Piotr Wais

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

#### **1. Introduction**

342 Heat Exchangers – Basics Design Applications

Rennie T.J., Raghavan, V. G. S., 2006b, "Effect of fluid thermal properties on heat transfer

Rennie, T.J., Raghavan, V. G S, 2006a, Numerical studies of a double-pipe helical heat

Rennie, T.J., Raghavan, V.G.S., 2007, Thermally dependent viscosity and non-Newtonian

Rogers, G. F. C. and Mayhew, Y. R., 1964, Heat transfer and pressure loss in helically coiled

Ruffel, A.E., 1974, The application of heat transfer and pressure drop data to the design of helical coil once-through boilers, Multiphase Flow Systems Meet., Glasgow Schmidt E. F., 1967, Wfirmeiibergang und Druckverlust in Rohrschlangen, G'zemieJng.-

Seban, R. A., and McLaughlin, E. F., 1963, Heat transfer in tube coils with laminar and

Shah, R. K. and Joshi, S. D. 1987, Convective heat transfer in curved ducts. Handbook of

Sreenivasan K. R. and P. J. Strykowski, "Stabilization Effects in Flow Through Helically

Srinivasan P.S., Nandapurkar, S.S. and Holland, F.A., 1968, Pressure drop and heat transfer

Srinivasan, P. S., Nandapurkar, S. S. and Holland, F. A., 1970, Friction factor for coils, Trans.

Stepanek, J. B. and G. Kasturi. 1972. Two phase flow – II. Parameters for void fraction and

Tarbell J M, Samuels M R. Momentum and heat transfer in helical coils. Chem Eng J

Vimal Kumar, Supreet Saini, Manish Sharma and K D P Nigam, 2006, Pressure drop and

Watanabe, O., K. Nakajima and H. Fujita. 1993, Characteristics of liquid-film thickness of

Whalley, P. B. 1980, Air-water two-phase flow in a helically coiled tube. Int J Multiphase

Xin RC, Awwad A, Dong ZF, Ebadian MA. 1997, An experimental study of single-phase and

Xin, R. C., A. Awwad, Z. F. Dong and M. A. Ebadian., 1996, An investigation and

Yildiz, C., Bicer, Y., Pehlivan, D., 1997, Heat transfer and pressure drop in a heat exchanger

helicoidal pipes. Int J Heat and Mass Transfer, Vol. 39( 4), pp 735-743. Yang, G. and Ebadian, M. A., 1996, Turbulent forced convection in a helicoidal pipe with

substantial pitch, Int. J Heat Mass Transfer, Vol 39(10), 2015 – 2032.

heat transfer in tube-in-tube helical heat exchanger, Chem. Eng. Sci. 61, 4403 – 4416

air-water annular two-phase flow in helically coiled tubes. Heat Transfer –

two-phase flow pressure drop in annular helicoidal pipes. Int J Heat Fluid Flow, 18,

comparative study of the pressure drop in air-water two-phase flow in vertical

with a helical pipe containing inside springs, Energy Convers. Mgmt., 38 (6), 619-

pressure drop correlations. Chem. Eng Sci, Vol. 27, pp 1881-1891.

Single-Phase Convective Heat Transfer, S. Kakac, R. K. Shah, and W. Hung (eds.),

tube with turbulent flow, Int J Heat Mass Transfer, 7, 1207-1216.

exchanger, Applied Thermal Engineering, 26, 1266-1273.

turbulent flow, Int. J Heat Mass Transfer, 6, 387-495.

Coiled Pipes", Experiments in Fluids 1, 31-36 (1983)

Wiley Interscience, New York, Chapter 3.

in coils, Chem. Eng. 218, CE113-CE119

Japanese Research, Vol. 22, No. 5, pp 447-461.

Inst. Chem. Eng., 48, T156 - T161.

1158-1165

6), 862-868

Tech., 39, 781-789.

1973;5:117–27.

482–488.

624.

Flow, Vol. 6, No. 345-356.

characteristics in a double pipe helical heat exchanger", Int. J. Thermal Sciences, 45,

flow in a double-pipe helical heat exchanger, Applied Thermal Engineering 27 (5-

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 transfer between a surface and an adjacent fluid exists.

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 temperature control of electronic components).

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

Fin-Tube Heat Exchanger Optimization 345

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 temperature is lower than the base (primary surface) temperature *T*<sup>0</sup> , the heat is transferred from the fin to the surroundings

(x)

QCONV 

(x)

x .

x d x

x

The temperature distribution can be calculated taking into consideration an energy balance

d x

CONV . d Q

Q <sup>x</sup> <sup>d</sup> <sup>x</sup> . Q

w

P(x) 2[w (x)]

A(x) (x) w

, where

( ) *x* . Its perimeter for surface convection

. Its cross-sectional area for heat

– fin thickness as a function of

Fig. 1. Straight fin of variable cross section.

The fin height is *l* , width is *w* , variable thickness

conduction at any cross section is *Ax x w* () ()

Fig. 2. Energy balance on a typical element.

depends on coordinate *x* and is *Px w x* ( ) 2[ ( )]

x

T0

l

on a typical element between *x* and *x dx* , shown in Figure 2.

(Shah & Sekulic, 2003).

Q0 

*x* , *w* - fin width.

fin mass by means of changing the shape of the fin. The fin shape modification influences not only the mass of the heat exchanger, but also affects the flow direction that causes the temperature changes on the fin contact surfaces. The air flow is considered in all 3D models. The numerical outcome of heat transfer coefficient is compared to the results received from the empirical equation for the fin-tube heat exchanger of uniform fin thickness. The correlation function is cited and the procedure how to verify the models is described. For modified fin shapes, mass flow weighted average temperatures of air volume flow rate are calculated in the outlet section and compared for different fin/tube shapes in order to optimize the heat transfer between the fin material and the air during the air flow in the cross flow heat exchanger.
