Summary

This module computes the convection heat transfer coefficient for external flow over a flat plate, a sphere, a cylinder, or an array of cylinders. The array of cylinders can be a staggered or inline arrangement. The heat transfer coefficient for laminar or turbulent flow of an incompressible fluid (gas or liquid) can be computed.

Background Information

Flat Plate

This module calculates the convection heat transfer coefficient for external flow over a flat plate. For laminar flow conditions and constant temperature conditions on the a flat plate, the Nusselt number on a flat plate is computed using equation (1).

	(1)

	(1)

where Re is the Reynolds number and is computed by using equation (2) and Pr is the Prandlt number and is computed using equation (3).

(2)

(3)

where vis is viscosity, c_p is specific heat capacity, k is thermal conductivity, rho is fluid density, u is velocity of the fluid, and lp is the length of plate

For turbulent flow conditions and constant heat flux conditions on the flat plate the Nusselt number is computed using equation (4).

(4)

If Re < 500,000 then flow type is Laminar
If Re >= 500,000 then flow type is Turbulent

Cylinder

For laminar flow, turbulent flow and constant temperature conditions in the cylinder, the Nusselt number is computed using equation (5):

(5)

where c and m are constants based on Reynolds number. Reynolds number Re is calculated using equation (6)

(6)

If Re < 40                                then c = 0.75 and m = 0.4
If 40 < Re < 1000                    then c = 0.51 and m = 0.5
If 1000 < Re < 200,000           then c = 0.26 and m = 0.6
If Re > 200,000                       then c = 0.076 and m = 0.7

If Re <= 100,000;     flow is laminar
If Re > 100,000;       flow is turbulent

Array Of Cylinders

This module calculates Convection heat transfer coefficient for external flow over an array of cylinders.The array of cylinders can be a staggered or an inline arrangement. The mean velocity across the array of cylinders is computed using a scale factor that depends on the geometric layout. For an inline arrangement the scale factor for velocity is computed using equation (7)

(7)

where s_t is the vertical spacing as depicted in Figure 1 , d_ec is diameter of a cylinder.

Figure 1.

Reynolds number is calculated using equation (8).

(8)

The mean velocity is computed using equation (8a) ,

	(8a)

For an inline arrangement of the array of cylinders the Nusselt number is computed using equation (9a , 9b , 9c)

If Re < 1000 ,

(9a)

If 1000 < Re < 200,000

(9b)

If 200,000 < Re

(9c)

For the staggered arrangement of the array of cylinders, the key geometric dimensions are depicted in Figure 2.

Figure 2.

For the staggered arrangement of the array of cylinders, the scale factor for velocity is computed as follows :

	(10)

For the staggered arrangement of the array of cylinders, the Nusselt number is computed using equation 10a , 10b , 10c , and 10d.

If Re < 1000 ,

(10a)

If 1000 < Re < 200,000

(10b)

(10c)

If 200,000 < Re

	(10d)

Sphere

This module computes the convection heat transfer coefficient for external flow over a sphere for laminar flow conditions and constant temperature conditions. Reynold's number for flow over a sphere is given by:

The Nusselt number for sphere is computed using equation (11a , 11b , 11c , 11d) .

If Re < 776

(11a)

If Re > 776

	(11a)

If Re < 7.6 e⁴

(11c)

If Re > 7.6 e⁴

(11d)

Input

The inputs for this module are depicted in Figure 3. The inputs consist of the geometric dimensions, fluid flow properties and flow conditions. The flow over cylinder is selected as an example to illustrate the inputs and outputs.

Figure 3: ETBX inputs for heat transfer computations.

Results

The results are displayed using standard ETBX output window shown in Figure 4 . The outputs are flow regime and heat transfer coefficient.

Figure 4. ETBX heat transfer coefficient module outputs

References

1. K.A. Hoffman, S.T. Chiang, S. Siddiqui, M. Papadakis, (1996) Fundamental Equations of Fluid Mechanics, A publication of engineering educational system.
2. R.H. Perry, (1984) Perry’s Chemical Engineer’s Handbook, McGraw-Hill.
3. J.P. Holman, (1968) Heat Transfer, McGraw-Hill.