5000 C w is driven by a electricity motor.3% ] 12. Two rods of identical shape and size are both supported on a heat source at 100 C and are 0 surrounded by air at 25 C. Treat steel shaft as fin with insulated end.060 C iii) T=273. what length of shaft should be specified between motor and the pump? It may be presumed that the thermal conductivity of shaft material is 35 w/mk and convective film coefficient between steel shaft and air is 157 w/m2k. Prove that the fins are effective. A copper cylinder 10cm diameter. If the unit is exposed to ambient air at 200 C with convective heat transfer coefficient of 20w/m2k. Three 10mm diameter rods A. [ Ans: Q1= 21. Assuming. Find the time required by the 0 cylinder to attain the temperature of -110 C .5mm. The fins are 2 mm thick and 20 cm long. Find the thermal conductivity of the rod material. 3 =8800kg/m . [ Ans : L=389.49 w/mk. Assume insulated end condition for the fins. [Ans: i) Q =3600w ii)Q=5519.And state significance of Biot number and Fourier number. They protrude out in ambient air at 200 C. which is maintained at 2000 C. 10 rectangular fins of brass (k=120w/mk) are welded horizontally to a plane vertical surface of a tank.[Ans: I)Q =33. One end of copper rod 30cm long is firmly connected to a wall which is maintained at 200 0 C.What is its thermal conductivity? [ Ans: k = 339. 14. Temperature of air is 380 C.36 w/mk] 8. Air is blown across the rod so that h=17w/m2k . Define the response time of a thermocouple.k=360W/mk. KB =159. ii) Heat transfer rate after putting the fins. 1 m wide and 1 m high. The length of all of them = 25cm. [ Ans: t=34.74w.4w iii)%increase in heat transfer after putting the fins=151.5cm. 13.338 min] . One rod is known to have a thermal conductivity of 43w/mk and its 0 midpoint temperature of the other rod is measured to be 49 C . find. evaluate their thermal conductivities if heat transfer coefficient =23w/m2k [ Ans : KA=93.Diameter of rod =12. What is the net heat lost to air in watts? Conductivity of copper = 300w/mk. Derive the quenching of a billet by lumped heat capacity method.56 w/mk] 7. The temperature of motor is limited to a maximum value of 600 C with ambient air at 250 C. 20cm long is removed from liquid nitrogen at -1960 C and exposed to air at 250 C with convection coefficient of 20w/m2k .6W ii) T=283. Q2=3W ] 10.930 C for ‘C’.43 w/mk] 9.70 C for ‘A’ . and 36. The other end is firmly connected to a wall which is maintained 930 C.the motor is coupled to the pump impeller by a steel shaft 25mm in diameter.They are uniformly spaced on the vertical surface of tank. the steady state 0 0 temperatures at two points 12 cm apart on the rod were found to be 120 C and 90 C 2 respectively. Take thermo physical properties as: c=380 J/kgk. The diameter of the rod is 1. It is placed in boiling water pan for 220 sec. density =7800kg/m3 and k=50 w/mk.diameter of junction=3mm. heat of copper=0. The 2 following data are given for the problem: h=100w/m k .147 min] 18. Neglect radiation heat losses. Assuming plate to be long having thermal conductivity of 380w/mk. A 6cm thick copper plate at 240 c is kept on a water surface so that its lower face is in contact with 0 0 water at 30 c and upper face is exposed to surroundings at 30 c.Total time=2. the steel cylinder is taken out from this fluid and immediately immersed in another fluid at 500c with h=10w/m2 k.A thermocouple is used to measure the temperature of a fluid having the property of spherical junction as: C=400 J/kgk. Steel properties are: Cp =0. find the time required to cool the plate upto 1200 C.An egg with 35mm mean diameter is initially at 250c.70c .20c ii) T=85. at atmospheric pressure and found to be of consumers taste.46 Kj/jgk.Find: i) ii) The time constant of thermocouple If the thermocouple is taken out from hot fluid after 8sec and is kept in surrounding air at 300c having h=9w/m2k .After a period of 5 minutes.80C ] 20. Find the Biot number and verify if lumped heat capacity heat conduction analysis is applicable. density =1200kg/m and k=10 w/mk.Thermal conductivity of copper=385W/mk.4811hrs ] 19. The junction is initially kept at 300c and it is immersed in to the fluid temperature maintained at 3600c . A copper plate 2mm thick is heated up to 440 C and then quenched in water at 25 C. Specific 3.A solid cylinder of steel of 5 cm diameter and 20 cm length. Also find i) 0 The time constant and ii) The time required for the plate to reach the temperature of 40 C.Find the temperature attained by thermocouple junction after 16sec.0 0 16. convective heat transfer coefficient is 100 w/m k [ Ans: time t=256sec] .density =7800kg/m3 and k=35 w/mk. density =8600kg/m3 and c=400 J/kgk. [ Ans: i) T=91. The convective heat transfer coefficient is 40 w/m2k. Convective heat transfer coefficient on 2 2 water and air side are 90 W/m k and 10 W/m k respectively. Density of Cu=8800kg/m -4 [ Ans: Biot number =0. [ Ans: t=29. Calculate the temperature of the cylinder when it was taken out from the first fluid and the total time required for it to achieve the temperature of 100 [ Ans: Temp=353. initially at a uniform temperature of 5000c is suddenly placed in a fluid at 2000c with h=100 w/ m2 k .Plate dimension =25m x 25m. ii)t=113.3sec ] 0 17.2597x10 . For how long a similar egg be boiled for the same consumers taste when taken out from refrigerator at 30c? Assume an egg to be of spherical shape and its properties as follows 3 2 C=2000 J/kgk.4 kJ/kg-k. Air at 20 c flows over a plate 0. Use the correlation: NuD=0. forms the plate if the air flows parallel to 1.Discuss the concept of hydrodynamic boundary layer.5m/min=2. Also derive the dimensionless numbers.8 . pressure drop at 20m/min=52. Pr=0. Discuss the concept of thermal boundary layer in case of flow of fluid over the plates. 6.6m from the leading edge. Find the new pressure drop/m length in the pipe.The tube wall temperature is 3000c and temperature at the inlet to the pipe is 2000c. Discuss the velocity boundary layer development in circular pipes.696and k=0. 3.i) State Newton’s law of viscosity.Pr 0. Take : Local value of Nusselet’s number Nu=0.Assuming unit width of the plate. Pr=0.Air at 300 c and at atmospheric pressure flows over a plate at 3m/s. 4.Unit -III 1.Discuss about forced convection correlations for flow through circular pipe.] 9. Water at 250c is flowing through a pipe at 3.5m/min of diameter 3 cm.what is dimensional analysis and what is its practical utility.2 m/s. In case the velocity of water is 20 m/min.332Re1/2 .5m wide x 1m long at a velocity of 3.Pr0.06kg/m3. Hence define thickness of velocity boundary layer in case of flow of fluid over the plate.97x 10-6 m2/s.23 ReD 0.635 N/m2 ] 7.3m and x2=0.0m side. The temperature of the plate is maintained at 1200c. For water at 250c density=997. 0 10. 2.Compare the relative merits of water under pressure and liquid sodium as coolant.1w] 8. Kinematic viscosity =18.16x 10-6 m2/s. Pr=0.495x 10-6 m2/s. [Ans: Q2-Q1=90. Determine the pressure drop per m length.938and k=0. find the heat transfer from the portion at x1=0. Kinematic viscosity =. Hence define the dynamic and kinematic viscosities ii)Differentiatebetween laminar and turbulent flows.1kg/m3.33 . The plate is maintained at a constant temperature of 900c .0075and k=80w/mk [Ans: h(for water) =39468 w/m2k .75 cm ID with a velocity of 5m/s.C=1005 J/kgk. when flowing through a stainless steel tube of 0.3 w/m2k.334 Properties of air at 600c are density=1. h(for liquid sodium) =392213.3094 N/m2 .665w/mk Properties of liquid sodium:Kinematic viscosity =0. Hence. Find: i) Heat loss per min.8933x 10-6 m2/s [Ans: pressure drop at 3. 5. define entry length. . Properties of water:Kinematic viscosity =0. How does it differ from velocity boundary layer.0283w/mk. Pr0.Dynamic viscosity =7.C=4174 J/kgk. If the bulk mean temperature of air is 270c.67m. and k=0. estimate heat transfer rate from it.4 forlaminar flow Nu=4. Now. K=0. If the disc(open surface) is maintained at 1200c.364 for turbulent flow Nu=0.02x 10-6 m2/s. Properties of water:density=995kg/m3.89x 10-6 m2/s at T=300 k. from the plate if the air flows parallel to 0.076x 10-6 m2/s Use the following correlations : . Pr=0.332 Re1/2 . Kinematic viscosity =2.029kg/m3.5m side with all quantities remaining the same.707 Ans: i) Q=58.5w ii)Q=184.023 Re0.C=1009 J/kgk. Use correlation Nu=0. duct wall temperature is 100c higher than air temperature through out the length of the duct.Air flows with a velocity of 0.697. As a result. Find out the length of the duct required. Pr1/3 Take the properties of air at mean temperature Tm=700c as:density=1. Pr0.8 .36 [Ans: L=3.623w/mk Conductivity of duct material =35w/mk.ii)What shall be the heat loss per min.4 Take:density=1. The duct is heated by condensing the steam on its outer surface.C=1009 J/kgk.8w . For air at 700c . c)Disc is kept vertical. The duct is heated uniformly through out its length.65kg/min of water is heated from 30 c to 60 c by passing through the duct of 3 cmx 2 cm.Find the percentage change in rate of heat transfer between this case and the previous case: Correlations for laminar flow Nu =4. Calculate the rate of heat transfer between duct and air.42m] 12. Kinematic viscosity =15.023 Re0.65x 10-4 kg/ms.1W ] 0 0 11.03w/mk. Kinematic viscosity =20.1614kg/m3. A circular disc insulated from other side of diameter 25 cm is exposed to air at 200c .5m/s through a rectangular cross sectioned duct with dimensions 10cm x 5 cm and length =5. Pr=0.45 w ii)Q=492. when: a) Disc is kept horizontal with (open) hot surface facing towards.8 . Use correlation :for turbulent flow Nu=0. air velocity is made=2m/sec.696and k=0. The duct wall temperature is 200c higher than the air temperature throughout its length.02964w/mk [Ans: i) Q= 349. b)Disc is kept horizontal with (open) hot surface facing downwards. Percentage increase in Q=215.9%] 13. pr=0. The plate is 2m long and 1. t=0.59(Gr.Nu=.Pr)0.023(Re) Pr 0. t=0.3000kg of water per hour is heated from 300C to 700C by pumping it through a heated pipe.Thermal conductivity= 0.00743m. Compare the heat transfer coefficient using . Heat transfer from entire plate=8882w]. [Ans: L=3.0305 w/mk [Ans: a.Pr)0.8 You may use following correlation for turbulent flows thorough pipes. Diameter of tube is 25mm and its surface temperature is 1100c. Properties of 0 water at 85 c are : Pr=1.64.Thermal conductivity= 0. Nu=0. Nu=0.Pr)0.Air at 200c having average velocity of 4 m/sec is flowing along a heated plate at 1400c . Local skin friction coefficient at 40cm from leading edge.56KJ/s] 16.336w/m2k. d.C=4226 J/kgk At 1700c Dynamic viscosity =158x 10-6 kg/ms . c.Estimate the length of the tube and rate of heat transfer from tube water.14 (Gr.C=1009 J/kgk.25 for vertical surface.03m.0024. Also estimate the required length of the duct. Pr=0.k=0.168 w/m2k and average value of heat transfer coefficient=12.5 m wide.Local skin friction coefficient=0. Q( disc is vertical) =101. Heat transfer from entire plate. Dynamic viscosity =265x 10-6 kg/ms .09x 10-6 m2/s .Tate equation.00674m . e.27(Gr. e. Assume properties of air at mean temperature of 800c are: density=1kg/m3.b. [Ans: Q(disc facing up)=172.692. Determine: a. Thickness of thermal BL at 40cm from leading edge.5W ] 14. Nu=0. 15.9 w. The feed water flows at the rate of 3000kg/min .In a power plant feed water is flowing through a rectangular duct 8cm x 4 cm and the wall temperature 0 is maintained at 170 c throughout.25 for downward/bottom surface.i) Dittus – Boelter equation ii) Sieder.667w/mk. Dynamic viscosity =355x 10-6 kg/ms .33 . d. enters at a temperature of 200c and is heated to 1500c.C=4187 J/kgk 0. Local heat transfer coefficient =6. Thermo physical properties of water at 800c are: density=972kg/m3.58w . Thickness of hydro dynamic boundary layer at 40cm from leading edge.334 for upward/top surface. b. Q(disc is facing down)=65.683w/mk. Q=139. Local heat transfer coefficient and average value of heat transfer coefficient. Kinematic viscosity =21. c. Time required to cool up to 800C = 1067.2 sec. The plate has a mass of 20 kg and specific heat of 0.0393 W/mK. (a) Disc is kept horizontal with (open) hot surface facing upwards. find total heat loss rate by the cylinder and initial rate of cooling.58 W. Initial rate of cooling of plate = 8. initial rate of cooling the plate and time required in cooling of the plate from 1200C to 800C. Pr)0. K=0. Pr=0.59 Ra0. Pr)0.85 x 10 m /s Use the following correlations: Nu = 0.] . k-0. Time required to cool from 1200C to 800C = 556.25 if laminar Ra <105.Heat transfer rate when disc is facing down = 65. (c) Disc is kept vertical.9 W.14 (Gr. [Ans: h = 7.33 if turbulent Ra > 105.Pr) 0. Cp= 0.25 for lower horizontal surface Nu = 0. Use the following thermo physical properties of the air. If the emissivity of cylinder surface is 0.56 (Gr. Heat transfer rate when disc is kept vertical = 101.] 19. estimate heat transfer rate from it.8. For air at 700C.5 m at 1800C is kept in still air at 200C with 0. (b) Disc is kept horizontal with (open) hot surface facing downwards. v=2.688 Nu=0.54 (Ra) 0.14 Ra0.59 (Gr. determine heat transfer coefficient.746 kg/m .74 sec.03 W/mK. v=23.94 sec. Use the following correlation: Nu=0. Pr=0. v = 34.8160C/min.A hot plate 1 m x 0.697.] 18.13 x 10-6 m2 /s.0 17.5 m side vertical.25 for downward/bottom surface Nu=0. Pr)0.27 (Gr.25 for vertical surface. k=0.1280C/sec.A circular disc insulated from other side of diameter 25 cm is exposed to air at 20 C. If convection takes place from both the sides of the plate.25 for upper horizontal surface [Ans: Total heat flow by convection and Radiation = 0.42 kJ/kg) of 12 cm diameter and 30 cm length at 0 0 380 C is suspended vertically in a large room at temperature 20 C.334 for upward/top surface Nu=0.032 W/mK. [Ans: Heat transfer rate when disc is facing up = 172. Time required to cool up to 1200C = 511.5 W. Nu=0.076x10-6 .3474 W/m2 K. when. density = 0.4 kJ/kg K. If the disc (Open surface) is maintained at 1200C.25 for vertical surface Nu = 0.A solid cylinder of steel (density = 8000 Kg/m3 . Take properties of air at 2000C as follows: 3 -6 2 Cp= 1026 J/kg K.27 (Ra)0. 0 0 20. 2. 6. (i) Two parallel Infinite Plane Surfaces (ii) Radiation Heat Exchange between Two Concentric Infinitely Long Grey Cylinders . The mass of the plate is 40 kg.State and explain Lambert cosine law. Explain about heat exchange between Gray bodies.A thin hot plate 0. Assume thermo physical properties of air at mean temperature as : K = 0. v=23. (b) Time required to cool the plate from 1500C to 500C. 5.5 x 10-6 m2 /s. 7.Define following terms: (i) Reflectivity. [Ans: Initial rate of cooling = 0.5 m high and 2 m long is kept at 200 C having the surrounding air at 20 C.Define intensity of radiation. Find : (a) Initial rate of cooling of plate. The heat is convected naturally from both sides. C = 380 J/kg K.Discuss about the Thermal Radiation heat exchange concepts.State and Prove Planck’s law of radiation and Wien’s displacement law.IV 1.032 W/mK. 8.7 Specific heat of plate.Write a short note on thermal radiation and Discuss about theories of Radiation. Pr = 0. 4.236 min.] Unit . Time required to cool the plate from 1500C to 500C = 299.01470C/sec.State and explain Stefan Boltzmann’s law.State the value of Stefan Boltzmann’s constant. absorptivity and transmissivity (ii) Black body and Gray body (iii) Opaque body (iv) Emissive Power (v) Emissivity (vi) Monochromatic emissive power (vii) Monochromatic emissivity (viii) Radiosity 3.Derive an expression for radiant heat exchange between two Finite Black surfaces by Radiation. (ii) Total emissive power. (iii) Monochromatic emissive power at wavelength of 1 µm. 13. The radiation to the surface by the enclosure is 8000 W/m2.9W. Find the following : (i) wavelength at which emission is maximum and the magnitude of emissive power at this wave length. The absorption of 2 2 the surfaces A and B are 1000 W/m and 6800 W/m . find its emissive power. Two small surfaces A and B are place in an isothermal enclosure maintained at constant temperature considered as black body.62µm.1592 x 10-6 m and maximum emissive power = 2.12m3is 5270C.A black surface is maintained at 5000 K.3799 x 10 W (iv) Total emissive power = 4.9 kW/m2]. (ii) The temperature and heat flux to each surface. 9. Intensity of normal radiation = 7392.(iii) Radiation Heat Exchange between Two Concentric Spheres.Write short notes on Green house effect.5 kW/m2. Under the conditions of steady state find : (i) Absorptivity of each surface.7 µm. Wavelength of max monochromatic emissive power = 3.5µm to λ2 =0. (ii) Maximum valve of monochromatic emission power and the wave length at which it occurs. Find: (i) Heat flux due to thermal radiation.5137 x 1012 W. The area of furnace is 2 m2 .018 x 1013W/m2(iii) Fraction of radiations emitted between λ1= 0. 11. Effective temperature of a body having an area of 0. (iii) Fraction of radiations emitted between λ1= 0.What are radiation shields? Explain. . [Ans : (i) Maximum wavelength = 1.58594 x 10 W (iii) Monochromatic emissive power = 2.92. (ii) Maximum value of monochromatic emissive power and wave length = 4. why using radiation shields the heat transfer rates are reduced by analytical analysis.] 14.5 W/m sr. (iv) Consider the furnace as real body having emissivity as 0.(ii) 6 12 Total emissive power = 4.5µm to λ2 =0.] 12.7 µm = 7851. 10.The furnace of a boiler may be assumed as a black body having a temperature of 2500 K.0753 x 106W. [Ans: (i) qb= 35437. Calculate the following: a) Rate of radiation energy emission b) Intensity of normal radiation c) Wave length of maximum monochromatic emissive power 2 [Ans: Q=2786. 7. 6.9 K.16%. What will be the percentage reduction in the heat transfer rate due to insertion of radiation shield. And determine the overall heat transfer coefficient in shell and tube type heat exchangers. Derive the effectiveness of a counter flow heat exchanger.6. 2. [Ans: (i) Absorptivity of surface A = 0.2.A double-walled thermos flask may be assumed to be equivalent to two infinite parallel plates. [Ans: 134. [Ans: 6.Calculate shape factor between two opposite sides of hollow cube if shape factor between two adjacent sides of it is 0.125. 5.06 is inserted between them. Find the heat transfer rate by radiation through the flask if inside surface temperature is 90 0C and outside surface at 30 0C under steady state.r.43 W/m2.5m.] 19. The emissivities of wall are 0. (ii) T=612. [Ans: 0.(iii) Emissive power of each surface and their emissivity. Find the radius of outer sphere so that shape factor of outer sphere w. Derive the log mean temperature difference for counter flow heat exchanger. One of the faces of the oven forms the door.] 18. Draw the temperature distribution for Parallel flow and counter flow heat exchangers.Emissive power of each surface = 1000 W/m2 and 6800 W/m2. Space between them is evacuated. 3.A cubical oven has inside sides equal to 0.2334 kW.Define Heat Exchanger and give the three broad classes of heat exchangers along with application. If the five other inside faces are black and maintained at 6000C.] Unit –V 1.8 respectively is evacuated.2. 4.The space between the two infinite parallel plates having emissivities 0.4 and 0. Derive the log mean temperature difference for parallel flow heat exchanger.Derivethe effectiveness of a parallel flow heat exchanger. A polished Aluminium shield with emissivity of 0.] 15.3 and 0. the inner sphere is 0.A sphere of radius 5 cm is concentric with another sphere. Absorptivity of surface B = 0. [Ans: 92. . How the cross-flow and multipass heat exchangers are analyzed using LMTD method? Define correction factor and state its significance.7 respectively.t.45 cm]. 17. find the rate of heat loss if the oven door is kept open.85. [Ans: 8.85.] 20.(iii) Emissivity of each surface = 0. is as follows: (a) Convective heat transfer coefficients on inner tube: hi = 1000 W/m2 K. The condenser tube is having 3 cm O.Hot air at 660C is cooled upto 380C by means of cold air at 15.8kg/sec from 0 0 0 0 30 C to 80 C with hot oil entering at 120 C and leaving at 85 C.A counter flow shell and tube type heat exchanger is used to heat water at a rate of 0.Uo = 278.E. Th2 = 3000C 0 Inlet temperature of air.50C. U=80 W/m2 K.A parallel flow heat exchanger has its tubes of 5 cm internal and 6 cm external diameter.The outer tube concentric to inner tube has a diameter of 4 cm.1 kg/s as cooling medium. The data available regarding this H. ho = 1400 W/m2 K (b) Fouling factors on both sides of inner tube :Rfi = 0.0001 m2 K/W Calculate the following per metre length of tube: (i)Total thermal resistance.8.] 12. Take specific heat for water as 4180 j/kg0C. The air flows inside the tubes and receives heat from hot gases circulated in the annular space of the tube at the rate of 100 kW. Find the area of the heat exchanger for parallel flow configuration. Calculate the size of heat exchanger required . If the same exchanger is operated in counter flow mode. Given: Inlet temperature of hot gases.Specific heat of hot and cold air are 1. The thermal conductivity of inner tube material is 300 w/mk. Cp water =4180 J/kg k. Th1 = 5000C Outlet temperature of hot gases.25 kg/s and 1. (ii)Overall heat transfer coefficient based on inner and outer surface areas of the tube. Inside and outside heat transfer coefficients are 250 W/m2 K and 400 W/m2 K respectively. Mass flow rates of hot and cold air are 1.6 cm and outer diameter of 2 cm. Calculate the exit temperature of this water. [Ans: 28. 6 kg/s respectively.] 11.374 0C. Over all heat transfer coefficient is 125 2 w/m C .0005 m2 K/W and Rfo = 0.05724 k/W.(ii) Ui = 347.873 m2. and 22 m of length. Tc2 = 1400C Calculate : . Area required for counter flow for H. [Ans:Exit temperature of water = 57.06 W/m2K. 9. = 17.In a double pipe heat exchanger has its inner tube of internal diameter of 1.E. [Ans:Area needed for parallel flow for H. Steam condenses at 1000C on the outside of the tube. = 39.236 m2. Tc1 = 50 C Exit temperature of air. find the exit temperatures of both the fluids.05 kJ/kg K.53 W/m2K.] 10.4m2]. Overall heat transfer coefficient based on the tube outer surface are = 100 W/m2 K. If the cooling water enters the heat exchanger at 300C.A steam condenser uses water flowing at the rate of 0.D.E. [Ans: (i) Total thermal Resistance = 0. What are its types and state the difference between them.5 m wide is maintained at 400C and the saturated steam at 100 0C and at atmospheric pressure condenses over it. [Ans:m=0. N= 47.2 mm and 0.18 m3 at 300 K.668 W/m-K.ρ = 947 kg/m3.] .Define and explain condensation. Calculate the diffusivity of air in rubber. the various regimes of pool boiling. The tube dimensions are.5 m below the top end of plate and its maximum velocity at this section. (iii) Thickness of film at bottom end and its maximum velocity.088 m. Neglect the thermal resistance of the tube. The solubility of air in rubber is 0.Saturated steam at 850C condenses on the outer surface at 256 horizontal tubes arranged in 16 x 16 array.kf = 0. Calculate the following: (i)Heat transfer rate.A vertical plate 1 m long and 0.] 13.Uo 136. The volume of air in tyre is 0.664 W/m K.6265 m/s (iv) m = 177. (iii) ) Thickness of film at bottom end and its maximum velocity = 0. 16.000238 m & 0. Tube surface temperature = 750C.3 cm. (ii)Length of tube required to affect the heat transfer rates.3168 kg/s in horizontal tubes. (iv) Condensation rate in kg/hr. 15.] 19.m = 0. 14.. Take at mean temperature :ρ = 980 kg/m3.278 kg/s in vertical tubes. = 1.µ = 434 x 10-6 kg/ms.Write a short note on forced convection boiling.State and explain the Fick’s law of diffusion and compare it with Fourier’s law of heat conduction. (ii) Thickness of film at 0. L=138.] 18.08 m3 of air/m3 of rubber at 1 bar.432 kg/hr. hfg = 2309 x 103 J/kg. length = 1 m. [Ans: .(ii) Thickness of film and maximum velocity = 0.9 bar.443m/s. [Ans:the diffusivity of air in rubber = 2. O. Properties of condensate : K=0. Also calculate this rate if all these tubes (256 no. 20. hfg = 2257 kJ/kg [Ans:(i) Q = 111240W.Calculate the rate of condensation in kg/s in this case.D.4m2 and wall thickness of 20 mm. The tyre is filled with air 3 bar and after 15 days the pressure drops to 2.) are arranged vertically.Discuss in detail.5226 x 10-8 m2/s. (iii)If each tube is 3 m length. find the number of tubes required.Thetyre tube of a vehicle has a surface area of 2.(i)Overall heat transfer coefficient based on outer surface area.99 W/ m2 K.State the assumptions of Nusselt’s theory of filmwise condensation. 17.µ = 355 x 10-6 kg/m-s.