Problem 6.1

This is an internal forced convection problem.

Scaling gives estimates of Lh and Lt .

Exact solutions for Lh and Lt are available for laminar flow through channels.

Exact solutions for Lt depend on channel geometry and surface boundary conditions.
Problem 6.2

This is an internal forced convection problem.

Scaling gives estimates of Lh and

Exact solutions for Lh and Lt are available for laminar flow through channels.

Exact solutions for Lt depend on channel geometry and surface boundary conditions.
Problem 6.3

This is an internal force convection problem.

The channel is a long tube.

The surface is maintained at a uniform temperature.

Since the tube section is far away from the entrance, the velocity and temperature can be
assumed fully developed.

Tube diameter, mean velocity and inlet, outlet and surface temperatures are known. The
length is unknown.

The fluid is air.
Problem 6.4

This is an internal force convection in a tube.

The surface is heated at uniform flux.

Surface temperature increases along the tube and is unknown.

The flow is assumed laminar and fully developed.

The heat transfer coefficient for fully developed flow through channels is constant.

According to Newton’s law of cooling, surface temperature is related to mean fluid
temperature, surface heat flux and heat transfer coefficient.
Problem 6.5

This is an internal force convection in a tube.

The surface is heated at uniform flux.

Surface temperature increases along the tube and is unknown.

The flow is assumed laminar and fully developed.

The heat transfer coefficient for fully developed flow through channels is constant.

According to Newton’s law of cooling, surface temperature is related to mean fluid
temperature, surface heat flux and heat transfer coefficient.
Problem 6.6

This is an internal forced convection problem in a tube.

The surface is heated at uniform flux.

Surface temperature changes along the tube and is unknown.

The Reynolds number should be checked to determine if the flow is laminar or turbulent.

If hydrodynamic and thermal entrance lengths are small compared to tube length, the
flow can be assumed fully developed throughout.

For fully developed flow, the heat transfer coefficient is uniform.

The length of the tube is unknown.

The fluid is water.
Problem 6.7

This is an internal force convection problem.

The channel is a tube.

The surface is maintained at a uniform temperature.

Entrance effect is important in this problem.

The average Nusselt number for a tube of length L depends on the average heat transfer
coefficient over the length.
Problem 6.8

This is an internal forced convection problem.

The fluid is heated at uniform wall flux.

Surface temperature changes with distance along the channel. It reaches a maximum
value at the outlet.

The Reynolds and Peclet numbers should be checked to establish if the flow is laminar or
turbulent and if this is an entrance or fully developed problem.

The channel has a square cross-section.

Application of Newton’s law of cooling at the outlet relates outlet temperature to surface
temperature, surface flux and heat transfer coefficient.

Application of conservation of energy gives a relationship between heat added, inlet
temperature, outlet temperature, specific heat and mass flow rate.
Problem 6.9

This is an internal forced convection problem in tubes.

The flow is laminar and fully developed.

The surface is maintained at uniform temperature.

All conditions are identical for two experiments except the flow rate through one is half
that of the other.

The total heat transfer rate depends on the outlet temperature.
Problem 6.10

This is an internal forced convection problem.

The channel has a rectangular cross section.

Surface temperature is uniform.

The Reynolds and Peclet numbers should be checked to establish if the flow is laminar or
turbulent and if entrance effects can be neglected.

Channel length is unknown.

The fluid is air.
Problem 6.11


This is an internal force convection problem.
The channel is a rectangular duct.

The surface is maintained at a uniform temperature.

The velocity and temperature are fully developed.

The Reynolds number should be checked to determine if the flow is laminar or turbulent.

Duct size, mean velocity and inlet, outlet and surface temperatures are known. The
length is unknown. (vii) Duct length depends on the heat transfer coefficient.

The fluid is water.
Problem 6.12

This is an internal forced convection problem in a channel.

The surface is heated at uniform flux.

Surface temperature changes along the channel. It reaches a maximum value at the outlet.

The Reynolds number should be checked to determine if the flow is laminar or turbulent.

Velocity and temperature profiles become fully developed far away from the inlet.

The heat transfer coefficient is uniform for fully developed flow.

The channel has a square cross section.

tube length is unknown. (ix) The fluid is air.
Problem 6.13

This is an internal forced convection problem in tubes.

The flow is laminar and fully developed.

The surface is maintained at uniform temperature.

All conditions are identical for two tubes except the diameter of one is twice that of the
other.

The total heat transfer in each tube depends on the outlet temperature.
Problem 6.14

This is an internal forced convection problem.

Equation (6.3) gives scaling estimate of the thermal entrance length.

Equation (6.20b) gives scaling estimate of the local Nusselt number.

The Graetz problem deals with laminar flow in the entrance of a tube at uniform surface
temperature.

Graetz solutions gives the thermal entrance length (distance to reach fully developed
temperature) and local Nusselt number.
Problem 6.15

This is an internal forced convection problem.

Equation (6.20b) gives scaling estimate of the local Nusselt number.

The Graetz problem deals with laminar flow in the entrance of a tube at uniform surface
temperature.
Problem 6.16

This is an internal forced convection problem in a tube.

The velocity is fully developed.

The temperature is developing.

Surface is maintained at uniform temperature.

The Reynolds number should be computed to establish if flow is laminar or turbulent.

Tube length is unknown.

The determination of tube length requires determining the heat transfer coefficient.
Problem 6.17

This is an internal forced convection problem in a tube.

The velocity is fully developed.

The temperature is developing.

Surface is maintained at uniform temperature.

The Reynolds number should be computed to establish if flow is laminar or turbulent.

Outlet mean temperature is unknown.

The determination of outlet temperature
coefficient.

Since outlet temperature is unknown, air properties can not be determined. Thus a trial
and error procedure is needed to solve the problem.
requires determining the heat transfer
Problem 6.18

This is an internal forced convection problem in a tube.

The velocity is fully developed and the temperature is developing.

The surface is heated with uniform flux.

The Reynolds number should be computed to establish if the flow is laminar or turbulent.

Compute thermal entrance length to determine if it can be neglected.

Surface temperature varies with distance from entrance. It is maximum at the outlet. Thus
surface temperature at the outlet is known.

Analysis of uniformly heated channels gives a relationship between local surface
temperature, heat flux and heat transfer coefficient.

The local heat transfer coefficient varies with distance form the inlet.

Knowing surface heat flux, the required power can be determined.

Newton’s law of cooling applied at the outlet gives outlet temperature.
Problem 6.19

This is an internal forced convection problem in a rectangular channel.

The velocity is fully developed and the temperature is developing.

The surface is maintained at uniform temperature.

The Reynolds number should be computed to establish if the flow is laminar or turbulent.

Compute entrance lengths to determine if they can be neglected

Surface flux varies with distance from entrance. It is minimum at outlet.

Newton’s law gives surface flux in terms of the local heat transfer coefficient h(x) and
the local mean temperature Tm (x ) .

The local and average heat transfer coefficient decrease with distance form the inlet.

The local mean temperature depends on the local average heat transfer coefficient
h (x). (x) Surface temperature is unknown.