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Problem 7.2

This is an external free convection problem over a vertical plate.

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

The solution for laminar flow is given in Section 7.4

For laminar flow, Fig.7.2 gives the viscous boundary layer thickness  and Fig. 7.3 gives
the thermal boundary layer thickness  t .

Newton’s law of cooling gives the heat transfer rate.

Equation (7.23) gives the average heat transfer coefficient h . (vii) The fluid is water.
Problem 7.3

This is an external free convection problem for flow over a vertical plate.

Laminar flow solution for temperature distribution for a plate at uniform surface
temperature is given in Fig. 7.3 .

The dimensionless temperature gradient at the surface is given in Table 7.1.

The solution depends on the Prandtl number.
Problem 7.4

This is a free convection problem.

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.

As a first approximation, radiation can be neglected.

Newton’s law of cooling gives the rate of heat transfer.

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

For laminar flow the solution of Section 7.4 is applicable.
Problem 7.5

This is a free convection and radiation problem.

The geometry is a vertical plate.
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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.

For laminar flow the solution of Section 7.4 is applicable.

Since radiation heat transfer is considered in this problem, all temperatures should be
expressed
Problem 7.6

This is a free convection problem.

The power dissipated in the electronic package is transferred to the ambient fluid by
free convection.
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As the power is increased, surface temperature increases.
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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.

For laminar flow the solution of Section 7.4 is applicable.

The fluid is air.
Problem 7.7

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.

For laminar flow the solution of Section 7.4 is applicable.

The fluid is water.
Problem 7.8

This is a free convection problem.
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The surface is maintained at uniform temperature.
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Newton’s law of cooling determines the heat transfer rate.

Heat transfer rate depends on the heat transfer coefficient.

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.

For laminar flow the solution of Section 7.4 is applicable.
Problem 7.9
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This is a free convection problem over a vertical plate.

The surface is maintained at uniform temperature.
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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 determine if the flow is laminar or
turbulent. For

Laminar flow the solution of Section 7.4 is applicable.

The fluid is air.
Problem 7.10

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.
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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).

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

For laminar flow the analysis of Section 7.5 gives surface temperature distribution.

The fluid is air.

Properties depend on the average surface temperature Ts . Since Ts is unknown, the
problem must be solved by trail and error.
Problem 7.11

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).

The Rayleigh number should be computed to determine if the flow is laminar or
turbulent.

For laminar flow the analysis of Section 7.5 gives surface temperature distribution.

The fluid is air.

Properties depend on the average surface temperature Ts . Since Ts is unknown, the
problem must be solved by trail and error.
Problem 7.12
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This is a free convection problem over a vertical plate at uniform surface temperature.
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In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.
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The integral method can be used to determine the velocity and temperature distribution.
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Application of the integral method reduces to determining the velocity and temperature
boundary layer thickness.
Problem 7.13

This is a free convection problem over a vertical plate at uniform surface heat flux.

In general, to determine the Nusselt number it is necessary to determine the velocity and
temperature distribution.

The integral method can be used to determine the velocity and temperature distribution.

Application of the integral method reduces to determining the velocity and temperature
boundary layer thickness.