Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Heat Transfer for Engg.

Chemical Engineering : Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

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Illustration 4.1
Pressurized air is to be heated by flowing into a pipe of 2.54 cm diameter. The air at 200oC and 2 atm pressure enters in the pipe at 10 m/s. The temperature of the entire pipe is maintained at 220oC. Evaluate the heat transfer coefficient for a unit length of a tube considering the constant heat flux conditions are maintained at the pipe wall. What will be the bulk temperature of the air at the end of 3 m length of the tube?

The following data for the entering air (at 200oC) has been given,

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Solution 4.1

Reynolds number can be calculated from the above data,

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

The value of Reynolds number shows that the flow is in turbulent zone. Thus the Dittus-Boelter equation (eq.4.3) should be used,

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Thus h can be calculated for the known values of k, and d, which comes out to be

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Energy balance is required to evaluate the increase in bulk temperature in a 3 m length of the tube,

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Therefore the temperature of the air leaving the pipe will be at 210.81oC.

4.3.2 Laminar flow
Hausen presents the following empirical relations for fully developed laminar flow in tubes at constant wall temperature.

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev            (4.8)

The heat transfer coefficient calculated from eq. 4.8 is the average value over the entire length (including entrance length) of tube Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev .
Sieder and Tate suggested a simple relation for laminar heat transfer in tubes.

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

The condition for applicability of eq. 4.9:

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

where, μ is the viscosity of the fluid at the bulk temperature and μw is that at the wall temperature Tw . The other fluid properties are at mean bulk temperature of the fluid. Here also the heat transfer coefficient calculated from eq. 4.9 is the average value over the entire length (including entrance length) of tube Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev .

The empirical relations shown in eq. 4.2-4.9 are for smooth pipe. However, it case of rough pipes, it is sometimes appropriate that the Reynolds analogy between fluid friction and heat transfer be used to effect a solution under these conditions and can be expressed in terms of Stanton number.

In order to account the variation of the thermal properties of different fluids the following equations may be used (i.e. Stanton number multiplied by Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev),

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev(4.10)

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev(4.11)

where, Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev   is the mean free velocity. The friction factor can be evaluated from Moody’s chart.

4.3.3 Flow through non-circular ducts
The same co-relations as discussed in section 4.4.1 can be used for the non-circular ducts. However, the diameter of the tube has to be replaced by the hydraulic diameter or equivalent diameter for the non-circular ducts. The hydraulic diameter is defined as

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

Where rh is hydraulic radius.

4.3.4. Flow over a flat plate
Heat transfer in flow over a plate occurs through the boundary layer formed on the plane. Therefore at any location the heat transfer coefficient will depend on the local Reynolds and Prandtl number. For local heat transfer coefficient in laminar boundary layer flow, the following correlation can be used to find the local Nusselt number. It depends upon the distance from the leading edge (x) of the plate.

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev (4.13)

where,Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev  and  are the local Nusselt and Reynold numbers, respectively.
An average value of the heat transfer coefficient over a distance l may be obtained by,

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev               (4.14)

Forced Convective Heat Transfer (Part - 3) Chemical Engineering Notes | EduRev

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