Problem 10.1

This is an external forced convection problem.

The geometry can be modeled as a flat plate.

Surface temperature is uniform.

Newton’s law of cooling gives heat transfer rate from the surface to the air.

The average heat transfer coefficient must be determined.

The Reynolds number should be evaluated to establish if the flow is laminar, turbulent or
mixed.

Analytic or correlation equations give the heat transfer coefficient.
Problem 10.2

This is an external forced convection problem.

The geometry can be modeled as a flat plate.

Surface temperature is uniform.

To determine the heat flux at a given location, the local heat transfer coefficient must be
determined.

The average heat transfer coefficient is needed to determine the total heat transfer rate.

Newton’s law of cooling gives surface flux and total heat transfer rate.

The Reynolds number should be checked to establish if the flow is laminar, turbulent or
mixed.

Analytic or correlation equations give the heat transfer coefficient.
Problem 10.3

This is an external forced convection problem of flow over a flat plate.

Surface temperature is assumed uniform.

The heat transfer coefficient in turbulent flow is greater than that in laminar flow.
Thus higher heat transfer rates can be sustained in turbulent flow than laminar flow.

The Reynolds number should be checked to establish if the flow is laminar, turbulent or
mixed.

Heat loss from the surface is approximately equal to the power dissipated in the package.

Newton’s law of cooling gives a relationship between heat transfer rate, surface area, heat
transfer coefficient, surface temperature and ambient temperature.

The fluid is air.
Problem 10.4

This is an external forced convection problem.

The geometry is a flat plate.

Surface temperature is uniform.

Newton’s law of cooling gives the heat transfer rate.

The Reynolds number should be checked to establish if the flow is laminar, turbulent or
mixed.

Analytic or correlation equations give the heat transfer coefficient.

If the flow is laminar throughout, heat transfer from the first half should be greater than
that from the second half.

Second half heat transfer can be obtained by subtracting first half heat rate from the heat
transfer from the entire plate.

The fluid is water.
Problem 10.5

The chip is cooled by forced convection.

This problem can be modeled as a flat plate with an unheated leading section.

Newton's law of cooling can be applied to determine the rate of heat transfer between the
chip and the air.

Check the Reynolds number to establish if the flow is laminar or turbulent.
Problem 10.6

Heat transfer from the collector to the air is by forced convection.

This problem can be modeled as a flat plate with an unheated leading section.

Newton's law of cooling can be applied to determine the rate of heat transfer between the
collector and air.

The heat transfer coefficient varies along the collector.

The Reynolds number should be computed to establish if the flow is laminar or turbulent.
Problem 10.7

This is an external forced convection problem.

The flow is over a flat plate.

Surface temperature is uniform.

Plate orientation is important.

Variation of the heat transfer coefficient along the plate affects the total heat transfer.

The heat transfer coefficient for laminar flow decreases as the distance from the leading
edge is increased. However, at the transition point it increases and then decreases again.

Higher rate of heat transfer may be obtained if the wide side of a plate faces the flow. On
the other hand, higher rate may be obtained if the long side of the plate is in line with the
flow direction when transition takes place

The fluid is water.
Problem 10.8

This is an external forced convection problem.

The flow is over a flat plate.

The problem can be modeled as flow over a flat plate with uniform surface heat flux.

Surface temperature varies with distance along plate. The highest surface temperature is
at the trailing end.

Tripping the boundary layer at the leading edge changes the flow from laminar to
turbulent. This increases the heat transfer coefficient and lowers surface temperature.

Newton’s law of cooling gives surface temperature.
Problem 10.9

This is an external forced convection problem.

The flow is normal to a tube.

Surface temperature is uniform.

Tube length is unknown.

Newton’s law of cooling can be used to determine surface area. Tube length is related to
surface area.
The fluid is water.

Problem 10.10

Heat is removed by the water from the steam causing it to condense.

The rate at which steam condenses inside the tube depends on the rate at which heat is
removed from the outside surface.

Heat is removed from the outside surface by forced convection.

This is an external forced convection problem of flow normal to a tube. (v) Newton’s law
of cooling gives the rate of heat loss from the surface.
Problem 10.11

Electric power is dissipated into heat and is removed by the water.

This velocity measuring concept is based on the fact that forced convection heat transfer
is affected by fluid velocity.

Velocity affects the heat transfer coefficient which in term affects surface temperature.

Newton’s law of cooling relates surface heat loss to the heat transfer coefficient, surface
area and surface temperature.

This problem can be modeled as external flow normal to a cylinder.

The fluid is water.
Problem 10.12

This is an external forced convection problem.

The flow is normal to a rod.

Surface heat transfer rate per unit length is known. However, surface temperature is
unknown.

In general, surface temperature varies along the circumference. However, the rod can be
assumed to have a uniform surface temperature.

This problem can be modeled as forced convection normal to a rod with uniform surface
flux or temperature.

Newton’s law of cooling gives surface temperature.

The fluid is air.
Problem 10.13

Electric power is dissipated into heat and is removed by the fluid.

This velocity measuring instrument is based on the fact that forced convection heat
transfer is affected by fluid velocity.

velocity affects the heat transfer coefficient which in term affects surface temperature and
heat flux.

Newton’s law of cooling relates surface heat loss to the heat transfer coefficient, surface
area and surface temperature.

This problem can be modeled as external flow normal to a cylinder.

The fluid is air.
Problem 10.14

The sphere cools off as it drops. Heat loss from the sphere is by forced convection.

The height of the building can be determined if the time it takes the sphere to land is
known.

Time to land is the same as cooling time.

Transient conduction determines cooling time.

If the Biot number is less than 0.1, lumped capacity method can be used to determine
transient temperature.

Cooling rate depends on the heat transfer coefficient.
Problem 10.15

The electric energy dissipated inside the sphere is removed from the surface as heat by
forced convection.

This problem can be modeled as external flow over a sphere.

Newton’s law of cooling relates heat loss from the surface to heat transfer coefficient,
surface area and surface temperature. (iv) The fluid is air.
Problem 10.16

The sphere cools off as it drops. Heat loss from the sphere is by forced convection.

This is an external flow problem with a free stream velocity that changes with time.

This is a transient conduction problem. The cooling time is equal to the time it takes the
sphere to drop to street level.

If the Biot number is less than 0.1, lumped capacity method can be used to determine
transient temperature.

Cooling rate depends on the heat transfer coefficient.
Problem 10.17

This is an internal forced convection problem.

The channel is a tube.

The outside surface is maintained at a uniform temperature.

Neglecting tube thickness resistance means that the inside and outside surface
temperatures are identical.

Fluid temperature is developing.

Inlet and outlet temperatures are known.

The Reynolds number should be determined to establish if the flow is laminar or
turbulent.

The required tube length depends on the heat transfer coefficient.

The fluid is water.
Problem 10.18

This is an internal force convection problem.

The channel is a tube.

The surface is maintained at a uniform temperature.

The velocity is fully developed.

The temperature is developing.

The outlet temperature is unknown.

The Reynolds number should be checked to establish if the flow is laminar or turbulent.

The fluid is air.
Problem 10.19

This is an internal forced convection problem

Tube surface is maintained at uniform temperature.

The velocity is fully developed.

The length of tube is unknown.

The temperature is developing. However, depending on tube length relative to the
thermal entrance length, temperature may be considered fully developed throughout.

The Reynolds number should be checked to determine if the flow is laminar or turbulent.

The fluid is water.
Problem 10.20

This is an internal forced convection problem.

Tube surface is maintained at a uniform temperature.

The velocity and temperature are developing. Thus, entrance effects may be important.

The outlet temperature is unknown.

The fluid is air.
Problem 10.21

This is an internal forced convection problem.

Tube surface is maintained at uniform temperature.

The section of interest is far away from the inlet. This means that flow and temperature
can be assumed fully developed and the heat transfer coefficient uniform.

It is desired to determine the surface flux at this section. Newton’s law of cooling gives a
relationship between local flux, surface temperature and heat transfer coefficient.

The Reynolds number should be checked to determine if the flow is laminar or turbulent.

The fluid is water.
Problem 10.22

This is an internal forced convection problem in a tube.

Both velocity and temperature are fully developed.

Tube surface is maintained at uniform temperature.

The Reynolds number should be computed to establish if flow is laminar or turbulent.

Mean velocity, mean inlet and outlet temperatures and tube diameter are known.

The fluid is air.
Problem 10.23

This is an internal forced convection problem.

The surface of each tube is maintained at uniform temperature which is the same for both.

The velocity and temperature are fully developed. Thus, the heat transfer coefficient is
uniform.

Air flows through each tube at different rates.

The Reynolds number should be computed to establish if the flow is laminar or turbulent.

Surface heat flux depends on the heat transfer coefficient.
Problem 10.24

This is an internal forced convection problem.

The geometry consists of two concentric tubes.

Air flows in the inner tube while water flows in the annular space between the two tubes.

The Reynolds number should be computed for both fluids to establish if the flow is
laminar or turbulent.

Convection resistance depends on the heat transfer coefficient.
Problem 10.25

This is an internal forced convection problem.

The geometry consists of a tube concentrically placed inside a square duct,.

Water flows in the tube and the duct.

The Reynolds number should be computed for the two fluids to establish if the flow is
laminar or turbulent.

Far away from the inlet the velocity and temperature may be assumed fully developed.
Problem 10.26

Heat is lost from the door to the surroundings by free convection and radiation.

To determine the rate of heat loss, the door can by modeled as a vertical plate losing
heat by free convection to an ambient air and by radiation to a large surroundings.

Newton’s law of cooling gives the rate of heat transfer by convection and StefanBoltzmann relation gives the heat loss by radiation.
Problem 10.27
 This is a free convection and radiation problem.

The geometry is a vertical plate.

Surface temperature is uniform.

Newton’s law of cooling gives convection heat transfer rate while Stefan-Boltzmann law
gives radiation heat transfer rate.

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

Since radiation heat transfer is considered in this problem, all temperatures should be
expressed in degrees kelvin.

The fluid is air.
Problem 10.28

This is a free convection problem.

The power dissipated in the electronic package is transferred to the ambient fluid by
free convection.

As the power is increased, surface temperature increases.

The maximum power dissipated corresponds to the maximum allowable surface
temperature.

Surface temperature is related to surface heat transfer by Newton’s law of cooling.

The problem can be modeled as free convection over a vertical plate.

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

The fluid is air.
Problem 10.29

This is a free convection problem.

The power dissipated in the electronic package is transferred to the ambient fluid by
free convection.

As the power is increased, surface temperature increases.

The maximum power dissipated corresponds to the maximum allowable surface
temperature.

Surface temperature is related to surface heat transfer by Newton’s law of cooling.

The problem can be modeled as free convection over a vertical plate.

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

The fluid is water.
Problem 10.30

This is a free convection problem.

The surface is maintained at uniform temperature.

The heat transfer coefficient decreases with distance from the leading edge of the plate.

The heat transfer rate from the lower half 1 is greater than that from the upper half 2.

Total heat transfer from each half can be determined using the average heat transfer
coefficient.

Heat transfer from the upper half is equal to the heat transfer from the entire plate minus
heat transfer from the lower half.
Problem 10.31

This is a free convection problem.

The surface is maintained at uniform temperature.

The heat transfer coefficient decreases with distance from the leading edge of the plate.

The width of each triangle changes with distance from the leading edge.
Problem 10.32

This is a free convection problem over a vertical plate.

The surface is maintained at uniform temperature.

Local heat flux is determined by Newton’s law of cooling.

Heat flux depends on the local heat transfer coefficient.

Free convection heat transfer coefficient for a vertical plate decreases with distance from
the leading edge. Thus, the flux also decreases.

The Rayleigh number should be computed to select an appropriate Nusselt number
correlation equation.

The fluid is air.
Problem 10.33

This is a free convection problem over a vertical plate.

The power dissipated in the chips is transferred to the air by free convection.

This problem can be modeled as free convection over a vertical plate with constant
surface heat flux.

Surface temperature increases as the distance from the leading edge is increased. Thus,
the maximum surface temperature occurs at the top end of the plate (trailing end).

Newton’s law of cooling relates surface temperature to heat flux and heat transfer
coefficient.

The fluid is air.
Problem 10.34

Power supply to the disk is lost from the surface to the surroundings by free convection
and radiation.

To determine the rate of heat loss, the disk can by modeled as a horizontal plate losing
heat by free convection to an ambient air and by radiation to a large surroundings.

Newton’s law of cooling gives the rate of heat transfer by convection and StefanBoltzmann relation gives the heat loss by radiation.

Free convection correlations give the heat transfer coefficient.

Conservation of energy at the surface gives the emissivity, if it is the only unknown.
Problem 10.35

This is a free convection problem.

The geometry is a flat plate.

Heat transfer from two plates is to be compared. One plate is vertical and the other is
inclined. Both plates fit in the same vertical space. Thus, the inclined plate is longer than
the vertical plate.

Both plates are maintained at uniform surface temperature.

Heat transfer depends on surface area and average heat transfer coefficient.
Problem 10.36

This is a free convection problem.

The kiln has four vertical sides and a horizontal top.

All surfaces are at the same uniform temperature.

Newton’s law of cooling gives the heat transfer rate.

The sides can be modeled as vertical plates and the top as a horizontal plate.

The fluid is air.
Problem 10.37

Heat transfer from the surface is by free convection and radiation.

The burner can be modeled as a horizontal disk with its heated side facing down.

Newton’s law of cooling gives heat transfer by convection and Stefan-Boltzmann
relations gives heat transfer by radiation.

Both convection and radiation depend on surface temperature.

If the burner is well insulated at the bottom heated surface and its rim, then the electric
power supply is equal to surface heat transfer.
Problem 10.38

Heat transfer from the surface is by free convection and radiation.

The sample can be modeled as a horizontal disk with its heated side facing down or up.

Newton’s law of cooling gives heat transfer by convection and Stefan-Boltzmann relation
gives heat transfer by radiation.

Radiation depends on surface emissivity.

If the disk is well insulated at the heated surface and its rim, then the electric power
supply is equal to surface heat transfer.

Since the electric power is the same for both orientations, it follows that surface heat
transfer rate is also the same.

Each orientation has its own Nusselt number correlation equation.
Problem 10.39

This is a free convection problem.

Heat is transferred from the cylindrical surface and top surface of tank to the ambient air.

Under certain conditions a vertical cylindrical surface can be modeled as a vertical plate.

Newton’s law of cooling gives the heat transfer rate from tank.

The fluid is air.
Problem 10.40

This is a free convection problem.

The geometry is a horizontal round duct.

Heat is transferred from duct surface to the ambient air.

According to Newton’s law of cooling, the rate of heat transfer depends on the heat
transfer coefficient, surface area and surface and ambient temperatures.
Problem 10.41

This is a free convection problem.

The geometry is a horizontal pipe.

Heat is transferred from pipe surface to the ambient air.

Adding insulation material reduces heat loss from pipe.

According to Newton’s law of cooling, the rate of heat transfer depends on the heat
transfer coefficient, surface area and surface and ambient temperatures

Heat transfer coefficient and surface area change when insulation is added.

The fluid is air.
Problem 10.42

This is a free convection problem.

The geometry is a horizontal wire (cylinder).

Under steady state conditions the power dissipated in the wire is transferred to the
surrounding air.

According to Newton’s law of cooling, surface temperature is determined by the heat
transfer rate, heat transfer coefficient, surface area and ambient temperature.

The fluid is air.
Problem 10.43

This is a free convection problem.

The geometry is a horizontal tube.

Under steady state conditions the power dissipated in the neon tube is transferred to the
surrounding air.

According to Newton’s law of cooling, surface temperature is determined by the heat
transfer rate, heat transfer coefficient, surface area and ambient temperature.

The fluid is air.
Problem 10.44

This is a free convection problem.

The geometry is a round horizontal round duct.

Heat is transferred from the ambient air to the duct.

According to Newton’s law of cooling, the rate of heat transfer to the surface depends on
the heat transfer coefficient, surface area and surface and ambient temperatures.

The fluid is air.
Problem 10.45

This is a free convection and radiation problem

The geometry is a sphere.

Under steady state conditions the power dissipated in the bulb is transferred to the
surroundings by free convection and radiation and through the base by conduction.

According to Newton’s law of cooling and Stefan-Boltzmann radiation law, heat loss
from the surface depends on surface temperature.

The ambient fluid is air.
Problem 10.46

At steady state, power supply to the sphere must be equal to the heat loss from the surface

Heat loss from the surface is by free convection.

The surface is maintained at uniform temperature.
Problem 10.47

Heat is transferred from the ambient air to the water in the fish tank.

Adding an air enclosure reduces the rate of heat transfer.

To estimate the reduction in cooling load, heat transfer from the ambient air to the water
with and without the enclosure must be determined.

) Neglecting the thermal resistance of glass, the resistance to heat transfer form the air to
the water is primarily due to the air side free convection heat transfer coefficient.

Installing an air cavity introduces an added thermal resistance.

The problem can be modeled as a vertical plate and as a vertical rectangular enclosure.

The outside surface temperature of the enclosure is unknown.

Newton’s law of cooling gives the heat transfer rate.

The Rayleigh number should be determined for both vertical plate and rectangular
enclosure so that appropriate correlation equations for the Nusselt number are selected.
However, since the outside surface temperature of the enclosure is unknown, the
Rayleigh number can not be determined. The problem must be solved using an iterative
procedure.
Problem 10.48

Heat is transferred from the inside to the outside.

Adding i an air enclosure reduces the rate of heat transfer.

To estimate the savings in energy, heat transfer through the single and double pane
windows must be determined.

The double pane window introduces an added glass conduction resistance and a cavity
convection resistance.

the problem can be modeled as a vertical rectangular enclosure.

Newton’s law of cooling gives the heat transfer rate

The aspect ratio and Rayleigh number should be determined for the rectangular enclosure
so that an appropriate correlation equation for the Nusselt number can be selected.
Problem 10.49

Heat is transferred through the door from the inside to the outside.

Newton’s law of cooling gives the heat transfer rate.

The aspect ratio and Rayleigh number should be determined for the rectangular enclosure
so that an appropriate correlation equation for the Nusselt number can be selected.

The baffle divides the vertical cavity
Problem 10.50

Heat is transferred through the skylight from the inside to the outside.

Newton’s law of cooling gives the heat transfer rate.

The aspect ratio and Rayleigh number should be determined for the rectangular enclosure
so that an appropriate correlation equation for the Nusselt number can be selected.
Problem 10.51

Power requirement is equal to the heat transfer rate through the enclosure.

The problem can be modeled as a rectangular cavity at specified hot and cold surface
temperatures.

The inclination angle varies from 0 o to 175 o .

Newton’s law of cooling gives the heat transfer rate.

The aspect ratio and critical inclination angle should be computed to determine the
applicable correlation equation for the Nusselt number.
Problem 10.52

The absorber plate is at a higher temperature than the ambient air. Thus heat is lost
through the rectangular cavity to the atmosphere

The problem can be modeled as an inclined rectangular cavity at specified hot and cold
surface temperatures.

Newton’s law of cooling gives the heat transfer rate.

The aspect ratio and critical inclination angle should be computed to determine the
applicable correlation equation for the Nusselt number.
Problem 8.53

Heat is transferred through the annular space from the outer cylinder to the inner.

Newton’s law of cooling gives the heat transfer rate.

The Rayleigh number should be determined for the enclosure formed by the concentric
cylinders so that an appropriate correlation equation can be selected.

The cylinders are horizontally oriented.