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Problem 5.1

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution

Fluid velocity for Pr  1 is assumed to be uniform, u  V . This represents a
significant simplification.
Problem 5.2

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Fluid velocity for Pr  1 is assumed to be linear, u  V ( y /  ) .
Problem 5.3

The velocity is assumed to be uniform, u  V , throughout the thermal boundary layer.

A leading section of length xo is unheated.

at x  xo , surface heat flux is uniform.

The determination of the Nusselt number requires the determination of the temperature
distribution.

Surface temperature is unknown.

The maximum surface temperature for a uniformly heated plate occurs at the trailing end.
Problem 5.4

The velocity distribution is known.

Surface temperature is uniform.

The determination of the Nusselt number requires the determination of the temperature
distribution.

Newton’s law of cooling gives the heat transfer rate. This requires knowing the local heat
transfer coefficient.
Problem 5.5

The velocity distribution is known

Total heat transfer is equal to heat flux times surface area.

Heat flux is given. However, the distance x = L at which  t  H / 2 is unknown.
Problem 5.6

The determination of the Nusselt number requires the determination of the velocity and
temperature distributions.

Velocity is assumed uniform.

Surface temperature is variable.

Newton’s law of cooling gives surface heat flux. This requires knowing the local heat
transfer coefficient.
Problem 5.7

The determination of the Nusselt number requires the determination of the velocity and
temperature distributions.

Velocity is assumed linear.

Surface temperature is variable.

Newton’s law of cooling gives surface heat flux. This requires knowing the local heat
transfer coefficient.
Problem 5.8

The determination of the Nusselt number requires the determination of the velocity and
temperature distributions.

Velocity is assumed uniform.

Surface temperature is variable.

Newton’s law of cooling gives surface heat flux. This requires knowing the local heat
transfer coefficient.
Problem 5.9

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Surface heat flux is variable. It decreases with distance x.

Surface temperature is unknown.

Newton’s law of cooling gives surface temperature. This requires knowing the local heat
transfer coefficient. (v)  t /   1.
Problem 5.10

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Fluid velocity for Pr  1 is assumed to be uniform, u  V . This represents a
significant simplification.

Surface heat flux is variable. It increases with distance x.

Surface temperature is unknown. Since flux increases with x and heat transfer coefficient
decreases with x, surface temperature is expected to increase with x. Thus maximum
surface temperature is at the trailing end x = L.

Newton’s law of cooling gives surface temperature. This requires knowing the local heat
transfer coefficient.
Problem 5.11

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Fluid velocity for Pr  1 is assumed to be uniform, u  V . This represents a
significant simplification.

Surface heat flux is variable. It increases with distance x.

Surface temperature is unknown. Since flux increases with x and heat transfer coefficient
decreases with x, surface temperature is expected to increase with x. Thus maximum
surface temperature is at the trailing end x = L.

Newton’s law of cooling gives surface temperature. This requires knowing the local heat
transfer coefficient.
Problem 5.12

This problem is described by cylindrical coordinates.

Velocity variation with y is negligible.

Conservation of mass requires that radial velocity decrease with radial distance r.

Surface temperature is uniform.
Problem 5.13

This problem is described by cylindrical coordinates.

Velocity variation with y is negligible.

Conservation of mass requires that radial velocity decrease with radial distance r.

Surface heat flux is uniform

Surface temperature is unknown.
Problem 5.14

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Fluid velocity for Pr  1 is assumed to be uniform, u  V . This represents a
significant simplification.

The plate is porous.

Fluid is injected through the plate with uniform velocity.

The plate is maintained at uniform surface temperature.

A leading section of the plate is insulated.
Problem 5.15

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

Fluid velocity for Pr  1 is assumed to be uniform, u  V . This represents a
significant simplification.

The plate is porous.

Fluid is injected through the plate with uniform velocity.

The plate is heated with uniform surface flux

Surface temperature is unknown, (vii) A leading section of the plate is insulated.
Problem 5.16

There are two thermal boundary layers in this problem.

The upper and lower plates have different boundary conditions. Thus, temperature
distribution is not symmetrical.

The lower plate is at uniform temperature while heat is removed at uniform flux along the
upper plate.

Fluid velocity is assumed uniform throughout the channel.