[Tests and exam questions for Ch 1 to 5 and Ch 11 and 12 for 2006.doc] Vraag 1 / Question 1 [25 punte / 25 marks] June examination 2006 Die termokoppel (TC) installasie op ‘n sneeukarretjie-enjinsilinderkop (vir die moontlike gebruik by die SANAE basis, Antarktika) word in die skets vertoon. Die TC drade is vasgeheg aan die boonste en onderste oppervlaktes van die silindriese soldeerkraletjie. Die basis van die krael is vasgeheg aan die silinder wat teen 385 °C opereer, en daar is ‘n kontak weerstand tussen die silinder en krael wat as R con = 1/(2k head D sol ) gegee kan word. Die TC drade is baie lank en word blootgestel aan koue lug by -10 °C en met ‘n konveksie warmteoordragskoëffisiënt van 100 W/m 2 K. Die ander numeriesewaardes word in die skets weergegee. Die doelwit van hierdie probleem is om ‘n termiese model te ontwikkel wat die temperatuur verskil tussen die twee TC draadkoneksies weergee. Neem aan daar is geen warmteoordrag vanaf die sykante oppervlak van die kraeltjie nie. Ignoreer straling. i) Skets die termieseweerstandsdiagram van die installasie, en verskaf die toepaslike byskrifte (bv. temperature, termieseweerstande en warmtevloeie) in die skets. ii) Skryf die termieseweerstandsformules neer en bereken hul waardes. iii) Gebruik die termiese weerstandstroombaan om (T 1 -T 2 ) en hul temperatuur waardes te bereken. iv) Gee kommentaar oor die geldigheid van u aannames. The thermocouple (TC) installation on a snowmobile engine cylinder (earmarked for possible use at the SANNAE base, Antarctica) is shown in the schematic. The TC wire leads are attached to the upper and lower surfaces of the cylindrical solder bead. The base of the bead is attached to the cylinder head operating at 385 °C, and the contact themal resistance between the cylinder head and the bead may be expressed as R con = 1/(2k head D sol ). The TC wire leads are very long and experience heat loss to the air at -10 °C with a convective heat transfer coefficient of 100 W/m 2 K. Values of other geometrical and thermal parameters are given in the schematic. The objective of this problem is to develop a thermal model that can be used to determine the temperature (T 1 –T 2 ) between the two TC junctions. Assume that the solder bead does not experience any heat loss from its lateral surface. Ignore radiation. i) Sketch a thermal resistance circuit of the installation, labeling temperatures, thermal resistances and heat flow rates. ii) Write expressions for each of the thermal resistances and calculate their values. iii) Use your thermal circuit to evaluate (T 1 -T 2 ) for the prescribed conditions and calculate their temperatures. iv) Comment on the assumptions made in building your model. Sodeerselkraeltjie silinderkop Diameter
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[Tests and exam questions for Ch 1 to 5 and Ch 11 and 12 for 2006.doc] Vraag 1 / Question 1 [25 punte / 25 marks] June examination 2006 Die termokoppel (TC) installasie op ‘n sneeukarretjie-enjinsilinderkop (vir die moontlike gebruik by die SANAE basis, Antarktika) word in die skets vertoon. Die TC drade is vasgeheg aan die boonste en onderste oppervlaktes van die silindriese soldeerkraletjie. Die basis van die krael is vasgeheg aan die silinder wat teen 385 °C opereer, en daar is ‘n kontak weerstand tussen die silinder en krael wat as Rcon = 1/(2kheadDsol) gegee kan word. Die TC drade is baie lank en word blootgestel aan koue lug by -10 °C en met ‘n konveksie warmteoordragskoëffisiënt van 100 W/m2K. Die ander numeriesewaardes word in die skets weergegee. Die doelwit van hierdie probleem is om ‘n termiese model te ontwikkel wat die temperatuur verskil tussen die twee TC draadkoneksies weergee. Neem aan daar is geen warmteoordrag vanaf die sykante oppervlak van die kraeltjie nie. Ignoreer straling.
i) Skets die termieseweerstandsdiagram van die installasie, en verskaf die toepaslike byskrifte (bv. temperature, termieseweerstande en warmtevloeie) in die skets.
ii) Skryf die termieseweerstandsformules neer en bereken hul waardes. iii) Gebruik die termiese weerstandstroombaan om (T1-T2) en hul temperatuur
waardes te bereken. iv) Gee kommentaar oor die
geldigheid van u aannames.
The thermocouple (TC) installation on a snowmobile engine cylinder (earmarked for possible use at the SANNAE base, Antarctica) is shown in the schematic. The TC wire leads are attached to the upper and lower surfaces of the cylindrical solder bead. The base of the bead is attached to the cylinder head operating at 385 °C, and the contact themal resistance between the cylinder head and the bead may be expressed as Rcon = 1/(2kheadDsol). The TC wire leads are very long and experience heat loss to the air at -10 °C with a convective heat transfer coefficient of 100 W/m2K. Values of other geometrical and thermal parameters are given in the schematic. The objective of this problem is to develop a thermal model that can be used to determine the temperature (T1 –T2) between the two TC junctions. Assume that the solder bead does not experience any heat loss from its lateral surface. Ignore radiation.
i) Sketch a thermal resistance circuit of the installation, labeling temperatures, thermal resistances and heat flow rates.
ii) Write expressions for each of the thermal resistances and calculate their values. iii) Use your thermal circuit to evaluate (T1-T2) for the prescribed conditions and
calculate their temperatures. iv) Comment on the assumptions made in building your model.
Sodeerselkraeltjie
silinderkop
Diameter
Vraag 1 / Question 1 [20 punte / 20 marks] March Class test 1 2006 ‘n Vlekvryestaalbuis (AISI 304, soos per tabel A-3), wat gebruik word om verkoelde water te vervoer, en het ‘n binnedeursnee van 36 mm en ‘n wanddikte 2 mm. Die verkoelde water en die omgewingslug temperature is 6°C en 23°C, onderskeidelik, terwyl die ooreenstemende binne en buite konveksie warmteoordragskoëffisiënt 400 W/m2K en 6 W/m2K is.
(a) Wat is die warmtetoegevoeging per eenheidslengte? Ignoreer straling. (b) Wat is die warmtetoegevoeging per eenheids lengte van die buis indien ‘n 10 mm
dik laagie isolasie (k = 0.05 W/mK) aangebring word? Ignoreer straling. (c) Wat is die algehelewarmteoordragskoëffisiënt van die geisoleerde buis, gebaseer
op die binneoppervlakarea? Ignoreer straling. (d) Wat is die temperatuur van die buiteoppervlak van die isolasie? (e) Indien straling op die buiteoppervak van die geisoleerdepyp in ag geneem moet
word en die omgewingsmure ook by dieselfede temperatuur as die lug is, gee die termiese weerstandsdiagram en bereken die hitteaanwins. Neem aan die isolasie emissiwiteit is ε = 0.89 en dat die stralingswarmteoordragskoëffisiënt as 6ε benader kan word.
A stainless steel (AISI 304, as per table A-3) tube used to transport chilled water has an internal diameter of 36 mm and a wall thickness of 2 mm. The chilled water and the ambient air are at a temperature of 6 °C and 23 °C, respectively, while the corresponding inner and outer convection heat transfer coefficients are 400 W/m2K and 6 W/m2K.
(a) What is the heat gain per unit tube length? Ignore radiation. (b) What is the heat gain per unit tube if a 10 mm thick layer of insulation (k = 0.05
W/mK) is applied to the tube? Ignore radiation. (c) What is the overall heat transfer coefficient of the insulated tube, based on the inside
surface area? Ignore radiation. (d) What is the temperature of the outside surface of the insulation? (e) If radiation on the outside of the insulated pipe is to be taken into account and the
surroundings walls are at the same temperature as the air, give the thermal resistance diagram and calculate the heat gain. Assume that the emissivity of the insulation is 0.89 and the radiation heat transfer coefficient can be approximated as 6ε.
Vraag 2 / Question 2 [25 punte / 25 marks] March Class test 1 2006 ‘n Persoon sit ‘n paar apples in die vrieshokkie van ‘n yskas by -15°C, om vinnig af te koel vir gaste wat binnekort gaan opdaag. Die appels is oorspronklik by ‘n temperatuur van 20 °C, en die warmteoordragskoëffisiënt op die oppervlak is 8 W/m2K.
a) Beskou die appels as sfere van 90 mm diameter en bepaal die middelpunt en oppervlak temperature na 1 uur in die yskas. Bepaal ook die hitte oorgedra uit elk van die appels.
b) Beskou transiënte maar slegs een-rigtings warmtegeleiding in die radiaal rigting van die apples. Lei af vanaf basiese beginsels, deur gebruik te maak van die energiebalans-metode, die vergelyking (geskik vir rekenaar programmeering) van ‘n tipiese binneknoop temperatuur en sy beheervolume element indien ‘n eksplisiete eindige verskil numeriese metode gebruik word. Neem die hitte opgewek (respirasiewarmte)
in Watts as G& . 2sfeer π4 rA = , ( )3
i3oyfsferiesesk π
3
4rrV −=
A person puts a few apples into the freezer at -15°C to cool them quickly for guests that are about to arrive. Initially the apples are at a uniform temperature of 20 °C, and the heat transfer coefficient on the surface is 8 W/m2K.
a) Treating the apples as 90 mm diameter spheres, determine the centre and surface temperatures of the apples in 1 hour. Also determine the amount of heat transfer from each apple.
b) Consider transient one-dimensional heat conduction in the radial direction in the apples. Derive from basic principles, using the energy balance method, the equation for the temperature (suitable for inclusion into a computer program) of a typical interior node and its volume element using the expicit finite difference numerical method. Take the heat generated within the apple (heat of respiration) in Watts as G& .
2sphere π4 rA = , ( )3
i3odisk spherical π
3
4rrV −=
Vraag 4 / Question 4 [25 punte / 25 marks] June Exam 2006 ‘n Lang unievorm rondestaaf van diameter 50 mm en van termiesegeleidingkoëffisiënt k = 15 W/mK word intern verhit met ‘n volumetriesewarmte opwekking van 20 kW/m3. Die staaf is aksiaalsimmetries ge-oriënteer binne ‘n groter ronde buis van diameter 60 mm en sye temperatuur word by 500 °C onderhou. Die anulêre spasie tussen die staaf en die buis is evakueer, en hul oppervlakte is lugsppreidend (diffuse) en grys (gray) en albei se emissiwiteite is 0.2. (a) Bepaal die senter en oppervlak temperatuur van die staaf. (b) Bepaal die senter en oppervlak temperatuure van die staaf indien daar atmosferiese lug in die anulêre spasie bestaan, neem aan vloei as gevolg van dryfkragte is weglaatbaar klein in die anulêre spasie. A long uniform round rod of 50 mm diameter with a thermal conductivity of k = 15 W/mK is heated internally by a volumetric energy generation of 20 kW/m3. The rod is positioned coaxially within a larger circular tube of 60 mm diameter whose surface is maintained at 500 °C. The annular region between the rod and the tube is evacuated, and their surfaces are diffuse and grey with an emissivity of 0.2. (a) Determine the centre and surface temperature of the rod. (b) Determine the centre and surface temperature of the rod if atmospheric air occupies the annular space, assume that buoyancy driven flow is negligible in the annular space.
Vraag 1 / Question 1 [20 punte / 20 marks] April Test 2 2006 Stoom by ‘n temperatuur van 250 °C vloei binne ‘n staalpyp (AISI 316, soos per tabel A-3) van binnedeursnee 60mm en buitedeursnee 75mm. Die konveksie warmteoordragskoëffisiënt tussen die stoom en die binneoppervlak is 500 W/m2K, terwyl die warmteoordragskoëffisiënt tussen die buite oppervlak en die omgewingslug 25 W/m2K is. Die temperatuur van die omgewingslug is 25°C, maar die temperatuur van die omgewingsmure is 30°C. Die pyp se emissiwiteit is ε = 0.8.
(a) Teken die termiese weerstandsdiagram. (b) Wat is die hitteverlies per eenheidslengte van die pyp? (c) Wat is algehele warmteoordragskoëffisiënt, gebasseer op die buite oppervlak?
Steam at a temperature of 250 °C flows through a steel pipe (AISI 316, as per table A-3) of 60 mm inside diameter and 75 mm outside diameter. The convection coefficient between the steam and the inner surface of the pipe is 500 W/m2K, while that between the outer surface of the pipe and the surrounding air is 25 W/m2K. The temperature of the air is 25 °C but the temperature of the surrounding walls is 30 °C. The pipe emissivity is ε = 0.8.
(a) Draw the thermal resistance diagram (b) What is the heat loss per unit length of heat pipe? (c) What is the overall heat transfer coefficient, based on the outer surface?
Vraag 2 / Question 2 [20 punte / 20 marks] April Test 2 2006 ‘n Blok van spesiale metaal (ρ = 5000 kg/m3, cp = 460 J/kgK and k = 12 W/mK) met dimensies soos aangetoon in die figuur en by ‘n univorme temperatuur van 650 °C, word in ‘n groot tenk vloeistof by 150°C gedompel. Die konveksie warmteoordragskoëffisiënt kan as 150 W/m2K geneem word.
a) Deur die Biot en Fourier getalle te bereken, bepaal die geldigheid van die versamelde termiese kapasiteitsmodel (“lumped capacitance model”) of die een-term benadering (of Heislerkaarte) indien die transiënte temperatuurverspreiding in die blok benodig word.
b) Bepaal met behulp van die een-term benadering (of Heislerkaarte) die temperature by punte B en A, soos aangetoon in die figuur, 250 s nadat die blok in die vloeistof gedompel is.
c) Bereken die temperatuur in die blok na 250 s indien die versamelde termiese kapasiteitsmodel gebruik word.
A block of dimensions as shown in the figure and of a special metal (ρ = 5000 kg/m3, c = 460 J/kgK and k = 12 W/mK) at a uniform temperature of 650 °C is dumped into a large tank of liquid at 150°C. The convection heat transfer coefficient may be taken as 150 W/m2K.
a) By calculating the Biot and Fourier numbers establish the validity of using either the lumped thermal capacity model or the one-term approximation (or Heisler charts) in order to determine the transient temperature distribution in the block.
b) Determine using one-term approximation (or Heisler charts) the temperature at points B and A, as indicated in the figure, 250 seconds after being dumped into the liquid.
c) Calculate the temperature of the block after 250 s but use now the lumped thermal capacity model.
80
S S
40
80
40
S - S
30
30
20
20
20 A
A
B
B
Dimensions in mm
NB Please check this answer using the first order approximatrions
Vraag 1 / Question 1 [25 punte / 25 marks] June Her-Exam 2006 Een muur van ‘n elektriese houer word van koper plaat (k = 400 W/mK), 160 mm x 160 mm wyte en 5 mm dik, vervaardig. Om warmteoordrag deur die plaat te verbeter word dit voorsien van 400 koper vinne op elke kant van die plaat. Elke vin is 4 mm diameter en 20 mm lank en op ‘n 8 mm steek tussen senters en is intergraal-vervaardig (dws vervaardig op so ‘n manier dat daar geen termiese kontakweerstand is tussen die vin en die basisplaat). Daar is warm lug by 65 °C binne die houer en as gevolg van natuurlikke konveksie is die gemiddelde warmteoordragskoëffisiënt op die binne oppervlak 5 W/m2K. Geforseerde kamer-lug by 20 °C veroorsaak ‘n gemiddelde konveksie warmteoordragskoëffisiënt van 100 W/m2K op die buite oppervlak van die plaat. Ignoreer straling.
(a) Gee die termieseweerstands tekening, bepaal elk van die individuele weerstande and dus ook die warmteoordrag deur die plaat. Neem aan dieselfde warmteoordragskoëffisiënt vir die geval sonder vinne en bepaal ook die verbetering in warmteoordrag as gevolg van die vinne.
(b) Om kostes te verminder moet die pen-vinne vas aan die plaat gesoldeer word. Indien die kontakweerstand as gevolge van die solder proses 5 x 10-6 m2K/W is, bepaal die warmteoordrag deur die plaat. One wall of an elecrical enclosure is made from copper plate (k = 400 W/mK), 160 mm x 160 mm wide and 5 mm thick. To improve heat transfer through the plate, 400 copper pin fins, each of 4 mm diameter and 20 mm length, are integrally machined (in order to eliminate contact resistance) on both sides of the plate in a square pitch of 8 mm between centers. Warm air in the enclosure is at 65 °C, and natural convection provides an average convection heat transfer coefficient of 5 W/m2K on the inner surface of the plate. A forced flow of ambient air at 20 °C provides an average heat transfer coefficient of 100 W/m2K on the outer surface of the plate. Ignore raiation.
(a) Give the thermal resistance diagram, deterime each of the individual resistances separately and hence determine the rate of heat transfer through the plate. Assuming the same convection coefficients without the fins, determine the heat transfer improvement when using the pins.
(b) It is recommended that manufacturing costs be reduced by soldering the pins to the plate. If a contact resistance of 5 x 10-6 m2K/W is thus introduced what is the heat transfer through the plate?
Elektriese geleiers, in die vorm van parallel plate met ‘n lengte L = 40 mm, word op ‘n keramiek isolasie basis gemonteer soos in die skets en op ‘n afstand van w = 10 mm uit mekaar uit. Die plate is blootgestel aan ‘n groot omgewing by ‘n temperature van Tsurr = 300 K. Die oppervlaktes van die geleier (1) en die keramiek (2) is albei lugspreidend (diffuse) en grys (gray) met emissiwiteite van ε1 = 0.8 en ε2 = 0.6, onderskeilik. Vir ‘n voorgeskrewe geleier bedryfs temperatuur van T1 = 500 K
(a) Bepaal die elektiesedrywing wat van die geleier verwyder moet word deur stralings warmteoordrag vir ‘n een meter lengte, q′& en wat is die temperatuur van die geisoleerde basis T2?
(b) Bepaal q′& en T2 indien die oppervlaktes ook blootgestel word aan ‘n lugstroom by 300 K en konveksie warmteoordragskoëffisiënt van h = 25 W/m2K.
Electrical conductors, in the form of parallel plates of length L = 40 mm, have one end mounted to a ceramic insulation base and are spaced a distance w = 10 mm apart as shown in the sketch. The plates are expose to a large isothermal surroundings at Tsurr = 300 K. The conductor (1) and ceramic (2) surfaces are diffuse and grey with emissivities of ε1 = 0.8 and ε2 = 0.6, respectively. For a prescribed operating current their temperature is T1 = 500 K
(a) Determine the electrical power dissipated in a conductor and that must be removed by radiation heat transfer for a one-meter length, q′& as as a result of radiant heat transfer (ignoring convection) and what is the temperature of the insulated base T2? (b) Determine q′& and T2 when the surfaces also experience an air stream at 300 K and a convection heat transfer coefficient of h = 25 W/m2K.
