Total No. of Questions : 12] [Total No. of Pages : 4 P876 [2863]-408 T.E. (Mechanical) Heat Transfer (2003 Course) Time : 3 Hours] k [Max. Marks :100 Instructions to the candidates : 1) Answer any one question from each unit 2) Answers to the two sections should be written in separate answer books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. QI) a) Explain in brief the analogy between the heat flow and electricity with its significance. [6] b) A composite insulating wall consists of three layers. These are held together by 2 cm, diameter aluminium rivet per 0.1m? of surface. The layers consists of 10cm thick brick with hot surface at 190°C, lem thick y wood with cold surface at 20°C. These two layers are interposed by a third layer of insulating material 25 cm thick. Assuming one dimensional heat flow, calculate the percentage increase in heat transfer rate due to rivets. The conductivity of the materials are, - Kye = 1 WANK, K,..iisgo) = 0-2 W/mK, K,, = 220 W/mK, K voy = 0.2 WimK. [10] OR Q2) a) Define thermal diffusivity and explain its significance. {4 b) Derive the equation for total heat transfer rate through a hollow cylinder having inner and outer radii r, and r, respectively. It’s inner and outer surface temperatures are T, and T, respectively. There is no heat generation and its conductivity is constant. (91 ©) Explain the concept of log mean area. 13] PTO.3) a) b) 3) Q4) a) b) 05) a) b) Q6) a) [2863}-408 UNIT- I What do you mean by critical radius of insulation? Why it’s concept is not used in case of plane walls? (41 Write a short note on “Thermal conductivity of gases’ (4) A chemical reaction takes place in a packed bed between two co-axial cylinders with radii 1cm and 3cm. The inner surface is at 500°C and it is insulated. Assuming the reaction rate of 6 x 10° Wim’, in the reactor volume, find the temperature at the outer surface of the reactor. Take conductivity for packed material as 0.5 W/mK. Derive the equation you used. , [10] OR Find steady flow heat flux through a composite slab made of two materials ‘A & B. Thermal conductivity of two materials vary linearly with temperature as, K, = 0.4(1+0.008T) and K, =0.5(1+0.001T), where T is the temperature in °C. The inner side temperature of slab A is 500°C and outside temperature of slab B is 40°C. Take L, = 12cm and L,, = 6em. 19] A hot gas at 330°C with convection coefficient of 222 W/mK is flowing through a steel tube of outside diameter Sem and thickness 1.3cm. It is, covered with an insulating material of thickness 2em, having conductivity of 0.2 WimK. The outer surface of the insulation is exposed to ambient air at 25°C, with convection coefficient of 55 W/mK. Calculate : i) Heat loss to air from Sm long tube. ii) The temperature drop due to thermal resistances of the hot gases, steel tube, the insulation layer and the outside air. Take conductivity of steel = 50 W/mK. 9 UNIT - 1 Derive an expression for a temperature distribution and a rate of heat flow from a pin fin with negligible heat loss from its tip with usual notations. (10) Explain the significance of dimensionless parameters used in transient heat conduction, [6] OR Differentiate between efficiency and effectiveness of the fin. [3] 2b) Q7) a) b) - 8) a) b) Q9) a) b) [2863)-408 A batch reactor provided with submerged steam coil, 1000 kg mass of reactants is there in reactor having specific heat of 3.8 kJ/kgK. Coil area is Im? and steam is fed at 120°C. Assuming no heat loss to the surroundings, calculate the time taken to heat the material from 20°C to 90°C. The overall heat transfer coefficient is 600 W/mK. If the external area of the vessel, is 10m? and outside heat transfer coefficient is 9 W/mK, what will be the time taken to heat the reactants over the same temperature range. [13] SECTION - IT UNIT - IV Explain the physical significance of the following. i) Nusselt Number. ii) Prandtl Number. iii) Grashoff Number. iv) Reynolds Number. [12] Write short note on thermal and velocity boundary layer. 6] OR In which type of convection, the heat transfer coefficient will be more and why? Explain in brief. [6] Acubical furnace of Im side is installed on the conerete floor. The outside temperature of furnace walls is 75°C and the surrounding air temperature is 25°C. Neglecting convective heat loss from base of the furnace, calculate rate of heat loss from the furnace. ‘The properties of air film at temperature of 50°C are, v= 18 x 10°m%sec, K= 0,029 W/mK, Pr = 0.68, Cp = 1.005 ki/kgK. Use following co-relations. Nu = 0.59 (Gr Pr)" for vertical surface, =0.15 (Gr Pr)" for upper surface. (12) UNI Explain the radiation from real surfaces. [8] Calculate the rate of heat loss from a thermoflask if the polished silvered surfaces have emissivities of 0.05. The liquid in the flask is at 100°C and the casing is at 20°C. Calculate the loss if both surfaces are black. {8]OR Q10)a) Write short notes on the following. i) Green house effect. ii) Radiation shields. v7 b) The space between the two infinite parallel plates having emissivities 0.4 and 0.8 respectively is’evacuated. A polished Aluminium shield with emissivity of 0.06 is inserted between them. What will be the percentage reduction in the heat transfer rate due to insertion of radiation shield [9] UNIT - VI Ql1)a) — Whatis fouling and fouling factor? What are the factors causing fouling? What is its effect on performance of heat exchanger? [6] b) The steam is condensed at atmospheric pressure in a shell and tube type of heat exchanger using water as a coolant. During condensation water is heated from 28°C to 48°C. Water flows through the tubes and the steam condenses on the outside. Size of the tubes is as follows - LD. = 2.6 cm, O.D. = 3 cm, Length = 2.5 m. Flowrate of water is 30,000 kg/hr. Coefficient of heat transfer on steam , and water side are 8000 and 3000 Wim?K respectively. Neglecting all other resistances, calculate the number of tubes required. [10] OR Q12)a) Compare filmwise and dropwise condensation. (4) b) What is burnout point? Explain its significance. (4) c) A surface condenser is designed for a condensation of vapour at the rate of 60 kg/hr. It contains 81 tubes ina array of 9 x 9. Out side diameter of the tubes is 10 mm and the length is Im. What will be the condensation rate in vertical position, if it is installed in vertical position instead of horizontal position? [8] oooe [2863]-408 -[2963-212 T.E. (Mech / Mech S/W) HEAT TRANSFER (2003 Course) Time : 3 Hours} [Max. Marks : 100 Instructions to the Candidates : 1) Answer Three questions from Section and Three questions from Section Il. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Black figures to the right indicate full marks. 5) Use of Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, ifnecessary. SECTION -1 UNIT=1 Q.1 a) Using appropriate assumption, calculate the radiation heat transfer coefficient [06] for a small hot surface having temperature of 152 °C with emissivity of 0.85 dissipates heat by radiation into a hot surrounding area. b) A 60 Watts lamp is buried in soil (K = 0.83 W/m.K) at 0°C and switched on. [06] Find the temperature 0.3 m away from the lamp, when steady state is reached. ©) The quantity of radiation received by earth from the Sun is 1.4 KWim’. [06] Assuming that the Sun is an ideal radiator, calculate the surface temperature of the Sun. The ratio of the radius of the earth’s orbit to the radius of the sun is 216. OR Q2 a) Derive an expression for temperature distribution and conduction heat flow in [08] a circular conical rod with diameter at any section is given by D = Ax where x" is the distance measured from the apex of the cone and A is a certain numerical constant. Assume no heat generation, steady state and the lateral surface is well insulated. b) A homogeneous wall of area ‘A’ and thickness ‘L” has left and right hand [10] surface temperature of 0 °C and 40 °C respectively. Determine the temperature at the centre of the wall. i) How much material must be added and to which side of the wall if the temperature at the centre is to be raised by 5 °C? fi) How much material must be removed and from which side of the wall if the temperature at the centre line of the wall is to be lowered by 5°C?Q3 a) ») Qt a ») Qs a b) Q6 a) -2- [29 63]-312 UNIT-1I ‘A hollow sphere of inside and outside radii ‘r;" and ‘t, respectively is heated such that its inner and outer surfaces are maintained at uniform temperature “and ‘ts’. Ifthe material of which the sphere is composed has a thermal conductivity which varies with temperature according to the expression K=Kj+(K2 et | tot Find the heat flow rate through the sphere. A pipe of outside diameter 20 mm is to be insulated with asbestos which has a mean thermal conductivity of 0.1 Wim-deg, The local coefficient of connectivity heat transfer is $ W/m?-deg. Comment upon the suitability of asbestos as the insulating material. What should be the minimum value of thermal conductivity of insulating material to reduced heat transfer? OR of gases and liquids vary with temperature? How do thermal conductiv An aluminium alloy conductor carries a current of 800 amp. The square cross section of the conductor is 6.25 cm? and three of its sides are perfectly insulated. ‘The exposed surface is in contact with ait at 30 °C and h = 16.28 Wim°K. Calculate the maximum temperature of the conductor at steady state. Specific resistance of aluminium is 5 x 10* Q cm’/m and K = 203.5 W/m- K. Derive the equation you have used, UNIT~1 If 1p is termed as the temperature effectiveness of a fin, then the total heat transfer rate is given by : g=No-h.As ['s—Teo} then Aen] Where n¢ =fin efficiency ‘otal heat transfer area Prove that no = Af= fin area Define the following terms : i) Time constant ii) Dimension less time iii) Response time iv) Biot number OR ‘Two long rods of the same diameter, one made of brass (K = 85 Wim-leg) and the other of copper (K = 375 W/m-deg) have one of their ends inserted into a furnace. At a certain section 10.5 cm away from the furnace, the temperature of the brass rod is 120°C. At what distance from the furnace end, the same temperature would be reached in the copper rod. Both rods are exposed to the same environment. [08] [08] (04) (12) [08] {08}by Q7 a » ° Qs a) b) °) Qo a) ») -3- [29é3]-312 ‘An egg with mean diameter of 4 om and initially at 25 °C is placed in a boiling ‘water pan for 4 minutes and found to be boiled to the consumer's taste. For how long should a similar egg for same consumer be boiled when taken from a refrigerator at 5°C? Assume following properties K=12Wim-deg, h= 125 Wim? deg, Specific heat=2KJ/Ke-K, — Densit SECTION - 11 UNIT-IV Define Prandtl number and give its physical significance. Give its relation with thermal boundary layer and velocity boundary layer. Also give its value for liquid metals, heavy oils, water and air. ‘Show that for laminar flow over flat surface 1 average = 2% Focal Write Dittus ~ Boelter equation and specify the conditions for determining the heat transfer coefficient. OR What is meant by thermal entrance length. Explain the significance of thermal boundary layer and velocity boundary layer. Ina power plant feed water is flowing through a rectangular duet 8 em x 4.em ‘and the wall temperature is maintained at 170 °C through out. The feed water flows at the rate of 300 Kg/min, enters at a temperature of 20 °C and is heated to 150°C. Compare the heat transfer coefficient obtained using i) Dittus - Boelter equation and ii) Sieder ~ Tate equation. ‘Also estimate the required length of the duct. Properties of water at 105 °C are Pr=1.64, j= 265 x 10° Ke/ms, Cp = 4.226 KKK, K =683 x 10°KW/m-K, pty at 170°C = 158 x 10° Kg /m.s UNIT-V Define solid angle and Intensity of radiation. Give its unit. A long steel rod 20 mm in diameter is to be heated from 427 °C to 538°C. It js placed concentrically in a long cylindrical furnace which has an inside dismeter of 160 mm, The inner surface of the furnace is at a temperature of 1093 °C and has an emissivity of 0.85. If the surface of the rod has an emissivity of 0.6. Estimate the time required for heating operation. Density of steel = 700 Kg/m3 Specific heat = 0.67 KI/Kg-K [08] (06) {08} [04] [02] (04) (12) (04) (12)(2968]-312 OR Q.10 a) Explain the radiation error in high temperature measurement, {0s} b) Explain the difference between radiation from gases and that from solids. 103) ©) The radiation shape factor of the circular surface of a thin hollow cylinder of [08] 10 cin diameter and 15 cm length is 0.165. What is the shape factor of the curved surface of the cylinder with respect to itself. NIT- VI ~ Q.11 a) What is compact heat exchanger? {02} b) Define effectiveness, L.M.T.D., Capacity ratio and NTU for heat exchanger. [04] ¢) Hot water having specific heat 4200 J/Kg-K flows through a heat exchanger at [10] the rate of 4 Kg/min with an inlet temperature of 80°C. a cold fluid having Specifie heat 2400 WKg-K flows in at a rate of 8 Kg/min with inlet temperature of 20 °C. Make calculations for the maximum possible effectiveness if the fluid flows in i) Parallel flow arrangement i) _ Counter flow arrangement OR Q.12 8) Explain the phenomenon of nucleate boiling. List the factors that affect [06] nucleate boiling. b) Draw variation of film thickness and film coefficient with plate height. (02) c) A condensation experiment for steam on plate type vertical condenser has [08] been setup for a particular fluid with a given temperature difference. The ‘same set up was subsequently used with another fluid. ‘The thermo-physical properties ratio of two fluids are h =06 28-95 #212 Kalo PL hye MH Ky If the temperature difference is reduced to 80 percent. Calculate percentage change in the convection coefficient.[3163] - 312 HEAT TRANSFER (2003 Course) 3 Hours Max. Marks : 100 Instructions : 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Black figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - 1 Unit -1 1. A) A furnace wall lining is made up of a material with k = 2.5 Wim.K. The temperatures of the inner and outer surfaces of this plane wall lining are 810° C and 330° C respectively. The outer surface is exposed to ambient air at 30° C with convective heat transfer coefficient = 10 W/m?-K. Calculate : i) The rate of heat flow per unit area ii) Thickness of lining in given situation. iii) The thickness of lining required if the heat flow rate is to be reduced by 50%. 8 B) Derive the general three-dimensional conduction equation in Cartesian co-ordinates for isotropic material for unsteady state condition and with uniform internal heat generation. Reduce this equation to, i) Steady state condition, ii) Unsteady state without internal heat generation, iii) Steady state without internal heat generation condition. 8 OREEE EE EEE EE [3163] - 312 se 2 A) B) A) B) - A) Derive an expression for thermal resistance offered by a long hollow cylinder. A long hollow cylinder has an-inner radius of 10 em and an outer radius of 20 cm. Thermal conductivity of the cylinder material = 50 Wim-K. The Suter surface is maintained at 0° C. The inner surface is heated uniformly at the rate of q, = 1.16 x 10° W/n?. Considering unit length of the cylinder, calculate, i) Rate of heat flow (radial), ii) Temperature of the inner surface, The inner surface with radius = ‘a’ and outer surface with radius = ‘b’ of a hollow sphere having constant thermal conductivity *k’ are maintained at uniform temperatures T, and T, (T, > T,) respectively. Develop expressions for steady state radial heat flow rate and thermal resistance of the hollow sphere. Unit - 2 Consider a'slab of 1 em thickness with constant conductivity of 20 Wim-K. Uniform rate of internal heat generation is 8 x 10” W/m? .One face of this slab is insulated and the other face dissipates heat by convection to a fluid at 4a temperature of 100° C with heat transfer coefficient = 4000 W/m?-K. Calculate the temperatures of both the surfaces, “Insulating @ hot cylindrical object does not always reduce the heat loss from it” Explain the above statement and derive an expression for critical radius for such an object. OR A thick, walled copper cylinder has inside diameter of 2 em and outside diameter of dem. Inner and outer surfaces are maintained at 200° C and 250° C ‘espectively. Conductivity "K’ of the cylinder varies with temperature as, K=3719[1-9.25x10 (T-150}. Determine the rate of heat loss per unit Iength of the cylinder.“3 [3163] - 312 B) Write short notes (any two) : i) Overall heat transfer coefficient ii) Contact resistance iii) Thermal diffusivity. 8 Unit - 3 5. A) A sphere of 10 mm diameter made of steel is initially at a temperature of 300° C. It is exposed to a stream of air at a temperature of 30° C with convective heat transfer coefficient of 100 W/m? - K. Find, i) The time required for the sphere to reach a temperature of 50°C. ii) Instantaneous rate of heat transfer after one minute from the start of the cooling process. Properties of steel : p=7897kg/m?, C, = 0.452 ki/kg-K k= 73 Wim-K, 4 =2.026x 10> m?/S. 10 B) Starting from the standard differential equation, derive expressions for the following parameters in case of a long fin. i) Temperature distribution ii) Rate of heat flow iii) Efficiency of fin iv) Effectiveness of fin. 8 OR[3163] - 312 4 6. A) 10 rectangular fins of brass (k = 120 W/m-K) are welded horizontally to a ©) plane vertical surface of a tank, 1 m wide and Im high. The fins are 2 mm thick and 20 cm long. They are uniformly spaced on the vertical surface of . tank, which is maintained at 200° C. If the unit is exposed to ambient air at 20° € with convective heat transfer coefficient of 20 Wim’ K, find 8. A) i) Heat transfer rate before putting the fins. ii) Heat transfer rate after putting the fins, Prove that the fins are effective. Assume insulated end condition for the fins. 10 B) Derive an expression for temperature variation during quenching of a billet =~ by ‘lumped heat capacity method’. State the assumptions made. 8 SECTION ~ Il Unit - 4 7. A) Treating a human body as a vertical cylinder with 30 cm diameter and 1.6m height, having surface temperature of 37° C, calculate the rate of heat loss from the said body while standing in cold air at a temperature of -13° C. Nu = 0.59 Ra’™ for Ra < 10° = 0.14 Ra ™ for Ra > 10° Properties of dry air Pe. [Temp aye | ® (m/S) k (Wim-K) Pr (ats 12.1 x10* 0.023 0.719 | 14.5 x10° 0.025 0.712 37 16.7 x 10 0,028 0.705 | B) What is ‘hydraulic diameter’ of a duct ? What is its significance in forced convection heat transfer ? 4ae [3163] - 312 C) Explain the mechanism of formation of hydrodynamic boundary layer when cold air is blown over a hot flat plate. 4 OR 8. A) Air at 27° C blows along one side of a horizontal brick slab along its 15 m long length. The slab is at 55° C initially. The velocity of air is 4.5 m/s, Sp. heat of slab = 0.84 kJ/kg.K, density of slab = 1600 kg/m*, volume of slab = 1.5 m*. Properties of air : P = 1.128 kg/m? H = 19.1 x 10° kg/ms k = 0.0276 W/m - K Pr = 0,699 Nu = 0.664 Re” Pr°* for Re < 5 x 10° = 0.037 Re" Pr°* for Re > 5 x 10 For unit width of the slab, calculate , i) The rate of convective heat loss from the slab, ii) rate of radiative heat loss from slab, iii) initial rate of cooling of the slab per hour. Take emissivity of slab as 0.9. 12 B) Explain various dimensionless numbers used in natural convection heat transfer, 4[3163] - 312 6 Unit - 5 9. A) Two large parallel planes “A’ and ‘D" are maintained at temperatures of 1500 K and 600 K respectively. Their emissivities are 0.9 and 0.4 respectively. Two radiation shields ‘B’ with emissivity = 0.5 and ‘C’ with emissivity = 0.2 are inserted in between them, such that A, B, C, and D are placed one after the RD other. Calculate. i) Heat transfer rate without radiation shields, ii) Heat transfer rate with radiation shields, iii) Temperatures attained by planes ‘B’ and ‘C’. B) State and explain any 4 properties/rules of radiation shape factor. 6 OR |. A) The size of a room is 3m x 3m x 3m, The walls and ceiling are maintained at a temperature of 315 K. The floor of the room is at 308 K. Calculate the net rate of heat transfer by radiation to the floor. If floor is considered as surface “1 and (ceilings + walls) is considered as surface ‘2’, calculate, F,,,. F, B) A black body emits radiation of maximum intensity ata wavelength of 0.5 jm. Calculate its surface temperature and emissive power. State the laws of radiation heat transfer, which you have used to solve this problem 6s Unit - 6 . A) Hot air at 66° C is cooled upto 38° C by means of cold air entering at 15.5° C. Mass flow rates of hot and cold air are, 1.25 kg/s and 1.6 ke/s respectively. Sp.heat of hot and cold air = 1.05 ki/kg.K. U = 80 W/m? K. Find the area of the heat exchanger for parallel flow configuration. If the same exchanger is operated in counterflow mode, find the exit temperatures of both the fluids. 12ae [3163] - 312 B) Explain “film boiling’ phenomenon in pool boiling process and show this region on the pool boiling curve. 6 OR 4. A) Saturated steam at 85° C condenses on the outer surface of 256 horizontal tubes arranged in 16 x 16 array. The tube dimensions are, O.D. = 1.3 em, length=1 m, Tube surface temperature = 75° C. Calculate the rate of condensation in kg/sec. in this case. ‘Also calculate this rate if all these tubes (256 no.) are arranged vertically. 100) _ é Properties of condensate : w= 355 x 10° kg/m-s h,, = 2309 x 10° J/kg. 12 B) Explain the following (any two) : i) Fouling factor in heat exchanger ii) LMTD 10) iii) Compact heat exchangers. 6 + 68 — = CK Bi0772,600 12 +Time : 3 Hours v [3263] - 312 HEAT TRANSFER (2003 Course) Instructions : 1) Answers to the wo sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Black figures to the right indicate full marks. 4) Assume suitable data, if necessary. SECTION - 1 Unit -1 a) What is the purpose of insulation ? Prove that heat transfer rate will always reduce when the insulation is applied to wall/plate but it may not be so when the insulation is applied on the outside surface of the sphere or cylinder. b) A steel tube of 5 cm inner diameter and 8 cm outer diameter (K = 16 W/mK), is covered with an insulation of 3 cm thickness (K = 0.3 W/mk). A hot gas at 350° C with h = 400 W/m? K flows inside the tube, Outer surface of the insulation is exposed to air at 30° C with h = 60 W/m? K, Calculate the heat loss from the tube for 20 meter length. Also calculate the temperature at the interface of insulation and steel OR |. a) State and explain the following : i) Fourier’s Law of heat conduction ii) Newton's Law of cooling iii) Stefan Boltzmann’s Law of radiation. b) A wall of size 3m x 2m consists of 2 cm thick steel plate (K = 15 W/mK) followed by 50 cm thick asbestos insulation (k = 0.2 W/mk) and 4.cm thick layer of wood (K = 0.3 W/mK). These three layers are held together with the help of 10 mild steel bolts (K = 40 W/mK), each of 12 mm diameter. Find the rate of heat flow through this composite wall when the temperature of hot gases on the outside of steel plate is maintained at 500° C with convective heat transfer coefficient of 40 W/m?K and the wooden layer is exposed to ambient air at 20°C with convective heat transfer coefficient of 12 W/m?K. P.1.0. Max. Marks : 100 10 103263] - 312 & Unit - 11 3. a) Consider a solid cylinder of radius r = b, in which heat energy is generated at a constant rate of g W/m? uniformly. The cylinder is exposed to air at temperature Ta with convective heat transfer coefficient h. Develop an expression for one dimensional (radial) steady state temperature distribution T(x) through the cylinder. Also find centre temperature of the cylinder. Take K as the conductivity of the cylinder material. b) A cylindrical electrical conductor of 10mm diameter, insulated by plastic (K = 0.16 W/mK) is located in the air at 25° C having convective heat transfer coefficient of 8 W/m? K. If the surface temperature of the base conductor is 90° C. Calculate; under steady state condition, i) Current passing through conductor when 2 mm thick insulation is provided, Electrical resistance per meter length of the conductor is 9 x 10°ohm. ii) Current carrying capacity of the conductor when the insulation of critical radius is provided over it. OR 4. a) Surfaces of a plane wall of face area A are maintained at temperatures T, and T,. Thickness of the wall is b and its thermal conductivity varies with temperature as _K = Kf! + $} Show that rate of heat conduction through the wall is given by Al, iT Q=Koy | -T))+oIn | Also sketch temperature variation across the thickness of the wall for the values of @ as i) a 0 b) A 30 mm thick plate generates internal energy uniformly at the rate of 2.7% 10’ W/m' .Thermal conductivity of the plate material is 15 W/mk. Temperature of one surface is 110° C and that of the other surface is 100° C. Determine the maximum temperature in the plate and specify its location in the thickness of the plate.4 [3263] — 312 Unit - TL 5. a) State the assumptions made in Lumped Heat capacity method and derive the expression for temperature as a function of time T (t) for a spherical body of radius R when quenched in air at temperature Ta with h as convective heat transfer coefficient taking p as density and C, as the specific heat of the body 8 b) Fins are provided to increase the heat transfer rate from a hot surface. Which of the following arrangement will have maximum heat transfer rate : i) 6 Fins with 10 cm length or ii) 10 Fins with 6 cm length Take conductivity of the fin material as 300 W/mk, h = 20 W/m°K, cross sectional area of the fin’ = 2m’, perimeter of fin cross Section = 4 cm, temperature of the hot surface = 230 ° C, ambient temperature = 30° C. Assume fins of insulated ends. 8 OR 6. a) Explain any four of the following : 8 i) Fin Efficiency ii) Fin Effectiveness iii) Biot Number iv) Time constant of a Thermocouple v) Applications of Fins b) A solid cylinder of steel of 5 cm diameter and 20 cm length, initially at a uniform temperature of 500° C is suddenly placed in a fluid at 200° C with h = 100 Wim? K, After a period of 5 minutes, the steel cylinder is taken out from this fluid and immediately immersed in another fluid at 50° C with h= 10 Wim’. 8 Steel Properties are : : Cp = 0.46 kJ/kg K; p= 7800 kg/m and K = 35 W/mk. 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° C .(3263] ~ 312 a SECTION - II Unit - IV 7. A) Name various physical properties of a fluid which influence the value of heat transfer coefficient in i) Natural convection ii), Forced convection With this fluid as medium. B) Air flows with a velocity of 0.5 m/s through a rectangular cross-sectioned duct with dimensions 10 emx 5 cm and length = 5. 67 m. The duct is heated uniformly throughout its length. The duct wall temperature is 20° C higher than the air temperature throughout its length. If the bulk mean temperature of air is 27° C, calculate the rate of heat transfer between duct and air. Now, air velocity is made = 2m/s. As a result, duct wall temperature is 10° C higher than air temperature throughout the length of the duct. Find the percentage change in rate of heat transfer between this case and the previous case. Correlations: Nu = 4.364 for laminar flow = 0,023 Re °* Pr °* for turbulent flow. (Refer to air properties at the end of question paper for both cases). oR 8. A) List various dimensionless numbers used in i) Natural convection and ii) Forced convection, state their expressions and explain their significance in one sentence each. B) The CPU of a personal computer has dimensions of 10cm x 50 cm x 40 cm height. Its surface temperature is 39°C. Itis kept in still air at 15° C. Neglecting heat transfer from its bottom surface, find the rate of heat transfer from i) its top surface and ii) all 4 vertical surfaces. (Refer to the properties of air at the end of the question paper) 12 6- [3263] - 312 Correlations: Surface Correlation Range of ‘Ra’ | Vertical Nu = 0.59'Ra ™ 10*— 10° = 0.1 Ra’ 10? -10" Horizontal Nu = 0.54 Ra™ 102 x10" 6 * = 0.14 Ra? 2% 1072 10° [* For a rectangular horizontal surface, characteristic dimension ee = Average of lengths of 2 sides of the rectangle] 12 Unit -V 9. A) Write the statements and mathematical expressions of the following laws in radiation heat transfer : i) Planck's law ii) Wien’s law aa iii) Kirchoff's law iv) Lambert's cosine rule. 8 wir 8) Two large parallel planes with emissivities of 0.8 and 0.4 have temperatures of 427 °C and 27° C respectively. If they are kept facing each other, find the 6 rate of radiation heat transfer between them. . 1* aul IF this rate of heat transfer is to be reduced to of original value. Calculate the emissivity of radiation shield to be inserted in between them. The shield has same emissivity on both sides. 8 OR[3263] — 312 6 10.A) A gray opaque surface has an absorptivity = 0.7. It is maintained at 200° C. It receives an irradiation of 1,000 W/m?. Its surface area is 0.2 m*, Calculate, i) rate of heat absorption ii) rate of heat emission iii) rate of heat reflection iv) radiosity of the surface. B) State and explain 4 rules regarding radiation shape factor. Unit - VI 11.A) Explain the mechanism of laminar film condensation over a vertical flat plate. What are various physical properties of the condensate, which affect the value of heat transfer coefficient for this process ? B) Cold water at 0.5 kg/Sec. enters a parallel flow heat exchanger at 25° C to cool 0.25 kg/sec. of hot water entering at 70° C. Hot water is cooled upto 50° C. Overall heat transfer coefficient is 500 W/m? K. ‘Cp’ for hot and cold water = 4180 Ike K. i) Calculate the area required for this heat exchanger. ii) If the fluids are made to flow in counterflow configuration, what will be their exit temperatures ? [Heat capacities, in let temperatures are kept same] [Note : ‘NTU’ remains same for both the configurations]. OR 12. A) Draw a labelled sketch of pool boiling curve. Explain the following terms with reference to this curve : i) Nucleate boiling ii) Critical heat flux. B) A concentric tube type heat exchanger operates in counterflow mode. The OD and ID of the inner tube are 7 cm and 6 cm respectively. Hot oil is cooled from 70° C to 45 ° C while flowing through the inner tube at the rate of 2 kg/sec. Cp, = 1,500 Ikg K. 10-7- [3263] - 312 Fouling factor on oil side = 0.0001 m? k /W. Heat transfer coefficient on oil side = 400 W/m°K. Water flowing through the annulus at the rate of 3 kg / sec. enters at 20° C. CP oe; = 4180 J/kg K. Fouling factor on water side = 0.0001 m? K/W. Heat transfer coefficient on water side = 600 W/m? K. Conductivity of the inner 8 tube material = 220 W/mK. 8 Calculate the heat exchanger area required. Properties of air at 300 K. p = 1.1614 kg/m — — Cp= 1007} / kgK. v= 15.89 x10° m?/S 6 k = 0.0263 W/mk Pr = 0.707. 10-E BAUOT14,225 ew 6 10i a HEAT TRANSFER (2003 Course) Time.: 3 Hours Max. Marks : 1 Instructions : 1) Answer three questions from Section I and three questions from Section II. 2) Answers to the two Sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Black figures to the right indicate full marks, 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. SECTION -I UNIT -1 1. a) A brick (k = 1.2 W/m K) wall 0.15 m thick separates hot combustion gases of a furnace from the outside ambient air which is at 25°C. The outer surface temperature of the brick wall is found to be 100 °c. If the natural convection heat transfer coefficient on the outside surface of the brick wall is 20 W/m? K and its emissivity is 0.8, calculate the inner surface temperature of the brick wall. b) Show that the radial heat conduction through a hollow cylinder depends on le surfaces. the logarithmic mean area of the inside and out °) The inside surface of an insulating layer is at 270 °C. and the outside surface is dissipating heat by convection into air at 20 °C. The insulating layer is 40 mm thick and has a thermal conductivity of 1.2 W/m K. What is the minimum value of the heat transfer coefficient at the outside surface if the outside surface temperature should not exceed 70 °C ? OR [3363] - 312 PTO.[3363] - 312 2 Oe 2. a) Derive the equation for total heat transfer rate through a hollow sphere having inner and outer radii r, and r, respectively. Its inner and outer surface temperatures are T, and T, respectively. There is no heat generation and its conductivity is constant. by A circular plate heater (diameter 20 cm) is inserted between two circular plates (dia, = 20cm), slab A is'3 cm thick (K = 55 W/m/K) and slab B is 1.5 cm thick (K = 0.18 W/m K). The outside heat transfer coefficient on sides of A ‘and B are 200 and 65 W/m? K respectively. The temperature of surrounding air is 30 oC. If the rating of heater is 2 kW, find + i) Maximum temperature in the system ii) Outer surface temperature of two slabs iii) Draw equivalent electrical circuit of the system. UNIT -2 3, a) /A 1 mm diameter wire is maintained at a temperature of 400 °C and exposed to a convection environment at 40 °c with h = 120 Wim? °c. Calculate the thermal conductivity which will just cause an insulation of 0.2 mm to produce “critical radius”. How much of this insulation must be added to reduce the heat transfer by 75 percent from that which would be experienced by the bare wire. b) Derive an expression for the temperature distribution in a plane wall having uniformly distributed heat sources and one face maintained at a temperature TT, while the other face is maintained at T,, The thickness of the wall may be taken as 2L. OR 10 cfp< 4. a) Explain why an insulated small diameter wire has a higher current carrying capacity than an uninsulated one. b) A hollow cylindrical conductor (thermal conductivity K) with inside radius 1, Outside radius r, is perfectly insulated at its outside radius and is held at temperature T, by a coolant at the inside radius. Volumetric heat is generated within the conductor at the constant rate of q, W/m’. If the steady state conditions prevail and the temperature distribution is primarily radial, establish relation for the temperature as a function of the radial coordinate r and derive the same for maximum temperature. UNIT -3 a) Consider a sphere and a cylinder of equal volume made of copper. Both the sphere and the cylinder are initially at the same temperature, and are exposed to convection in the same environment, Which do you think will cool faster, the sphere or the cylinder ? Why ? b) Fins, 12 in number, having k = 75 W/m K and 0.75 mm thickness protrude 25 mm from a cylindrical surface of SO mm diameter and | m length placed in an atmosphere of 40 °C. If the cylindrical surface is maintained at 150 °C and the heat transfer coefficient is 23 W/m? K, calculate a) the rate of heat transfer b) the percentage increase in heat transfer due to fins ¢) the temperature at the centre of fins and d) the fin efficiency and the fin effectiveness. ‘The fins are rectangular in shape and cross-section and they are attached along the length of the cylinder OR 3 [3363] - 312 4 12 13[3363] - 312 4 a cH 6. a) Steel ball bearings (k = 50 W/m K, a = 1.3-x 10° m/s) having a diameter of. 40 mm are heated to a temperature 650 °C and then quenched in a tank of oil at 55 °C. If the heat transfer coefficient between the ball bearings and oil is 300 W/m? K. Determine : a) the duration of time the bearing must remain in’oil to reach a temperature of 200 °c, b) the total amount of heat remoyed from each bearing during this time and - ©) the instantaneous heat transfer rate from the bearings when they are first immersed in oil and when they reach 200 °c. 12 b) Ifa fin is thin and long and tip loss is negligible, show that the heat transfer from the fin is given by Q, = mkAg, tanh ml ; Where m = (hp/kA)'* 7 6 SECTION - II - UNIT -4 3 7. a) What is meant by ‘hydraulic diameter’ of a duct ? Explain its significance in convection heat transfer. 2 Calculate the hydraulic diameter for the following ducts — i) rectangular cross-sectioned, with sides = 10 cm and Sem ii) square cross -sectioned, with side = 2 em iii) circular cross-sectioned, with radius = 2cm. 6HN a . as [3363] - 312 b) A horizontal flat circular metallic plate is kept on its flat surface on a terrace ground in sunlight. Radius of plate = 2m. It attains a steady state temperature of 77°C. The ambient temperature is 27°C. Calculate the rate at which solar heat energy is received by the plate by means of convection only. Also calculate the rate of heat transfer per unit area of the plate. Take characteristic length of A, = ——sturface_ Plate = Perimeter For horizontal plate with hot surface up 12 Nu = 0.13 (GrPr)'* for GrPr <2 x 108 ; | = 0.16 (GrPr)! for GrPr > 2 x 10* Use following properties of air k = 0.0282 W/mk r v = 18.23 x10 m/s F Pr = 0.7025 10 , OR 8. a) Whatis meant by ‘characteristic dimension’ in natural convection heat transfer ? Explain its significance. 2 State the characteristic dimension for the following cases, Explain it with the help of a neat sketch in each case (not to scale). i) vertical cylinder with radius = Sem, height = 80 cm ii) horizontal cylinder with radius = Sem, length = 80 cm 6 iii) horizontal circular flat plate with radius = 5 cm. 6[3363] - 312 6 Ne b) Water flows at the rate of 0.1 kg/s through a thin metallic tube of | cm diameter and 3 m length, It enters the tube at 25°C. The outer surface of the tube is maintained at a constant temperature of 109°C. Calculate the exit temperature of water. Nu = 0.023 Re®* Pr? for turbulent flow =3.66 for laminar flow Properties of water Cp = 4174 ke K p = 5.62 x 10% ke/ms k = 0.644 W/mK. UNIT - 5 a) Define and explain the following terms : i) Black surface ii) Radiation shape factor iii) Intensity of radiation iv) Reflectivity of a surface. b) The dimensions of aroomare 10m x 10mx7m height. The roof temperature is 60°C, while the walls and the floor are at 30°C. Calculate the rate of heat transfer from the roof to the walls and floor together. Emissivity of walls and floor = 0.8. Emissivity of roof = 0.6. OR If the shape factor of a surface w.r.t. itself is 0.6, what may be the nature of this surface ? Explain with the help ofa sketch. Also sketch and explain the types of surface which has no shape factor w.r-t itself. 100 w/m? of energy is incident over an opaque surface maintained at 27°C. Emissivity of this surface = 0.2. Calculate the amount of energy flux reflected from it. Calculate its radiosity iii) The intensity of radiation in a direction normal to a black surface is 100 w/m2, Calculate the intensity in a direction making an angle of 30° with the normal. Also calculate the emissive power of the surface 10 4N00 000 . ee [3363] — 312 | iv) Explain the following terms : 4 } * Space resistance * Surface resistance. UNIT - 6 11. Write notes on : i) Compact heat exchanges ii) LMTD iii) Filmwise condensation process iv) Natural convection boiling. 16 OR 12. a) Explain the following terms : b) A steam condenser uses water flowing at the rate of 0.1 kg/see as cooling medium, The condenser tube is having 3 cm O.D. and 22 m of length. Steam condenses at 100°C on the outside of the tube. Overall heat transfer coefficient based on tube outer surface area = 100 w/m’k, C, water = 4180 J/kgK. If the cooling water enters the heat exchanger at 30°C, calculate the exit temperature of this water. : 8 i) Film boiling ii) Dropwise condensation process. 8 ; ‘ 1 1) B/VO8/1630muni [3663] - 112 'T.E. (Mechanical) (Sem, — I) Examination, 2009 (2003 Course) HEAT TRANSFER (Common with Mech. S/W for Sem. - II) Time : 3 Hours Max. Marks : 100 Instructions: 1) Answer 3 questions from Section I and 3 questions from Section IL. 2) Answers to the two Sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Black figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steant tables is allowed. 6) Assume suitable data, if necessary. SECTION -1 Unit -1 1. A) State the Fourier law of heat conduction and by using it derive an expression for steady state heat conduction through a plane wall of thickness L and maintaining its two surfaces at temperatures, T, and T,. 8 B) A long cylindrical rod of radius 12 cm, consists of nuclear reacting material (k =2 W/m.K) generating 30 kW/m uniformly throughout its volume. The rod is encapsulated within another cylinder (k = SW/m.k) whose outer radius is 24 cm and surface is surrounded by air at 30 °C with heat transfer coefficient of 20 W/m?.k. Find the temperature at the interface between the two cylinders and at the outer surface. 8 OR 2, A) Derive a general three dimensional heat conduction equation in Cartesian coordinate system. Reduce it as 1) Poisson equation, 2) Fourier equation, 3) Laplace equation. 8 B) A solid with thermal conductivity 38 W/m.K is having a temperature gradient of -350 °C/m. Determine the steady state heat flux. If the heat is exchanged by radiation from the surface (black) to the surrounding at 30 °C, determine the surface temperature of solid. 8 P.7.0.[3663] = 112 Unit - 2 3. A) Explain the following : 1) Thermal contact resistance 2) Critical radius and economic thickness of insulation 3) Variation of thermal conductivity with temperature in gases. B) Derive an expression for the temperature distribution in a hollow cylinder having inner radius R, and outer radius as R, with uniformly distributed heat sources and inner face maintained at a temperature T, while the outer face is maintained at T,. OR During the ripening process of an orange, the energy release estimated as 563 Wim’. If the orange is assumed to be homogeneous sphere with k = 0.15 Wim.K. Compute the temperature at the centre of orange and the heat flow from the outer surface. Assume a diameter of orange as 8'cm and outer surface temperature as 2°C. Derive the equation youuse. i Unit -3 w . A) Explain the following 1) Design criteria for thermo wells 2) Biot and Fourier numbers 3) Fin efficiency and fin effectiveness. B) Derive the expressions for temperature distribution in a body at time t during ‘Newtonian heating or cooling. OR A) It is better to use 10 fins of 5 cm length than 5 fins of 10 cm length. State and prove correctness of the statement. Use following data : Diameter of fin= 10 mm Thermal conductivity = 45 W/m.K Heat wansfer coefficient = 95 W/m.K. > B) The steel ball bearing (k = 50 W/m.K, c= 1.3 10-5 m?/s), 40 mm in diameter is heated to a temperature of 650 °C. It is then quenched in a oil bath at 50 °C, where the heat transfer coefficient is estimated to be 300 W/m?.K. Calculate (a) the time required for bearing to reach 200 °C, (b) the total amount of heat removed from a bearing during this time, and (c) the instantaneous heat transfer rate from the bearing when it is first immersed in oil bath and when it reaches 200 °C. 9 7 16 12 10EJ & SECTION ~ IL Unit —4 7. a) Consider a human body in Vertical position of height 167 cm at an average temperature of 37.3° C exposed to atmospheric air at -5.7° C at Nainital during winters. Human body can be approximated to.a cylinder of diameter 40 cm having surface emissivity of 0.3. Calculate total heat loss rate from the body by conyection and radiation, Neglect heat loss from the feet (bottom surface), You may use the following empirical correlations : Nu = 0.56 (GrPr)°** for vertical surface Nu = 0.14 (GrPr)** for horizontal upper surface Nu = 0.27 (Ra)"** for horizontal lower surface. ‘Take the following air properties : Pr = 0.715; k = 0.025 W/mK; v = 13.55 x 10 ms. Characteristic length for horizontal surface can be taken as A/P; where A is the area of the surface and P is its perimeter, b) Explain physical significance of any four Dimensionless Number used in Forced Convection. OR 8. a) Air at temperature of 10° C flows through a square duct of side 20 cm with a velocity of 12 m/s and leaves the duct at 30° C due to heating by duct surface uniformly maintained at 50° C. Find heat transfer rate to air, if the length of the duct is 5m. Use the following correlations : Nu = 0.023 Re?*Pr# for turbulent flow. Nu=3,66 for laminar flow. Air properties can be taken from Q.7 a) above. b) Differentiate between Natural Convection and Forced Convection. ©) Draw Boundary Layers (Natural Convection currents only) for horizontal and vertical cylinders exposed to ambient air. Horizontal cylinder iscolder than air while vertical cylinder is hotter than air. Unit - 5 Define Shape Factor. Find the shape factor of a cylindrical cavity of diameter D and depth H with respect to itself. Explain the following : i) Lambert Cosine Law ii) Wien’s Displacement Law. db) 0 1 Se [3663] ~ 112 ry[3663] - 112 4 Ov ) Calculate heat transfer rate by radiation between the surfaces of two long cylinders of radii 100 mm and 200 mm kept one inside the other. The axes of the cylinders are parallel to each other but separated by a distance of 20 mm. Outer surface of inner cylinder and inner surface of the outer cylinder are maintained at 127° C and 27° C having emissivities of 0.07 and 0.7 respectively. Assume the medium between the two cylinders as non-absorbing. 8 10. a) Using the concept of ‘Surface Resistance’ and ‘Space Resistance’, derive the expression for steady state heat transfer rate by radiation between the two long gray diffused parallel plates maintained at temperatures T, and'T,, of emissivities of e, and e, having a thin radiation shield of emissivity e, inserted in parallel between the two plates. 8 b) Why does error occur in measuring the temperature by thermocouple of hot gases flowing through a conduit ? Explain. 4 c) Calculate the error in measurement of temperature by using thermocouple (¢ = 0.6) of exhaust gases flowing through a tube. Temperature of the tube is 20° C and thermocouple measures a temperature of 500° C. Take h = 200 W/mK between the thermocouple and exhaust gases. 4 Unit - 6 1. a) Explain the Six Regimes of pool boiling with the help of neat curve. 9 b) A hot fluid at 200° C enters a heat exchanger at a mass flow rate of 10000 kg/ hour, Its specific heat is 2 KI/kgK. It is to be cooled by another fluid entering at 25° C with a mass flow rate of 2500 kg/hour and specific heat of 400 J/kgK. The overall heat transfer coefficient based on outside area of 20 m? is 250 W/m’K. Find exit temperature of both the fluids when fluids are in parallel flow arrangement. 9 OR 12. a) Draw labelled temperature profiles of the following types of Heat Exchangers : i) Direct transfer type parallel flow ii) Direct transfer type counter flow iii) Condenser iv) Evaporator. 4 b) Differentiate between Film Wise Condensation and Drop Wise Condensation. 4 c) Saturated steam at 80° C condenses on outside of a horizontal tube of 10 cm diameter maintained at a temperature of 70° C. When the tube was kept vertical, it was observed that the rate of condensation was same as before. Find the length of the tube and rate of condensation per hour. Take latent heat for steam as 2300 kI/kg and the following properties of condensate ; p = 977.8 kg/m’; k = 0.668 W/mK; v = 0.415 x 10 m/s. 10 BAI/09/5,500