Waterflowsthroughashowerheadsteadily atarateof10L/min.Anelectricresistance heaterplacedinthewaterpipeheatsthe water from 16Cto4C. !a"ing the density ofwaterto#e1"g/L$determinetheelectric power input to the heater$ in "W. %n an effort toconser&eenergy$itisproposedtopassthe drained warm water at a temperature of 'C throughaheate(changertopreheatthe incomingcoldwater.%ftheheate(changer hasaneffecti&enessof0.)0*thatis$it reco&ersonlyhalfoftheenergythatcan possi#ly#etransferredfromthedrained water toincomingcold water+$ determinethe electricpowerinputre,uiredinthiscase.%f the price of the electric energy is -.) .s/"Wh$ determine how much money is sa&ed during a 10/minute shower as a result of installing this heat e(changer.Properties !he density and specific heat of water at room temperature are 0 1 1 "g/L and C 1 4.1- "2/"g3CAnswers: 18.8 kW, 10.8 kW, 11.3 Rs%t is well "nown that wind ma"es the cold air feel much colder as a result of the wind-chill effect that is due to the increase in the con&ection heat transfer coefficientwithincreasingair&elocity.!hewind/chilleffectisusually e(pressedintermsofthewind-chillfactor,whichisthedifference#etween theactualairtemperatureandthee,ui&alentcalm/airtemperature.4or e(ample$awind/chillfactorof50Cforanactualairtemperatureof)C means that the windy air at )C feels as cold as the still air at 1)C. %n other words$ a person will lose as much heat to air at )C with a wind/chill factor of 50C as he or she would in calm air at 1)C. 4or heat transfer purposes$ a standingmancan#emodeledasa0/cm/diameter$160/cm/long&ertical cylinderwith#oththetopand#ottomsurfacesinsulatedandwiththeside surfaceatana&eragetemperatureof4C.4oracon&ectionheattransfer coefficient of 1) W/m5 3 C$ determine the rate of heat loss from this man #y con&ection in still air at 50C. What would your answer #e if the con&ection heattransfercoefficientisincreasedto)0W/m53Casaresultofwinds7 What is the wind/chill factor in this case7 Answers: 336 W, 1120 W, 32.7CA 0.5/L glass of water at 50C is to #e cooled with ice to )C. 8etermine how much ice needs to #e added to the water$ in grams$ if the ice is at 0C. Also$ determine how much water would #e needed if the cooling is to #e done with cold water at 0C. !he meltingtemperatureandtheheatoffusionoficeatatmosphericpressureare0C and .6 "2/"g$ respecti&ely$ and the density of water is 1 "g/L.9lot the amount of ice that needs to #e added to the water as a function of the ice temperature in the range of 54C to 0C.Answers: 35.4 gms, 600 gmsAsphericalmetal#allofradiusr0isheatedinano&entoatemperatureofTi throughout and is then ta"en out of the o&en and dropped into a large #ody of water at Twhereitiscooled#ycon&ectionwithana&eragecon&ectionheattransfer coefficientofh.Assumingconstantthermalconducti&ityandtransientone/dimensionalheattransfer$e(pressthemathematicalformulation*thedifferential e,uation and the #oundary and initial conditions+ of this heat conduction pro#lem. 8o not sol&e.Waterflowsthroughapipeatana&eragetemperatureofT1)0C.!heinnerand outer radii of the pipe are r1 1 6 cm and r5 1 6.) cm$ respecti&ely. !he outer surface of the pipe is wrapped with a thin electric heater that consumes 00 W per m length of the pipe. !he e(posed surface of the heater is hea&ily insulated so that the entire heat generatedintheheateristransferredtothepipe.:eatistransferredfromtheinner surface of the pipe to the water #y con&ection with a heat transfer coefficient ofh = ))W/m53C.Assumingconstantthermalconducti&ityandone/dimensionalheat transfer$e(pressthemathematicalformulation*thedifferentiale,uationandthe #oundaryconditions+oftheheatconductioninthepipeduringsteadyoperation.8o not sol&e.%nafoodprocessingfacility$asphericalcontainerofinnerradiusr140cm$outer radius r541 cm$ and thermal conducti&ity k1.) W/m 3 C is used to store hot water andto"eepitat100Catalltimes.!oaccomplishthis$theoutersurfaceofthe containeriswrappedwitha)00/Welectricstripheaterandtheninsulated.!he temperature of the inner surface of the container is o#ser&ed to #e nearly 100C at all times.Assuming10percentoftheheatgeneratedintheheaterislostthroughthe insulation$ *a+ e(press the differential e,uation and the #oundary conditions for steady one/dimensionalheatconductionthroughthecontainer$*b+o#tainarelationforthe &ariation of temperature in the container material #y sol&ing the differential e,uation$ and*c+e&aluatetheoutersurfacetemperatureofthecontainer. Alsodeterminehow much water at 100C this tan" can supply steadily if the cold water enters at 50C..ate of water heated from 50 to 100C50d dTrdr dr _ ,( )( )51 11$ 5 100 $osdT rBC T r T C k qdr ( )55111 1sq rT r Tr r k _ + ,( )1100 5.-6 5.) T rr _ + ,( )5101.)oT r C 4.-4 /ppQQ mC T m kg hC T Consider a long solid cylinder of radius r0 1 4 cm and thermal conducti&ity k =5) W/m 3 C. :eat is generated in the cylinder uniformly at a rate of g0 1 ) W/cm. !he side surface of the cylinder is maintained at a constant temperature of Ts = -0C. !he &ariation of temperature in the cylinder is gi&en #y;ased on this relation$ determine *a+ heat conduction is steady or transient$ *#+ if it is 1$ 5 or8*c+ the &alue of heat flu( on the side surface of the cylinder at r = r0( )5555oosoor rodT rq kdrq r rkk rq r 1 _ 1 , ]55-0 /sq W cm 8oes heat generation in a solid &iolate the first law of thermodynamics$ which states that energy cannot #e created or destroyed7