**7. Nomenclature**


pitch is increased, higher velocity and higher temperature regions are observed on the

Increase in pipe diameter, keeping the inlet velocity constant, causes higher heat transfer coefficient and lower pressure drop. This effect is due to the influence of secondary flows. As the PCD is increased, the centrifugal forces decreases and this causes reduction of heat

Estimation of inner heat transfer coefficient for the two-phase flow was carried out by changing the void fraction and flow velocity. Results indicate reduction in heat transfer

The coil parameters, viz., PCD and pipe diameter and void fraction at inlet have significant effect on the heat transfer and pressure drop for two-phase flows through helical coils. However, the effect of pitch is negligible. It has been shown that the quantitative dependence of coil parameters on heat transfer is same for both single and two phase flows. Using the data generated from about 45 numerical experiments, a correlation to estimate

> *c <sup>r</sup> Re <sup>R</sup>*

bottom half of the pipe.

**7. Nomenclature** 

De

A area, m2

F Force term, N

H Tube pitch, m

L Length, m

p Pressure, Pa

Q Heat transferred, W q heat flux, W m-2

T Temperature, K

u Velocity, m s-1 u Velocity vector, m s-1

V volume, m3

**Greek** 

transfer coefficient and pressure drop.

coefficient with increase in void fraction.

two-phase heat transfer coefficient is developed.

**Symbol Description and units** 

Cp Specific heat, J kg-1 K-1 Dc Pitch Circle Diameter, m

Dean number

dimensionless

h Heat transfer coefficient, W m-2K-1

n unit vector along outward normal Nu Nusselt number, dimensionless

k Thermal conductivity, W m-1K-1

Pr Prandtl number, dimensionless

Rc Pitch circle radius of the pipe, m Re Reynolds number, dimensionless S Source term in governing equations

Void fraction, dimensionless

U Overall heat transfer coefficient, W m-2K-1

R Resistance to the flow of thermal energy, W-1 m2 K

r Inner radius of the tube, m


#### **8. Acknowledgement**

I express my sincere gratitude to Prof. Kannan N Iyer, Prof. S. M. Mahajani, Prof. J.C. Mandal and Prof. Vijayan P. K. for their meticulous guidance and extensive support during this research work.

## **9. References**


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**13** 

Piotr Wais

*Poland* 

**Fin-Tube Heat Exchanger Optimization** 

*Cracow University of Technology, Department of Thermal Power Engineering* 

Saving material and energy are common objectives for optimization. One of the important issues that should be defined during the design work, taking in consideration the cost of material, is the optimization of the heat efficiency. The optimization function can consider minimum weight for a specified heat flow, placement of individual fins to form channels or fin profile based on a set of specified conditions (for instance the dissipation from the fin faces, minimum mass, minimum pressure drop etc). In order to intensify the heat transfer from the heat exchanger surface to fluid, it is possible to increase convection coefficient (by growing the fluid velocity), widen temperature difference between surface and fluid or increase the surface area across which convection occurs. Extended surfaces, in the form of longitudinal or radial fins are common in applications where the need to enhance the heat

Fins are commonly used in extended surface exchangers. Conventional fin-tube exchangers often characterize the considerable difference between liquids' heat transfer coefficients. In a gas-to-liquid exchanger, the heat transfer coefficient on the liquid side is generally one order of magnitude higher than that on the gas side. To minimize the size of heat exchangers, fins are used on the gas side to increase the surface area and the heat transfer rate between the heat exchanger surface and the surroundings. Both the conduction through the fin cross section and the convection over the fin surface area take place in and around the fin. When the fin is hotter than the fluid to which it is exposed then the fin surface temperature is generally lower than the base (primary surface) temperature. If the heat is transported by convection to the fin from the ambient fluid, the fin surface temperature will be higher than the fin base temperature, which in turn reduces the temperature differences and the heat transfer through the fin. Exchangers with fins are also used when one fluid stream is at high pressure. The temperature value is limited by the type of material and production technique. All above causes that finned tube heat exchangers are used in different thermal systems for applications where heat energy is exchanged between different media. Applications range from very large to the small scale (tubes in heat exchangers, the

The subject, which is investigated in the chapter, is inspired by the increasing need for optimization in engineering applications, aiming to rationalize use of the available energy. The performance of the heat transfer process in a given heat exchanger is determined for different fin profiles, considering the fluid flow as a variability often neglected for the fin optimization. The optimization task, defined in the chapter, is to increase heat transfer rates and reduce the

transfer between a surface and an adjacent fluid exists.

temperature control of electronic components).

**1. Introduction** 

