EXTERNAL FORCED CONVECTION 1. Flow of Hot Oil over a Flat Plate: Engine oil at 60 0C flows over the upper surface of a 5-m-long flat plate whose temperature is 20 0C with a velocity of 2 m/s. Determine the total rag force an the rate of heat transfer per unit with of the entire plate.
2. Prevention of Fire Hazard in the Event of Oil Leaa!e: !eat issipate from an engine in operation can cause hot spots on its surface. "f the outer surface of an engine is situate in a place where oil lea#age is possi$le% then when lea#e oil comes in contact with hot spots a$ove the oil&s auto ignition temperature% it can ignite spontaneously. Consier an engine cover that is mae of a stainless steel plate with a thic#ness of 1 cm an a thermal conuctivity of 1' (/m)*. +he stainless steel plate is covere with a 5-mm-thic# insulation insulation ,k 0.5 (/m)*. +he inner surface of the engine cover is epose to hot air at 50 0C with a convection heat transfer coefficient of (/m2)* ,ig. +he 2-m-long engine outer surface is coole $y air $lowing in parallel over it at m/s% in an environment where the am$ient air is at 60 0C. +o prevent fire ha3ar in the event of oil lea# on the engine cover% the engine cover surface shoul $e #ept $elow 1404C. "t has $een etermine that the 5-mm-thic# insulation layer is not sufficient to #eep the engine cover surface $elow 1400C. +o solve this pro$lem% one of the plant s upervisors suggeste austing the $lower capacity to provie an increase in the cooling air velocit y $y 10. Determine if this is a via$le metho for #eeping the engine cover surface $elow 140 0C. Evaluate the air properties at 120 0C.
. Coolin! of Pla"ti# $heet" %& For#ed Air: +he forming section of a plastics plant puts out a continuous sheet of plastic that is ' ft wie an 0.0' in thic# at a velocity velocity of 0 ft/min. +he temperature temperature of the plastic 0 sheet is 200 when it is epose to the surrouning air% an a 2-ft-long section of the plastic sheet is su$ecte to air flow at 40 0 at a velocity of 10 ft/s on $oth sies along its surfaces normal to the irection of motion of the sheet% as shown in fig. Determine , a the rate of heat transfer from the plastic sheet to air $y force convection an raiation an , b the temperature of the plastic sheet at the en of the cooling section. +a#e the ensity% specific heat% an emissivity of the plastic sheet to $e r 5 l$m/ft% cp 0.' 7tu/l$m0% an e 0.8.
'. Dra! For#e A#tin! on a Pi'e in a River: 9 2.2-cm-outer-iameter 2.2-cm-outer-iameter pipe is to span s pan across a river at a 0-mwie section while $eing completely immerse immerse in water ,ig+he ,ig+he average flow velocity velocity of water is ' m/s 0 an the water temperature is 15 C. Determine the rag force eerte on the pipe $y the river.
5. Heat Lo"" fro( a $tea( Pi'e in )ind& Air: 9 long 10-cm-iameter steam pipe whose eternal surface temperature is 110 0C passes through some open area that is not protecte against the wins ,ig. Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure an 10 0C an the win is $lowing across the pipe at a velocit y of 4 m/s.
*+ Coolin! of a $teel ,all %& For#ed Air: 9 25-cm-iameter stainless steel $all ,r 4055 #g/m% cp '40 :/#g.* is remove from the oven at a uniform temperature of 00 0C ,ig. +he $all is then su$ecte to the flow of air at 1 atm pressure an 25 0C with a velocity of m/s. +he surface temperature of the $all eventually rops to 200 0C. Determine the average convection heat transfer coefficient uring this cooling process an estimate how long the process will ta#e.
. "n an inustrial facility% air is to $e preheate $efore entering a furnace $y geothermal water at 120 0C flowing through the tu$es of a tu$e $an# locate in a uct. 9ir enters the uct at 20 0C an 1 atm with a mean velocity of '.5 m/s% an flows over the tu$es in normal irection. +he outer iameter of the tu$es is 1.5 cm% an the tu$es are arrange in-line with longituinal an transverse pitches of S L S T 5 cm. +here are 6 rows in the flow irection with 10 tu$es in each row% as shown in ig. Determine the rate of heat transfer per unit length of the tu$es% an the pressure rop across the tu$e $an#.
4. 9ir at 250C an 1 atm is flowing over a long flat plate with a velocity of 4 m/s. Determine the istance from the leaing ege of the plate where the flow $ecomes tur$ulent% an the thic#ness of the $ounary layer at that location.,$repeat for water 8. 9ir at 150C an 1 atm flows over a 0.-m-wie plate at 65 0C at a velocity of .0 m/s. Compute the following ;uantities at x 5 0. m< ,a !yroynamic $ounary layer thic#ness% m ,b =ocal friction coefficient
,c 9verage friction coefficient ,d +otal rag force ue to friction% > ,e =ocal convection heat transfer coefficient% (/m 2* , f 9verage convection heat transfer coefficient% (/m 2* , g ?ate of convective heat transfer% ( 10. Engine oil at 400C flows over a 10-m-long flat plate whose temperature is 0 0C with a velocity of 2.5 m/s. Determine the total rag force an the rate of heat transfer over the entire plate per unit with. 11. 9ir at 60eg flows over a 10-ft-long flat plate at ft/s. Determine the local friction an heat transfer coefficients at intervals of 1 ft% an plot the results against the istance from the leaing ege. 12. !ot car$on ioie ehaust gas at 1 atm is $eing coole $y flat plates. +he gas at 220 0C flows in parallel over the upper an lower surfaces of a 1.5-m-long flat plate at a velocity of m/s. "f the flat plate surface temperature is maintaine at 40 0C% etermine ,a the local convection heat transfer coefficient at 1 m from the leaing ege% ,b the average convection heat transfer coefficient over the entire plate% an , c the total heat flu transfer to the plate. 1. 9 transformer that is 10 cm long% 6.2 cm wie% an 5 cm high is to $e coole $y attaching a 10-cm @ 6.2cm-wie polishe aluminium heat sin# ,emissivity 0.0 to its top surface. +he heat sin# has seven fins% which are 5 mm high% 2 mm thic#% an 10 cm long. 9 fan $lows air at 25 0C parallel to the passages $etween the fins. +he heat sin# is to issipate 12 ( of heat an the $ase temperature of the heat sin# is not to ecee 600C. 9ssuming the fins an the $ase plate to $e nearly isothermal an the raiation heat transfer to $e negligi$le% etermine the minimum free-stream velocity the fan nees to supply to avoi overheating. 9ssume the flow is laminar over the entire finne surface of the transformer.
1'. Consier a refrigeration truc# traveling at 55 mph at a location where the air temperature is 40 0. +he refrigerate compartment of the truc# can $e consiere to $e a 8-ft-wie% 4-ft-high% an 20-ft-long rectangular $o. +he refrigeration system of the truc# can provie tons of refrigeration ,i.e.% it can remove heat at a rate of 600 7tu/min. +he outer surface of the truc# is coate with a low-emissivity material% an thus raiation heat transfer is very small. Determine the average temperature of the outer surface of the refrigeration compartment of the truc# if the refrigeration system is o$serve to $e operating at half the capacity. 9ssume the air flow over the entire outer surface to $e tur$ulent an the heat transfer coefficient at the front an rear surfaces to $e e;ual to that on sie surfaces. or air properties evaluations assume a film temperature of 40 0. "s this a goo assumptionA
15. 9ir at 1 atm an 20 0C is flowing over the top surface of a 0.5-m-long thin flat plate. +he air stream velocity is 50 m/s an the plate is maintaine at a constant surface temperature of 140 0C. Determine ,a the average friction coefficient% ,b the average convection heat transfer coefficient% an , c repeat part ,b using the moifie ?eynols analogy.
16. +he local atmospheric pressure in Denver% Colorao ,elevation 1610 m% is 4.' #Ba. 9ir at this pressure an at 00C flows with a velocity of 6 m/s over a 2.5-m 4-mflat plate whose temperature is 120 0C. Determine the rate of heat transfer from the plate if the air flows parallel to the , a 4-m-long sie an ,b the 2.5 m sie. 1. During a col winter ay% win at 55 #m/h is $lowing parallel to a '-m-high an 10-m-long wall of a house. "f the air outsie is at 5 0C an the surface temperature of the wall is 12 0C% etermine the rate of heat loss from that wall $y convection. (hat woul your answer $e if the win velocity was ou$leA 14. =i;ui mercury at 2500C is flowing in parallel over a flat plate at a velocity of 0. m/s. urface temperature of the 0.1-m-long flat plate is constant at 50 0C. Determine ,a the local convection heat transfer coefficient at 5 cm from the leaing ege an , b the average convection heat transfer coefficient over the entire plate. 18. +he upper surface of a metal plate is $eing coole with parallel air flow while its lower surface is su$ecte to a uniform heat flu of 410 (/m2. +he air has a free stream velocity an temperature of 2.5 m/s an 15 0C% respectively. Determine the surface temperature of the plate at x 1.5 m from the leaing ege. Hint: +he surface temperature has to $e foun iteratively. tart the iteration process with an initial guess of '5 0C for the surface temperature.
20. 9 long 4-cm-iameter steam pipe whose eternal surface temperature is 80 0C passes through some open area that is not protecte against the wins. Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure an 0C an the win is $lowing across the pipe at a velocity of 50 #m/h. 21. 9 heate long cylinrical ro is place in a cross flow of air at 20 0C ,1 atm with velocity of 10 m/s. +he ro has a iameter of 5 mm an its surface has an emissivity of 0.85. "f the surrouning temperature is 204C an the heat flu issipate from the ro is 16000 (/m2% etermine the surface temperature of the ro. Evaluate the air properties at 0 0C. 22. "n a geothermal power plant% the use geothermal water at 40 0C enters a 15-cm-iameter an '00-m-long uninsulate pipe at a rate of 4.5 #g/s an leaves at 0 0C $efore $eing reinecte $ac# to the groun. (iny air at 150C flows normal to the pipe. Disregaring raiation% etermine the average win velocity in #m/h.
2 Consier a 50-cm-iameter an 85-cm-long hot water tan#. +he tan# is place on the roof of a house. +he water insie the tan# is heate to 40 0C $y a flat-plate solar collector uring the ay. +he tan# is then epose to winy air at 140C with an average velocity of '0 #m/h uring the night. Estimate the temperature of the tan# after a '5-min perio. 9ssume the tan# surface to $e at the same temperature as the
water insie% an the heat transfer coefficient on the top an $ottom surfaces to $e the same as that on the sie surface. Evaluate the air properties at 50 0C. 2' 9 stainless steel $all ,r 4055 #g/m% cp '40 :/#g.* of iameter D 15 cm is remove from the oven at a uniform temperature of 50 0C. +he $all is then su$ecte to the flow of air at 1 atm pressure an 0 0C with a velocity of 6 m/s. +he surface temperature of the $all eventually rops to 250 0C. Determine the average convection heat transfer coefficient uring this cooling process an estimate how long this process has ta#en. 25 9 0.2 m @0.2 m street sign surface has an a$sorptivity of 0.6 an an emissivity of 0.% while the street sign is su$ecte to a cross flow win at 20 0C with a velocity of 1 m/s. olar raiation is incient on the street sign at a rate of 1100 (/m 2% an the surrouning temperature is 20 0C. Determine the surface temperature of the street sign. Evaluate the air properties at 0 0C. +reat the sign surface as a vertical plate in cross flow.
26 9 coate sheet is $eing rie with hot air $lowing in cross flow on the sheet surface. +he surface temperature of the sheet is constant at 80 0C% while the air velocity an temperature are 0. m/s an 110 0C% respectively. +he length of the sheet su$ecte to the $lowing hot air is 1 m long. Determine the convection heat transfer coefficient an the heat flu ae to the sheet surface. +reat the coate sheet as a vertical plate in cross flow.
FORCED INTERNAL CONVECTION -+ Heatin! of )ater in a T.%e %& $tea(: (ater enters a 2.5-cm-internal-iameter thin copper tu$e of a heat echanger at 150C at a rate of 0. #g/s% an is heate $y steam conensing outsie at 120 0C. "f the average heat transfer coefficient is 400 (/m 2*% etermine the length of the tu$e re;uire in orer to heat the water to 1150C
2. Avera!e Velo#it& and Te('erat.re in La(inar T.%e Flow: +he velocity an temperature profiles for a flui flowing in a circular tu$e of inner raius R ' cm are given as u,r 0.21- ,r / R2 ,in m/s+ T ,r 250F1200,r / R ,in * Determine the average flow velocity an the average flui temperature in the tu$e.
. Flow of Oil in a Pi'eline thro.!h a Lae: Consier the flow of oil at 20 0C in a 0-cm-iameter pipeline at an average velocity of 2 m/s . 9 200-m-long section of the hori3ontal pipeline passes through icy waters of a la#e at 00C. Geasurements inicate that the surface temperature of the pipe is very nearly 0 0C. Disregaring the thermal resistance of the pipe material% etermine , a the temperature of the oil when the pipe leaves the la#e% ,b the rate of heat transfer from the oil% an , c the pumping power re;uire to overcome the pressure losses an to maintain the flow of the oil i n the pipe.
'. Pre"".re Dro' in a )ater T.%e: (ater at 604 ,r 62.6 l$m/ft an H .56@ 10 I' l$m/fts is flowing steaily in a 2-in-internal-iameter hori3ontal tu$e mae of stainless steel at a rate of 0.2 ft /s. Determine the pressure rop an the re;uire pumping power input for flow through a 200-ft-long section of the tu$e.
5. Heatin! of )ater %& Re"i"tan#e Heater" in a T.%e: (ater is to $e heate from 15 0C to 65 0C as it flows through a -cm-internaliameter 5-m-long tu$e. +he tu$e is e;uippe with an electric resistance heater that provies uniform heating throughout the surface of the tu$e. +he outer surface of the heater is well insulate% so that in steay operation all the heat generate in the heater is transferre to the water in the tu$e. "f the system is to provie hot water at a rate of 10 =/min% etermine the power rating of the resistance heater. 9lso% estimate the inner surface temperature of the tu$e at the eit.
*+ Pi'e In".lation for Ther(al ,.rn Prevention: 9 10-m-long metal pipe ,k pipe 15 (/m)* has an inner iameter of 5 cm an an outer iameter of 6 cm is use for transporting hot saturate water vapor at a flow rate of 0.05 #g/s. +he water vapor enters an eits the pipe at 50JC an 280JC% respectively. "n orer to prevent thermal $urn on iniviuals wor#ing in the vicinity of the pipe% the pipe is covere with a 2.25-cm thic# layer of insulation ,k ins 0.85 (/m)* to ensure that the outer surface temperature Ts,o is $elow '5JC. Determine whether or not the thic#ness of the insulation is sufficient to alleviate the ris# of thermal $urn ha3ars.
. Heat Lo"" fro( the D.#t" of a Heatin! $&"te(: !ot air at atmospheric pressure an 40 0C enters an 4-mlong uninsulate s;uare uct of cross section 0.2 m @ 0.2 m that passes through the attic of a house at a rate of 0.15 m /s . +he uct is o$serve to $e nearly isothermal at 60 0C. Determine the eit temperature of the air an the rate of heat loss from the uct to the attic space.
4. +he velocity profile in fully evelope laminar flow in a circular pipe of inner raius R 10 cm% in m/s% is given $y u,r ',1 - r 2/ R2. Determine the mean an maimum velocities in the pipe% an the volume flow rate.
8. Consier a 25-mm-iameter an 15-m-long smooth tu$e that is use for heating fluis. +he wall is heate electrically to provie a constant surface heat flu along the entire tu$e. luis enter the tu$e at 50 0C an eit at 150 0C. "f the mass flow rate is maintaine at 0.01 #g/s% etermine the convection heat transfer coefficients at the tu$e outlet for water% engine oil% an li;ui mercury. 10. Consier a 25-mm-iameter an 15-m-long smooth tu$e that is maintaine at a constant surface temperature. luis enter the tu$e at 50 0C with a mass flow rate of 0.01 #g/s. Determine the tu$e surface temperatures necessary to heat water% engine oil% an li;ui mercury to the esire outlet temperature of 1500C. 11. (ater at 150C is flowing through a 200-m-long stanar 1-in cheule '0 cast iron pipe with a mass flow rate of 0.5 #g/s 12. "f accuracy is an important issue% use the appropriate e;uation to etermine , a the pressure loss an ,b the pumping power re;uire to overcome the pressure loss. 9ssume flow is fully evelope. "s this a goo assumptionA 1. Consier a 10-m-long smooth rectangular tu$e% with a 50 mm an b 25 mm% that is maintaine at a constant surface temperature. =i;ui water enters the tu$e at 20 0C with a mass flow rate of 0.01 #g/s. Determine the tu$e surface temperature necessary to heat the water to the esire outlet temperature of 400C.
1'. Consier the flow of oil at 10 0C in a '0-cm-iameter pipeline at an average velocity of 0.5 m/s. 9 1500-mlong section of the pipeline passes through icy waters of a la#e at 0 0C. Geasurements inicate that the surface temperature of the pipe is very nearly 0 0C. Disregaring the thermal resistance of the pipe material% etermine ,a the temperature of the oil when the pipe leaves the la#e% , b the rate of heat transfer from the oil% an ,c the pumping power re;uire to overcome the pressure losses an to maintain the flow of oil in the pipe. 15. =i;ui glycerin is flowing through a 25-mm-iameter an 10-m-long tu$e. +he li;ui glycerine enters the tu$e at 200C with a mass flow rate of 0.5 #g/s. "f the outlet mean temperature is '0 0C an the tu$e surface temperature is constant% etermine the surface temperature of the tu$e. 16. 9ir at 100C enters a 12-cm-iameter an 5-m-long pipe at a rate of 0.065 #g/s. +he inner surface of the pipe has a roughness of 0.22 mm% an the pipe is nearly isothermal at 50 0C. Determine the rate of heat transfer to air using the >usselt num$er relation given $y , a E;. 4I66 an ,b E;. 4I1. Evaluate air properties at a $ul# mean temperature of 200C. "s this a goo assumptionA 1. 9 10-m-long an 10-mm-inner-iameter pipe mae of commercial steel is use to heat a li;ui in an inustrial process. +he li;ui enters the pipe with +i 25 0C% K 0.4 m/s. 9 uniform heat flu is maintaine $y an electric resistance heater wrappe aroun the outer surface of the pipe% so that the flui eits at 5 0C. 9ssuming fully evelope flow an ta#ing the average flui properties to $e r 1000 #g/m% cp '000 :/#gA*% H 2 @ 102 #g/ms% # 0.'4 (/m*% an Br 10% etermine< ,a +he re;uire surface heat flu ;s% prouce $y the heater ,$ +he surface temperature at the eit% +s ,c +he pressure loss through the pipe an the minimum power re;uire to overcome the resistance to flow. 14. 9ir ,1 atm enters into a 5-cm-iameter circular tu$e at 20 0C with an average velocity of 5 m/s. +he tu$e wall is maintaine at a constant surface temperature of 160 0C% an the outlet mean temperature is 40 0C. Estimate the length of the tu$e. 18. 9n 4-m-long% uninsulate s;uare uct of cross section 0.2 m@ 0.2 m an relative roughness 10- passes through the attic space of a house. !ot air enters the uct at 1 atm an 40 0C at a volume flow rate of 0.15 m/s. +he uct surface is nearly isothermal at 60 0C. Determine the rate of heat loss from the uct to the attic space an the pressure ifference $etween the inlet an outlet sections of the uct. Evaluate air properties at a $ul# mean temperature of 40 0C. "s this a goo assumptionA 20. !ot air at 60 0C leaving the furnace of a house enters a 12-m-long section of a sheet metal uct of rectangular cross section 20 cm @ 20 cm at an average velocity of ' m/s. +he thermal resistance of the uct is negligi$le% an the outer surface of the uct% whose emissivity is 0.% is epose to the col air at 10 0C in the $asement% with a convection heat transfer coefficient of 10 (/m 2*. +a#ing the walls of the $asement to $e at 100C also% etermine ,a the temperature at which the hot air will leave the $asement an ,$ the rate of heat loss from the hot air in the uct to the $asement. Evaluate air properties at a $ul# mean temperature of 500C. "s this a goo assumptionA 21. 9 concentric annulus tu$e has inner an outer iameters of 25 mm an 100 mm% respectively. =i;ui water flows at a mass flow rate of 0.05 #g/s through the annulus with the inlet an outlet mean temperatures of 200C an 400C% respectively. +he inner tu$e wall is maintaine with a constant surface temperature of 1200C% while the outer tu$e surface is insulate. Determine the length of the concentric annulus tu$e. 9ssume flow is fully evelope.
22. =i;ui water flows at a mass flow rate of 0. #g/s through a concentric annulus tu$e with the inlet an outlet mean temperatures of 20 0C an 40 0C% respectively. +he concentric annulus tu$e has inner an outer iameters of 10 mm an 100 mm% respectively. +he inner tu$e wall is maintaine with a constant surface
temperature of 120 0C% while the outer tu$e surface is insulate. Determine the length of the concentric annulus tu$e.
