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Determination of the optimal design parameters for the wavy air fins used in the construction of automotive radiators.


On the matter of selecting the right heat exchanger from among several possible designs, the device of choice is the one that achieves the required heat rejection with minimum energy consumption for fluid circulation, while occupying the smallest space. A certain device cannot fulfill all these requirements at the same time. A diminished heat exchanger volume can be obtained either by increasing the circulation speed of the two fluids (for an existing device), or by altering the heat transfer surfaces, i.e. choosing a surface fitted with turbulence generators. Nevertheless, both methods lead to higher energy consumption for fluid circulation. The problem is resolved using statistical optimization of the geometrical parameters of the wavy air fins witch are used in the construction of radiators.


A water cooler in standard construction and a preset functioning regime have been chosen. Thermal performance calculations have been performed using air fins with different heights and pitches. In order to determine the heat rejection performance, the following have been used (Incropera & Dewitt, 2002):

--Similitude criteria Reynolds (Re)--denotes the flow pattern of the fluid (turbulence). The number Re is given by the fluid's flow speed, by the kinematic air viscosity and, also, by the hydraulic flow diameter; Coulburn (Cb)--this criterion is influenced by the global heat rejection coefficient k, determined by specific formulas;

--Thermo-dynamic parameters:

Friction (f)--coefficient which determines the air pressure drop and, consequently the air flow-rate; Coefficient (a)--named partial coefficient of heat rejection.

Heat rejection and Pressure drop (Q and [DELTA]p)--performance parameters.

In our case, the definition of the concept optimal is given by the correlation between air fin pitch and air fin height, and the result is: High heat rejection (Q in kW) vs. Low air pressure drop ([DELTA]p in mmH2O) (Nagi & Iorga, 2006).

The [DELTA]p parameter is closely correlated with the number Re, friction f, and also with the number Cb, and the Q parameter is linked to the a coefficient. Favorable results are obtained in the following situations (Kays & London, 1984):

The value of Re is high (Re<2320--laminar flow pattern, Re>10000--turbulent flow pattern, 2320<Re<10000--transitory regime);

The values of Cb and of the coefficient ([alpha]) are also high; The friction (f) values are small.


The statistical calculations were performed with ModeFrontiere software, in the following stages:

a) The parameterization sketch was drawn up in Mode Frontiere. This sketch has been built around a macro containing the thermal calculation algorithm. The macro will be used in a necessary number of iterations.

b) Within the work sketch, the input values-air fin pitch and height-have been parameterized. Each input value will be varied within a preset range.

c) Two types of output parameters, named objectives and objectives with constraints, have been set: Q has to be maximum, [DELTA]p minimum, Re >1700, f >0.05, a > 130, Cb > 1;

d) Predefining the parameters in the statistical calculation sequence DOE (Design of Experiment). The chosen method was "Random" and this method forms the basis of the experiment Design of Experiment. This method yields a uniform spread of data in the preset domain and it is based on the random number generating theory;

e) Choosing and predefining the "convergence" algorithm. For this stage the method Multivariate Adaptive Crossvalidating Kriging (MACK) has been chosen. This algorithm has been designed to improve the filling of the working space and to supply efficient data to the RMS method; this method is not an interactive one(***, 2008).


Considering the input data values that were constrained to vary between specified limits and the output data values with both constrained and non-constrained targets, statistical charts were plotted:

A. Multi-History 3D Ribbon chart is a three dimensional plot for the specified variables. This is how the optimization parameters' progress is monitored in time. Interpretation-the study of progress was conducted on parameters with comparable domains and these were: Pitch vs. Height which are interconnected, Fig. 1.

B. The Bubble 4D Chart is used when the data has a third and a fourth dimension that needs to be shown on the same chart. Each data point is displayed as a bubble. Two of the dimensions are axis represented. The Radius Variable (the third) value influences the bubble diameter: the larger the bubble, the greater the value. The Color Variable (the fourth) value influences the bubble color: blue represents a lower value, red an upper value. Interpretation- Bubble 4D charts were plotted, Fig. 2, for two series:

--Heat rejection vs. Air pressure drop, where the target values Colburn and friction are being presented (analysis input values vs. output values). The maximum values of the output parameters are focused in the area 25-28 kW Heat rejection, 18-20mmH2O Air pressure drop.

--Air fin height vs. Air fin pitch which can be interpreted in a similar manner, (analysis input values vs. output values).

C. The Correlation chart represents a measure of the linear association between two variables, Fig. 3. The degree of relationship receives the values: "1" (two variables are perfectly positively correlated); "0" (the variables are said to be uncorrelated, that means that they are linearly unassociated); "1" (the two variables are perfectly negatively correlated). Interpretation-in the first column, the Reynolds parameter is positively correlated (0.499) with the Air fin height parameter, which results in a medium influence on the relationship between the two variables output / input. The data on the other columns and rows will be interpreted identically.

D. The Parallel Coordinate Chart is used for visualizing data in a particular range, particularly by employing a filter (the green line), Fig.4. The user can set the lower and upper limits for the variables, and can spot the thermal performance solutions within the specified domain. Interpretation-the filter has been set to the maximum values, offering the opportunity to observe the full spectrum of feasible / non-feasible solutions (***, 2008).


This paper is highly original concerning the field of statistical study of the air fin performance. The paper initiates an optimization algorithm for the heat transfer phenomenon, which is applied to the air fins used in the construction of radiators. All possible combinations were performed between the input dimensions: pitch and height, Fig.1. From the analysis of the charts, the next conclusions were drawn: an optimal operating point is Q=25 kW, the value of Cb is high (1.18), f (0.057), and air pressure drop (16 mmH2O), Fig.2. The optimal value of heat rejection is obtained in the case of the following input dimension combination: the pitch is 6.5mm, the height is 11mm, and the value of the air pressure drop is 16 mmH2O, Fig.2. The fin pitch and height parameters are closely correlated with Re, Fig.3.

The whole spectrum of possible solutions for the fin pitch and fin height combinations was obtained from the statistical analysis.






Incropera F. P. & Dewitt D. P. ((2002). Fundamentals of Heat Mass transfer-Fifth Edition, ISBN 0-471-38650-2

Kays W. M. & London A. L. (1984). Compact Heat Exchanger-Third edition, ISBN 1-57524-060-2

Nagi M.& Iorga D.; (2006). Heat Exchangers, ISBN (10) 973-52-0001-5, Vol 1, Vol 2

*** (2008) ModeFrontiere software. Help and Tutorials

*** (2009) Kuli Component software. Help and Tutorials
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Author:Ilies, Paul; Naghi, Mihai; Mare, Ciprian; Sucila, Marius
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:4EUAU
Date:Jan 1, 2009
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