References are f
References are from: rom: Incropera, F.P. and De WiIncropera, F.P. and De Witt, D.P.,tt, D.P., Introduction to Heat Transfer, John Introduction to Heat Transfer, John Wiley and Sons
Wiley and Sons, 2, 2ndndEdition, New York, 1996.Edition, New York, 1996.
S.1 The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures S.1 The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20°C, respectively, has been determined to be 40 W/m
are 40 and 20°C, respectively, has been determined to be 40 W/m22. . What iWhat is the s the thermalthermal conductivity of the wood?
S.2 The inner and o
S.2 The inner and outer surface temperatures of a glass window 5 mm thick are uter surface temperatures of a glass window 5 mm thick are 15 and 5°C,15 and 5°C, respectively. What is the h
respectively. What is the heat loss through a wineat loss through a window that is 1 m by dow that is 1 m by 3 m on a side? 3 m on a side? The thermalThe thermal conductivity of glass
S.3 The convection
S.3 The convection heat transfer coefficient between a surface at heat transfer coefficient between a surface at 40°C and ambient air at 20°C is40°C and ambient air at 20°C is 20 W/m
S.4 Air at 300°C flows over a
S.4 Air at 300°C flows over a flat plate of dimensions 0.50 m by 0.25 flat plate of dimensions 0.50 m by 0.25 m. If the convection heatm. If the convection heat transfer coefficient is 250 W/m
transfer coefficient is 250 W/m22K, determine the heat transfer rate from the K, determine the heat transfer rate from the air to one side of theair to one side of the plate when the plate is maintained at 40°C.
S.5 A surface of area 0.5 m
S.5 A surface of area 0.5 m22, emissivity 0.8, and temperature 150°C is placed in a large,, emissivity 0.8, and temperature 150°C is placed in a large, evacuated chamber whose wa
evacuated chamber whose walls are maintained at 25°C. What is the rate lls are maintained at 25°C. What is the rate at which radiation isat which radiation is emitted by the surface? What
emitted by the surface? What is the net rate at which radiation is exchanged is the net rate at which radiation is exchanged between the surfacebetween the surface and the chamber walls?
S.6 A hot
S.6 A hot water pipe with outside radius r1 has a twater pipe with outside radius r1 has a temperatureemperature T T 11. A thick insulation applied to. A thick insulation applied to
reduce the heat loss has an outer radius
reduce the heat loss has an outer radius r r 22 and temperatureand temperature T T 22. On. On T±r T±r coordinates, sketch thecoordinates, sketch the
temperature distribution in the insulation for one-dimensional, steady-state heat transfer with temperature distribution in the insulation for one-dimensional, steady-state heat transfer with constant properties. Give a brief explanation,
S.7 Sections of the Alaskan pipeline run above the ground and are supported by vertical steel S.7 Sections of the Alaskan pipeline run above the ground and are supported by vertical steel shafts (k = 25 W/mK) which are 1 m long and have a cross-sectional area of 0.005 m
shafts (k = 25 W/mK) which are 1 m long and have a cross-sectional area of 0.005 m22. Under . Under normal operating conditions, the temperature variation along the
normal operating conditions, the temperature variation along the length of a shaft is known to length of a shaft is known to bebe governed by an e
governed by an expression of the form:xpression of the form: T T = 100 ± 150= 100 ± 150 x x + 10+ 10 x x22 where
where T T andand x x have units of °C have units of °C and meters, respectively. and meters, respectively. Temperature variations are negliTemperature variations are negligiblegible over the shaft cross section. Evaluate t
over the shaft cross section. Evaluate the temperature and conduction heat he temperature and conduction heat rate at therate at the shaft/pipeline joint (
shaft/pipeline joint ( x x = 0) and at the shaft/ground = 0) and at the shaft/ground interface (interface ( x x = 1 m). Explain the d= 1 m). Explain the difference inifference in heat rates.
S.8 The rear window o
S.8 The rear window of an automobile is defogged by passing warf an automobile is defogged by passing warm air at 40°C over its inner m air at 40°C over its inner surface, and the associated co
surface, and the associated co nvection coefficient is 30 W/mnvection coefficient is 30 W/m22K. Under conditions for which theK. Under conditions for which the outside ambient air temperature is -10°C and the a
outside ambient air temperature is -10°C and the a ssociated convection coefficient is 65 W/mssociated convection coefficient is 65 W/m22K,K, what are the inner and o
what are the inner and outer surface temperatures of the window? The window uter surface temperatures of the window? The window glass is 4 mmglass is 4 mm thick.
S.9 The rear window o
S.9 The rear window of an automobile is defogged by attf an automobile is defogged by attaching a thin, transparent, film-typeaching a thin, transparent, film-type heating element to its i
heating element to its inner surface. nner surface. By electrically heating thiBy electrically heating this element, a uniform heat fls element, a uniform heat fluxux may be established at the
may be established at the inner surface. What is the electrical power that must be proinner surface. What is the electrical power that must be pro vided per vided per unit window area to
unit window area to mainmaintain atain an inner surface temperature of 15°C when the n inner surface temperature of 15°C when the interior air interior air temperature and convection coefficient are 25°C and 10 W/m
temperature and convection coefficient are 25°C and 10 W/m22K and the exterior (ambient) air K and the exterior (ambient) air temperature and convection coefficient are -10°C and 65 W/m
temperature and convection coefficient are -10°C and 65 W/m22K? The window glass is 4 mmK? The window glass is 4 mm thick.
S.10 For laminar flow over a
S.10 For laminar flow over a flat plate, the local heat transfer coefficient,flat plate, the local heat transfer coefficient, hh x x, is known to vary as, is known to vary as
x
x-1/2-1/2, where, where x x is the distance from the leading edge is the distance from the leading edge (( x x=0) of the plate. What =0) of the plate. What is the ratio of theis the ratio of the average coefficient between the leading edge and some location
average coefficient between the leading edge and some location x x on the plate to the localon the plate to the local coefficient at
S.11 A fan that can provide air speeds up to 50 m/s is to be used in a low speed wind tunnel with S.11 A fan that can provide air speeds up to 50 m/s is to be used in a low speed wind tunnel with atmospheric air at 25°C. If one wishes to
atmospheric air at 25°C. If one wishes to use the wind tunnel to studuse the wind tunnel to study flat plate boundary layer y flat plate boundary layer behavior up to Reynolds numbers of 10
behavior up to Reynolds numbers of 1088, what is the minimum plate length? At , what is the minimum plate length? At what distancewhat distance from the leading edge wou
S.12 Experimental results for heat transfer over a
S.12 Experimental results for heat transfer over a flat plate with an extremely rough surface wereflat plate with an extremely rough surface were found to be correlated by an expression of the form
found to be correlated by an expression of the form
3 3 // 1 1 9 9 .. 0 0 Pr Pr Re Re 04 04 .. 0 0 Nu Nu x x !! x x where Nu
where Nu x x is the local value of the Nusselt number is the local value of the Nusselt number at a positionat a position x x measured from the leadingmeasured from the leading
edge of the plate.
edge of the plate. Obtain an expression for the ratio of the average heat Obtain an expression for the ratio of the average heat transfer coefficienttransfer coefficient between the leading edge and a location
S.13 Consider steady, parallel flow o
S.13 Consider steady, parallel flow of atmospheric air over a flat plate. The air has a f atmospheric air over a flat plate. The air has a temperaturetemperature and free stream velocity of 300
and free stream velocity of 300 K and 25 m/s.K and 25 m/s. a)
a) Evaluate the boundary layer thickness at distances of Evaluate the boundary layer thickness at distances of x x = 1, 10, and 100 mm from the= 1, 10, and 100 mm from the leading edge. If a second plate were installed parallel to and at a distance of 3 mm from leading edge. If a second plate were installed parallel to and at a distance of 3 mm from the first plate, what would be the distance from the leading edge at which the boundary the first plate, what would be the distance from the leading edge at which the boundary layer merger would occur?
layer merger would occur? b)
b) Evaluate the surface shear stress and tEvaluate the surface shear stress and the y-velocity component at the outer edghe y-velocity component at the outer edge of thee of the boundary layer for the single plate at
boundary layer for the single plate at x x = 1, 10, and 100 mm.= 1, 10, and 100 mm. c)
S.14 Consider water at
S.14 Consider water at 27°C in parallel flow over an isothermal, 1 m long 27°C in parallel flow over an isothermal, 1 m long flat plate with aflat plate with a velocity of 2 m/s. Plot the variat
velocity of 2 m/s. Plot the variation of the local heat transfer coefficient with distance along tion of the local heat transfer coefficient with distance along t hehe plate. What is the value of the average coefficient?
S.15 A thin, flat plate o
S.15 A thin, flat plate of lengthf length LL = 1 m separates two = 1 m separates two airstreams that are in parallel flow over airstreams that are in parallel flow over opposite surfaces of the plate. One a
opposite surfaces of the plate. One a irstream has a temperature of 200°C and a velocity oirstream has a temperature of 200°C and a velocity o f 60f 60 m/s, while the other has a t
m/s, while the other has a temperature of 25°C and a emperature of 25°C and a velocity of 10 m/s. What is the heat velocity of 10 m/s. What is the heat fluxflux between the two streams at t
S.16 Consider a rectangular fin that
S.16 Consider a rectangular fin that is used to cool a motorcycle engine. Tis used to cool a motorcycle engine. The fan is 0.15 he fan is 0.15 m longm long and at a temperature of 250°C, while the motorcycle is moving at 80 km/hr in air at 27°C. The and at a temperature of 250°C, while the motorcycle is moving at 80 km/hr in air at 27°C. The air is in parallel flow over both surfaces o
air is in parallel flow over both surfaces of the fin, and turbulent flow conditions may be assumedf the fin, and turbulent flow conditions may be assumed to exist throughout. What is the rat
S.17 One-hundred electrical components, each dissipating 25 W, are attached to one surface of a S.17 One-hundred electrical components, each dissipating 25 W, are attached to one surface of a 0.2 m square copper
0.2 m square copper plate, and all of the dplate, and all of the dissipated energy is transferred to water in parallel flowissipated energy is transferred to water in parallel flow over the opposite surface. A protu
over the opposite surface. A protuberance at the leading edge oberance at the leading edge of the plate acts to trip thef the plate acts to trip the boundary layer, and the p
boundary layer, and the plate itself may be assumed to be isotlate itself may be assumed to be isothermalhermal. The wat. The water velocity ander velocity and temperature are 2 m/s and 17
temperature are 2 m/s and 17°C.°C. a)
a) What is the temperature of the copper plate?What is the temperature of the copper plate? b)
b) If each component has a plate contact surface area of 1 cmIf each component has a plate contact surface area of 1 cm22 and the corresponding area-and the corresponding area-specific contact resistance is 2×10
S.18 A square aluminum plate 5 mm thick and 200 mm on a side is cooled while vertically S.18 A square aluminum plate 5 mm thick and 200 mm on a side is cooled while vertically suspended in quiescent a
suspended in quiescent air at 40°C. Determine the average heat ir at 40°C. Determine the average heat transfer coefficient for the platetransfer coefficient for the plate when its temperature is 15°C.
S.19 An aluminum plate,
S.19 An aluminum plate, heated to a uniform temperature of 227°C, heated to a uniform temperature of 227°C, is allis allowed to owed to cool whilecool while vertically suspended in a roo
vertically suspended in a room where the ambient air and surroundings are at m where the ambient air and surroundings are at 27°C. The plate is27°C. The plate is 0.3 m square with a t
0.3 m square with a thickness of 15 mm and an ehickness of 15 mm and an e missivimissivity oty of 0.25.f 0.25. a)
a) Develop an expression for tDevelop an expression for the time rate of change of the phe time rate of change of the p late temperature, assuming thelate temperature, assuming the temperature to be uniform at any t
temperature to be uniform at any t ime.ime. b)
b) Determine the initial rate of cooling (K/s) when tDetermine the initial rate of cooling (K/s) when t he plate temperature is 227°C.he plate temperature is 227°C. c)
S.20 The plate descr
S.20 The plate described in the previous problem has been used ibed in the previous problem has been used in an experiment to determinein an experiment to determine the free convection heat t
the free convection heat transfer coefficient. At an instant of time when the pransfer coefficient. At an instant of time when the plate temperaturelate temperature was 127°C, the time rate o
was 127°C, the time rate of change of this temperature was observed to f change of this temperature was observed to be -0.0465 K/s. What isbe -0.0465 K/s. What is the corresponding free convect
the corresponding free convection heat transfer coefficient? Compare this result with an estimateion heat transfer coefficient? Compare this result with an estimate based on a standard
S.21 A household oven door of 0.5 m height and 0.7 m width reaches an average surface S.21 A household oven door of 0.5 m height and 0.7 m width reaches an average surface temperature of 32°C during operation. Estimate the heat
temperature of 32°C during operation. Estimate the heat loss to the room with ambient air atloss to the room with ambient air at 22°C. If the door has an e
22°C. If the door has an emissivimissivity of 1.0 ty of 1.0 and the surroundings are aand the surroundings are also at 22°C, comment on thelso at 22°C, comment on the heat loss by free convect
S.22 An enclosure has a
S.22 An enclosure has an inside area of 100 m2, an inside area of 100 m2, a nd its inside surface is black and nd its inside surface is black and is maintainedis maintained at a constant temperature. A small opening in the enclosure has an area of 0.02 m2. The radiant at a constant temperature. A small opening in the enclosure has an area of 0.02 m2. The radiant power emitted from this opening is 70 W.
power emitted from this opening is 70 W. What is the temperature of the interior enclosure wall?What is the temperature of the interior enclosure wall? If the interior surface is maintained at this temperature,
If the interior surface is maintained at this temperature, but is now polished, what will be thebut is now polished, what will be the value of the radiant power emitted from the opening?
S.23 Under steady state operation, a 50 W incandescent light bulb has a surface temperature of S.23 Under steady state operation, a 50 W incandescent light bulb has a surface temperature of 135°C when the room air is at a temperature of 25°C. If the bulb may be approximated as a 60 135°C when the room air is at a temperature of 25°C. If the bulb may be approximated as a 60 mm diameter sphere with a diffuse, gray surface o
mm diameter sphere with a diffuse, gray surface o f emissivif emissivity 0.8, ty 0.8, what is the radiant heatwhat is the radiant heat transfer from the bulb surface to its surroundings?
