SARDAR PATEL UNIVERSITY ME – 451 HEAT AND MASS TRANSFER

ASSIGNMENT COMPOSITE WALL

1 Calculate the rate of hear transfer per unit area through a copper plate 45

mm thick, whose one face is maintained at 350o C and the other face at 50oC. Take thermal conductivity of copper as 370 W/moC.

2 A plane wall is 150 mm thick and its wall area is 4.5 M2 if its conductivity is 9.35 W/moC and surface temperatures are steady at 150oC and 45oC, determine: (i) Heat flow across the plane wall (ii) Temperature gradient in the flow direction.

3 The following data relate to an oven:

Thickness of side wall of the oven = 82.5 mm Thermal conductivity of wall insulation = 0.044 W/moC Temperature on inside of the wall = 175oC

Energy dissipated by the electrical coil Within the oven= 40.5 W Determine the area of wall surface perpendicular to heat flow, so that

temperature on the other side of the wall does not exceed 75oC. Ans: 0.76 m2

4 A hot plate 1m x 1.5 m is maintained at 300oC. Air at 20oC blows over the plate. If the convective heat transfer coefficient is 20W/m2oC, calculate the rate of heat transfer.

5 A wire 1.5 mm in diameter and 150 mm long is submerged in water at atmospheric pressure. An electric current is passed through the wire and is increased until the water boils at 100oC. Under the condition if convective heat transfer coefficient is 4500 W/m2C find how much electric power must be supplied to the wire to maintain the wire surface at 120oC ?

6 A storage tank of interior dimensions 10 m x 8 m x 2.5 m high. Inside surface temperature is – 20o C and out side surface is at 25o C. The wall and ceiling of the tank have three layers made of: 60 mm thick board ( k = 0.2 W/moC ) on the inside. 90 mm thick insulation ( k = 0.04 W/moC ) at mid. 240 mm thick concrete ( k = 1.8 W/moC ) on the out side. Neglect flow of heat through the floor. Determine the rate at which heat can flow towards inside of the tank. Ans : 2851.7 W

7 The inner surface of a plane brick wall is at 60oC and the outer surface is at 35oC calculate the rate of heat transfer per m2 of surface area of the wall, which is 220 mm thick. The thermal conductivity of the brick is 0.51 W/mC

8 Consider a slab of thickness L=0.25 m. One surface is kept at 100oC and the other surface at 0oC. Determine the net flux across the slab if the slab is made from pure copper. Thermal conductivity of copper may be taken as 387.6 W/m K.

9 A reactor wall with total thickness of 320 mm is made up of an inner layer of fire brick (k=0.84 W/moC) covered with a layer of insulation (k=0.16 W/moC). Inner temperature of fire brick is 1325oC and outer temperature of insulation is 25oC.

(i) Determine the thickness of fire brick and insulation. (ii) Calculate the heat loss presuming that the insulating material has a

maximum temperature of 1200oC. 10 The wall of house in cold region comprise of three layers.

15 cm outer brick work ( k = 0.75 W/moC ) 1.25 cm inner wooden panelling ( k= 0.2 W/moC ) 7.5 cm intermediate layer of insulating material. The insulating layer is stated to offer resistance twice the thermal resistance of brick work. If the inside and outside temperature of brick work are 20oC and -15oC respectively, determine rate of heat loss per unit area of the wall and thermal conductivity of the insulating material. Ans : 52.8 W, 0.1875 W/moC

11 A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered with a layer of magnesite brick 240 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magnesite

brick wall are 725oC and 110oC respectively. The contact thermal resistance between the two walls at the interface is 0.0035oC/W per unit wall area. If thermal conductivities of silica and magnesite bricks are 1.7 W/mC and 5.8 W/mC, calculate.

(i) The rate of heat loss per unit are of walls, and (ii) The temperature drop at the interface.

12 An exterior wall of a house may be approximated by a 0.1 m layer of common brick (k=0.7 W/mC) followed by a 0.04 m layer of gypsum plaster (k=0.48 W/mC) What thickness of loosely packed rock wool insulation (k=0.065 W/mC) should be added to reduce the heat loss or (gain) through the wall by 80 percent?

13 A furnace wall as composed of 220 mm of firebrick, 150 mm of common brick, 50 mm of 85 % magnesia and 3 mm of steel plate on the outside. If the inside surface temperature is 1500oC and outside surface temperature is 90oC, estimate the temperatures between layers and calculate the heat loss in kJ/h-M2. Assume, K (for fire brick) = 4 kJ/mC, K (for common brick) = 2.8 kJ/mC, k (for 85 % magnesia)=0.24 kJ/mC, and k (steel) = 240 kJ/mC

14 A cold storage room has walls made of 220 mm of brick on the outside, 90 mm of plastic foam, and finally 16 mm of wood on the inside. The outside and inside air temperatures are 25oC and

–3 oC respectively. If the inside and outside and outside heat transfer coefficients are respectively 30 and 11 W/m2C, and the thermal conductivities of brick, foam and wood are 0.9, 0.022 and 0.17 W/mC respectively, determine:

(i) The rate of heat removal by refrigeration if the total wall area is 85 m2;

(ii) The temperature of the inside surface of the brick. 15 It is proposed to carry pressurized water through a pipe imbedded in a 1.2

m thick wall whose surfaces are held at constant temperatures of 200oC and 60oC respectively. It is desired to locate the pipe in wall where the temperature is 120oC, find how far from the hot surface should the pipe be imbedded? The thermal conductivity of the wall material varies with the

temperature according to the relation, k=0.28(1+0.036t) where t is in degree Celsius and k is W/moC

16 The composite wall of furnace is made up with 120 mm of fire clay [k=0.25 (1+0.0009 t) W/mC ] and 600 mm of red brick (k=0.8 W/mC). The inside surface temperature is 1250oC and the outside air temperature is 40oC determine: 1) The temperature at the layer interface, and

2) The heat loss for 1m2 of furnace wall.

17 A furnace wall comprises two layers : 15 cm thick fire brick with k= ( 0.25 + 0.00025 T ) W/moC, Where T is in oC. 50 cm thick red brick with k = 0.8 W/moC The inside surface temperature of fire brick is 1200oC and the outside red brick is at 50oC. At contact surface, the temperature drops by 20oC due to uneven contact. Work out the heat loss per unit area of the furnace wall and temperature of the red brick surface which is in contact with the fire brick. Ans : 1125.6 W/m2, 816o c

18 The insulation boards for air-conditioning purposes are made of three layers. Middle being of packed grass 10 cm thick (k=0.02 W/moC) and sides are made of plywood each of 2 cm thickness (k=0.12 W/moC) They are glued with each other

1) Determine the heat flow per m2 area if one surface is at 35oC and other surface is at 20oC Neglect the resistance of glue.

2) Instead of glue, if these three pieces are bolted by four steel bolts of 1 cm diameter at the corner (k=40 W/moC) per m2 area of the board then fund the heat flow per m2 area of the combined board.

( 2.81 w/m2, 4.14 w/m2 )

19 An electric hot plate is maintained at a temperature of 350oC, and used to keep a solution boiling at 95oC. The solution is contained in a cast-iron vessel of wall thickness 25 mm, which is enameled inside to thickness of 0.8 mm. The heat transfer coefficient for the boiling solution is 5.5 kW/m2K, and the thermal conductivities of the cast iron and enamel are 50 and 1.05 W/mK, respectively, calculate:

1) The overall heat transfer coefficient 2) The rate of heat transfer per unit area.

20 A metal plate of 4 mm thickness (k=95.5 W/moC) is exposed to vapour at 100oC on one side and cooling water at 25oC on the opposite side. The heat transfer coefficients on vapour side and water side are 14500 W/m2C and 2250 W/m2C respectively. Determine:

(i) The rate of heat transfer,

(ii) The overall heat transfer coefficient (iii) Temperature drop at each side of heat transfer.

21 A wall of a furnace is made up of inside layer of silica brick 120mm thick covered with a layer of magnetite brick 240 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magnetite brick wall are 725 C and 110o C respectively. The contact thermal resistance between the two walls at the interface is 0.0035 C/W per unit wall area. If thermal conductivities of silica and magnetite bricks are 1.7 W/m C and 5.8 W/m C, calculate. 1. The rate of the heat loss per unit area of walls, and 2. The temperature drop at the interface. ( 5324 W/m2C, 18.8o C )

22 A furnace wall is made up of three layers of thicknesses 250 mm, 100 mm and 150 mm with thermal conductivities of 1.65, K and 9.2 W/mC respectively. The inside is exposed to gases at 1250 oC with a convection coefficient of 25 W/m2C and inside surface is at

1100 oC, the outside surface is exposed to air at 25oC with convection coefficient of 12 W/m2 C. Determine:

1. The unknown thermal conductivity ‘K’ 2. The overall heat transfer coefficient;

3. All surface temperatures. ( 2.81 W/mk, 3.06 W/m2C, 531.8oC, 398.6oC, 337.5oC )

23 A 240 mm stem main, 210 meters long is covered with 50 of high temperature insulation (k = 0.092 W/mC) and 40mm of low temperature

insulation (k = 0.062 W/mC). The inner and outer surface temperatures as measured are 390 C and 40 C respectively. Calculate:

(i) The total heat loss per hour. (ii) The heat loss per m2 of pipe surface.

(iii) The total heat loss per m2 of outer surface, and (iv) The temperature between two layers of insulation. Neglect heat conduction through pipe material. ( 231099.5kJ/hr, 1459 kJ/hrm2, 834 kJ/hr, 205.8oC )

24 An insulated stem pipe having outside diameter of 30 mm is to be covered with two layers of insulation, each having thickness of 20 mm, The thermal conductivity of one material is 5 times that of the other. Assuming that the inner and outer surface temperatures of composite insulation are fixed how much will heat transfer be increased when better insulation material is next to the pipe than it is outer layer? Ans : ( 50.9% )

CRITICAL THICKNESS 1 A steam pipe 10 cm outside diameter is covered with two layers of

insulation, each having a thickness of 2.5 cm. The average thermal conductivity of one material is 3 times that of other and the surface temperatures of the insulating pipe are fixed. Examine the position of better insulating layer relative to the steam pipe if heat dissipation from steam is to be minimum. What percentage saving in heat dissipation results from that arrangement? Ans ; q1/q2 = 3.99/4.73 = 0.843, 18.55%

2 An electrical cable of 5 mm radius is applied a uniform sheathing of plastic insulation ( k = 0.175 W/moC ). The convective film coefficient on the surface of a bare cable as well as insulated cable was estimated as 11.65 W/m2C and surface temperature of 55oC was noted when the cable was directly exposed to ambient air at 15oC. For keeping the wire as cool as possible, find the thickness of insulation. Also determine the surface temperature of insulated cable if the intensity of current carried by the conductor remains unchanged. Ans : 10 mm, 46oC

3 A hot fluid is being conveyed through a long pipe of 4 cm outer diameter and covered with 2 cm thick insulation. It is proposed to reduce the conduction heat loss to the surrounding to 1/3rd of the present rate by further covering with same insulation. Calculate the additional thickness of insulation.

4 A 160 mm diameter pipe carrying saturated stem is covered by a layer of lagging of thickness of 40 mm (k =0.8 W/m C). Later, an extra layer of lagging 10 mm thick (k = 1.2 W/m C) is added. If the surrounding temperature remains constant and heat transfer coefficient for both the lagging materials is 10 W/m C, determine the percentage change in the rate of heat loss due to extra lagging layer. ( 0.223 % )

5 A 10 mm cable is to be laid in atmosphere of 20 C with outside heat transfer coefficient 8.5 W/m2 C. The surface temperature of cable to be 65 C due to heat generation within, will the rubber insulation, K= 0.155 W/mC, be effective? If yes how much? ( Yes, 19.1W/m )

6 A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick insulation (k = 0.12 W/m C). The heat transfer coefficient (h) on the insulated surface is 35 W/m2 C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness id used, assuming the temperature difference between the surface of the wire and surrounding air remains unchanged. ( 3.43mm , 11.6% )

7 A wire of 6.5 mm diameter at a temperature of 60 C is be insulated by a material having k = 0.174 W/mC. Convection heat transfer coefficient (h) = 8.772 W/m2C. The ambient temperature is 20 C. For maximum heat loss, what is the minimum thickness of insulation and heat loss per meter length? Also find percentage increase in the heat dissipation too. ( 7.1 W/m, 15.5W/m, 118 % )

8 A refrigerant suction having outer diameter 30 mm is required to be thermally insulated. The outside air film coefficient of heat transfer is 12 W/m2 C. The thermal conductivity of insulation is 0.30 W/m C. (i) Determine whether the insulation will be effective;

(ii) Estimate the maximum value of thermal conductivity of insulating material to reduce heat transfer;

(iii) Determine the thickness of cork insulation to reduce the heat transfer

to 22 percent if the thermal conductivity of cork is 0.038 W/m C. ( 25 mm 0.18 W/m2, 21 mm )

9 A uniform plastic insulation (k = 0.18 W/m C) is applied to an electric cable of 8 mm diameter. The convective film coefficient on the surface of bare cable as well as insulated cable was estimated as 12.5 W/m2 C and a surface temperature of 45 C was observed when the cable was directly exposed to ambient air 20 C Determine: i. The thickness of insulation to keep the wire as cool as possible;

ii. The surface temperature of insulated cable if the intensity of current flowing through the conductor remains unchanged.

( 10.4 mm , 35.9oC ) HEAT GENERATION

1 A plate 2 cm thick and 10 cm wide is used to heat a fluid at 30 C. The heat

generation rate inside the plate is 7 × 106 W/m3. Determine the heat transfer coefficient to maintain the temperature of the plate below 180o C, Given k (plate) = 26 W/m C, Neglect heat losses from the edge of the plate.

( 512.8 w/m2C ) 2 The temperatures on the two surface of a 25 mm thick steel plate (k = 48

W/m C) having a uniform volumetric heat generation of 30 × 106 W/m3 are 180 C and 120 C, Neglecting the end effects, determine the following: (i) The temperature distribution across the plate: (ii) The value and position of the maximum temperature, and (iii) The flow of heat from each surface of the plate.

( 8.66 mm, 203oC, 259800 W/m2 ) 3 A plate wall is 1 m thick and it has one surface insulated while the other

surface is maintained at a constant temperature of 350o C. The thermal conductivity of wall is 25 W/m C and uniform heat generation per unit volume of 500 w/m3 exists throughout the wall Determine the maximum temperature in the wall and the location of the plane where it occurs. ( 0, 360oC )

4 A 2 cm thick steel plate of thermal conductivity 50 W/moC has a uniform volumetric heat generation of 40 x 10+6 W/m3. The temperature at one surface of the plate is 160oC and the other is 100oC. Find out value and position of the maximum temperature. Ans ; 0.00625m, Tmax = 175.6oC

5 A plan wall 90 mm thick (k =0.18 W/m C) is insulated on one side while the other side is exposed to environment at 80 C. The rate of heat generation within the wall is 1.3 × 105 W/m3. If the convective heat transfer coefficient is 520 W/m2C, determine the maximum temperature to which the wall will be subjected. ( 3027oC )

FIN

1 A longitudinal copper fin (k = 380 W/m°C) 600 mm long and 5 mm diameter is exposed to air stream at 20°C. The convective heat transfer coefficient is 20 W/m2°C. If the fin base temperature is 150°C, determine: (i) The heat transferred, and

(ii) The efficiency of the fin. Neglect heat loss from the fin tip.

( 22.6kJ/hr, 25.6% ) 2 A steel rod (k = 32 W/m°C), 12 mm in diameter and 60 mm long with an

insulated end. It is exposed to surrounding with a temperature of 60°C and a heart transfer coefficient of 55 W/m2C. The temperature at the base of fin is 95°C. Determine: (i) The fin efficiency

(ii) The temperature at the edge. (iii) The heat dissipation.

( 62.2%, 75oC, 2.7W ) 3 A mercury thermometer placed in oil well is rewired to measure

temperature of compressed air flowing in a pipe. The well is 140 mm long and is made of steel (k = 50 W/m°D) of 1mm thickness. The temperature recurred by the well is 100°C while pipe wall temperature is 52°C. Heat

transfer coefficient between the air and well wall is 30 W/m2C. Estimate true temperature of air. ( 103.5oC )

4 A steel rod ( k = 30 W/moC ) 1 cm in diameter and 5 cm long protrudes from a wall which is maintained at 100oC. The rod is insulated at its tip and is exposed to an environment ( h = 50 W/m2C ) of temperature 30oC. Calculate the fin efficiency, temperature at tip of fin and the rate of heat dissipation Ans : m = 25.8, 66.5%, 65.7o C, 3.7 W

5 Which of the following arrangement of pin fins will give higher heat transfer rate from a hot surface? 6 fins of 10 cm length. 12 fins of 5 cm length. The base temperature of the fin is maintained at 200oC and the fin is exposed to a convective environment at 15oC with convection coefficient 25 W/m2°C. Each fin has cross section area 2.5 cm2, perimeter 5 cm and is made of a material having thermal conductivity 250 W/m°C Neglect the heat loss from the tip of fin.

UNSTEADY STATE ( TRANSIENT ) HEAT CONDUCTION

1 A 50 cm x 50 cm copper slab 6.25 mm thick has a uniform temperature of 300°C. Its temperature is suddenly lowered to 36°C. Calculate the time required for the plate to reach the temperature of 108°C.

Take:

= 9000 kg/m3; c = 0.38 kJ/kg° C;

k =370 W/m°C h = 90 W/m2°C ( 154 s, Bi= 7.6 * 10-4 )

2 An aluminum alloy plate of 400 mm x 400 mm x 4 mm size at 200°C is suddenly quenched into liquid oxygen at -183° C. Starting from fundamentals or deriving the necessary expression determine the required time to reach a temperature of plate at 71°C. Assume h =20000 kJ/m2-h-°C, cp = 0.8 kJ/kg °C and = 3000 kg/m3. ( 1.05oC, Bi = 0.052 )

3 A solid copper sphere of 10 cm diameter [ = 8954 kg/m3, cp = 383 J/kg K, k= 386 W/m K] initially at a uniform temperature of 250o C, is suddenly

immersed in a fluid which is maintained at a uniform temperature of 50°C. The heat transfer coefficient between the sphere and the fluid is 200 W/m2

K. Determine the temperature of the copper block after 5 min after the immersion. ( Bi = 8.64 *10-3, 120oC )

4 An average convective heat transfer coefficient for flow of 90°C air over a flat plate is measured by observing the temperature time history of 40 mm thick copper slab initial temperature of the plate was 200°C, and in 4.5 minutes the temperature decreased by 35°C, Find heat transfer coefficient for this case. Neglect internal thermal resistance. ( 96.9 W/m2k )

5 The heat transfer coefficients for the flow of air at 28° C over 12.5 mm diameter sphere are measured by observing the temperature- time history of a copper ball of the same dimension the temperature of copper ball (c = 0.4 kJ/kg K and = 8850 kg /m3) was measured by two thermocouples, one located in the center and other near the surface. Both the thermocouples registered the same temperature at a given instant. In one test the initial temperature of the ball was 65° C and in 1.15 minute the temperature decreased by 11°C. Calculate the heat transfer coefficient for this in 1.15 minute the temperature decreased by 11° C, Calculate the heat transfer coefficient for this case. ( 37.7 W/m2k )

6 The flow rates of hot and cold water stems running through a parallel flow heat exchanger are 0.2kg/s and 0.5 kg/s respectively. The inlet temperatures on the hot and cold sides are 75°C and 20°C respectively. The exit temperature of hot water is 45°C. If the individual heat transfer coefficients on both sides are 650W/m2°C, calculate the heat exchanger.

HEAT EXCHANGER

1 The following data relate to a parallel flow heat exchanger in which air is heated by hot exhaust gases. Heat transferred per hour =155450kJ Inside heat transfer coefficient=120W/m2°C Outside heat transfer coefficient=195 W/m2C. Inlet and outlet temperatures of the hot fluid respectively=450°C and 250°C Inlet and outlet temperatures of the hot fluid respectively=60°C and 120°C Calculate the length of the tube required for the necessary heat transfer to

occur, Neglect the tube resistance. ( 14.65 M )

2 In a certain double pipe heat exchanger hot water flows at a rate of 50000 kg/h and gets cooled from 95°C to 65°C. At the same time 50000 kg/h of cooling water at 30°C enters the heat exchanger. The flow conditions are such that overall heat transfer coefficient remains constant at 2270 W/m2 k. Determine the heat transfer area required and the effectiveness. Assume two streams are in parallel flow and for both the streams cp= 4.2 kJ/kg K. ( 33 m2, 0.46 )

3 In a counter –flow double pipe heat exchanger, water is heated from 25°C to 65°C by oil with a specific heat of 1.45 kJ/kg K and mass flow rate of 0.9kg/s .The oil is cooled from 230°C to 160°C. If the overall j\heat transfer coefficient is 420 W/m2°C, calculate the following :

(i) The rate of heart transfer, (ii) The mass flow rate of water, and

(iii) The surface area of the hat exchanger. ( 91.4 kJ/s, 0.545 kg/s, 1.45 m2 )

4 An oil cooler for a lubrication system has to cool 1000 kg/h oil (cp = 2.09 kJ/kg °C) From 80°C to 40°C by using a cooling water flow of 1000kg/h at 30°C. Give your choice for a parallel flow or counter-flow heat exchanger, with reasons Calculate the surface area of the heat exchanger if the over all heat transfer coefficient is 24 W/m2°C. Take up cp of water = 4.18 kJ/kg°C. ( 53.2 m2 )

5 A counter-flow double pipe heat exchanger using superheated stem is used to heat water at the rate of 10500 kg/h. The steam enters the heat exchanger at 180oC and leaves at 130oC. The inlet and exit temperatures of water are 30°C and 80°C respectively. If overall heat transfer coefficient from stem to water is 814 W/m2°C. Calculate the heat transfer area. What would be the increase in area if the fluids flows were parallel? ( 7.5 m2, 8.24 m2, 9.87% )

6 The following data pertain to an oil cooler of the from tubular exchanger where oil is cooled by a large pool of stagnant water.

Temperature of stagnant water =20°C (assumed accountant), Inlet and outlet temperatures of oil =80°C and 30°C, Respectively, Inside diameter and length of the tube carrying oil=20 mm and 30m, respectively,

Specific heat and specific gravity of oil =2.5kJ/kg°C and 0.85 respectively, Average velocity of oil =0.55m/s Calculate the overall heat transfer coefficient obtainable from the system.

( 349 W/m2k ) 7 Stem at atmospheric pressure enter this shell of a surface condenser in

which the water flows though a bundle of tubes of diameter 25 mm at the rate of 0.05 kg/s. The inlet and outlet temperatures of water are 15°C and 70°C, respectively. The condensation of stem takes place on the outside surface of the tube .if the overall heat transfer coefficient is 230W/m2°C. Calculate the following, using NTU method (i) The effectiveness of the heat exchanger, (ii) The length of the tube, and

(iii) The rate of steam condensation. Take the latent heat of vaporization at 100°C=2257kJ/kg

( 0.65, 12 m, 18.3kg/hr ) 8 A counter-flow heat exchanger is employed to cool0.55 kg/s (cp = 2.45

kJ/kg°C) of oil from 115° C to 40°C by the use of water. The inlet and outlet temperatures of cooling water are 15°C and 75°C, respectively. The overall heat transfer coefficient is expected to be 1450 W/m2°C. Using NTU method, Calculate the following:

(i) The mass flow rate of water. (ii) The effectiveness of the heat exchanger; (iii) The surface area required ( 0.4kg/s , 0.75 , 2.2 m2 )

9 16.6kg/s of the product at 650°C (c=3.55 kJ/kg °C). In the overall heat transfer coefficient is 0.95 kW/m2°C and the installed heat transfer surface is 44m2, calculate the fluid outlet temperatures for the counter- flow and parallel flow arrangements. ( 265.8oC , 255.4oC )

10 The following data is given for counter-flow heat exchanger : mh = 1kg/s; mc = 0.25kg/s cph = 1.045 kJ/kg°C; cpc = 4.18kJ/kg°C

th1 = 1000°C tc2 =850°C;U =88.5 W/m2°C; A=10m2 Calculate th2 and tc1

( 867oC , 717oC ) 11 Water (cpc = 4200 J/kg°C) enter a counter-flow double pipe heat

exchanger at 38°C flowing at 0.076 kg/s. It is heated by oil (cP = 1880J/kg°C) flowing at the rate of 0.152kg/s from an inlet temperature of 116°C. For an area of 1m2 and U=340 W/m2°C, determine the total heat transfer rate. ( 13.3 kW )

12 Two fluids, A and B exchange heat in a counter heat exchanger fluid a enter at 420°C and has a mass flow rate 1 kg/s .Fluid B enter at 20°C and has a mass flow rate of 1 kg/s. Effectiveness of heat exchanger is 75%.

Determine (i) The heat transfer rate;

(ii) The exit temperature of fluid B. Specific heat of fluid A is 1 kJ/kg K and that of fluid B is 4kJ/Kg K. ( 300 kJ, 95oC )

13 A counter flow heat exchanger is to heat air entering at 400°C With a flow rate 6kg/s by the exhaust gas entering at 800°C with a flow rate of 4kg/s. The overall heat transfer coefficient is 100W/m2 k and the outlet temperature of the air is 551.5°C Specific heat at constant pressure for

both air and exhaust gas can be taken as 1100J/kg K. Calculate: (i) The heat transfer area needed; (ii) The number of transfer units. ( 48 m2, 1.09 )

14 A chemical having specific heat of 3.3 kJ/kg K flowing at the rate of 20000 kg/h enters a parallel flow heat exchanger at 120°C.The flow rate of cooling water is 50000 kg/h with an inlet temperature of 20°C. the heat transfer area is 10 m2 and the overall heat transfer coefficient is 1050 W/m2 K. Find :

(i) The effectiveness of the heat exchanger. (ii) The outlet temperature of water and chemical.

Take for water, specific heat = 4.186 kJ/kg K. ( 0.402, 32.7oC )

15 A counter-flow double pipe heat exchanger using superheated steam is used to heat water at the rate of 10500 kg/h. The steam enters the heat exchanger at 180oC and leaves at 130oC. The inlet and exit temperatures of water are 30°C and 80°C respectively. If overall heat transfer coefficient from steam to water is 814 W/m2°C. Calculate the heat transfer area. What would be the increase in area if the fluids flows were parallel?

Ans : 7.5 m2, 8.24 m2, 9.87%

FORCE CONVECTION

1 Air at 25o C flows over a flat plate at 3 m/s. The plate temperature is 100o

C with 30 cm x 60 cm size. Find the heat loss if air flow is parallel to 60 cm side of the plate. If 30 cm side is kept parallel to the air flow, what will be effect on heat transfer? The convective heat transfer in above case is describe by equation: Nux = 0.332 Pr1/3 Rex

1/2

Take following properties of air at mean temperature: = 1.06 kg/m3; cp = 1.005 kJ/kg° C; Pr = 0.696

k = 0.028 W/m°C ν = 18.97 x 10-6 m2/s 2 A flat plate 2 m wide and 3 m long is to be maintained at 100oC in air with

a free stream temperature of 10oC. Determine velocity at which the air must flow over the flat plate so that rate of energy dissipation from the plate is 4.0 kW. Assume that the flow over the plate is turbulent and it experiences the transition from laminar to turbulent flow at Recritical = 5 x 105 Use : Nul = ( 0.036 Rel

4/5 - 836 ) pr1/3

Take following properties of air at mean temperature: = 1.0877 kg/m3; cp = 1.007 kJ/kg° C; Pr = 0.703 k = 0.02813 W/m°C mu = 2.029 x 10-5 kg/ms

NATURAL CONVECTION 1 A hot square plate 40 cm x 40 cm at 100oC is exposed to atmospheric air

at 20oC. Find heat loss from both surface of the plate if (a) Plate is kept vertical (b) Plate is kept horizontal. The following empirical correlation have been suggested : Nu = 0.125 ( Gr Pr )0.33 for vertical position of the plate. Nu = 0.72 ( Gr Pr )0.25 for upper surface. Nu = 0.35 ( Gr Pr )0.25 for lower surface. Air properties at mean temperature are : = 1.06 kg/m3; cp = 1.008 kJ/kg° C;

k = 0.028 W/m°C ν = 18.96 x 10-6 m2/s Ans : 141 W, 126.5 W

RADIATION 1 Determine heat loss per meter length by radiation from a steel tube of

diameter 10 cm and length very large at a temperature 430oC if : (i) it is located in a large room with red brick wall at temperature of

25oC (ii) it is enclosed in a 30 cm x 30 cm red brick conduit at 25oC.

The emissivity of steel tube is 0.8 and emissivity of red brick is 0.93. 2 Assuming an industrial furnace as black body at 3500oC emitting the

energy by radiation, calculate:

(i) Monochromatic emissive power at 1.3 m length (ii) Wave length at which the emission is maximum (iii) Maximum emissive power (iv) Total emissive power

(v) Total emissive power if furnace is a real surface with emissivity is 0.8 3 For a hemispherical furnace, the flat floor is at 1000o K and has emissivity

of 0.5. The hemispherical roof is at 2000o K and has emissivity of 0.25. Find the net radiative heat transfer from roof to floor.

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