Optimizing the Design of Radiator using Genetic Algorithms

Abstract

This paper describes the application of genetic algorithms to achieve the optimal design of a radiator used in automobiles so as to achieve not only the required performance but also to find a cost effective solution. The performance of an automobile radiator is a function of overall heat transfer coefficient and total heat transfer area. The basic thermodynamic equations are utilised to enable the calculation of the overall heat transfer coefficient of the vehicle radiator core and thereafter the genetic algorithm is used for manipulating the design parameters to achieve the optimal solution.

1. Introduction

Radiators are heat exchangers responsible for controlling engine-operating temperatures. The heat carried by the cooling water jacket is generally 30% of the total energy produced in the engine. This energy must be removed constantly through the use of a heat exchanger, or a radiator. A suitable radiator is used to achieve not only the efficient performance of the engine but also the cost-effective solution for the cooling system. In radiators, heat carried by the coolant fluid is transported by convection and conduction to the fin surface and from there by thermal radiation into the atmosphere-free space. The hot and cold fluids are separated by an impervious surface and hence they are also referred to as surface heat exchangers. In the case of a radiator, the hot fluid flows inside the tubes and so the hot fluid is unmixed. However, the cold fluid flows over the tubes and is free to be mixed. The mixing tends to make the fluid temperature uniform in transverse direction; therefore, the exit temperature of a mixed stream exhibits negligible variation. The total heat transfer rate between the fluids is dependent on the overall heat transfer coefficient and the total heat transfer area.

The design optimization problem involves both explicit constraints (such as fixed frontal area) and implicit constraints (such as those specifying the heat transfer coefficient). Once the geometry is selected, additional constraints such as minimum and maximum values for the fin pitch, minimum and maximum number of tubes and the cross-section of the tubes are imposed, and thereafter the problem reduces to that of solving the problem within the ranges of variables specified to achieve the optimal design. The overall heat transfer coefficient is dependent on the number of tubes; in general, as the number of tubes increases the heat transfer coefficient improves. However, additional factors such as vibration damage (if the tubes are very close together), the need to access the outer surface of tubes for cleaning, and the limit on pressure drop across the radiator affect the decision on the number of tubes. Fins are attached to the tubes by brazing or soldering, thereby imparting strength to the whole assembly and enabling the exchanger to withstand high pressure. Fins not only enhance the overall heat transfer coefficient but also significantly increase the total heat transfer area and thus help enhance the performance of a radiator. However, if the fin pitch is high, the fluid in between the fins will move at a lower velocity (for constant pumping power) giving more time for fouling to occur and it further becomes difficult to clean the assembly. It is costly to have high fin pitch. Thus, fouling, maintenance, manufacturing, and cost considerations limit the fin pitch. The profile of the tube plays an important role as it affects the contact area between the two fluids without adding much cost, but the manufacturing process again limits the kinds of profiles that can be adopted economically.

The factor most often used to evaluate the performance of the radiator is the product of overall heat transfer coefficient, U, and the total heat transfer area, A. The overall heat transfer coefficient is a function of the heat transfer coefficient and a fouling factor. The fouling factor is a constant for given environmental conditions while the heat transfer coefficient can be calculated by using the following set of equations:
Heat Transfer Coefficient, h =

Reynolds Number, Re =

Mass Velocity, G =
where c_p is specific heat at constant pressure, A' is frontal area of radiator,  is density of air, v is velocity of air at inlet, A_c is free-flow area of radiator, Pr is Prandtl number, D_h is hydraulic diameter, St is Stanton number, and  is the dynamic viscosity of the radiator fluid.

The total surface area through which heat exchange occurs is dependent on the profile of both the tubes and the fins, the number of tubes, the fin pitch and the number of rows. The configuration of fins and tubes also affects the performance, but the current study is confined to only straight fins and inline tubes. Figure 1 shows the radiator core having straight fins and tubes.

Figure 1: Radiator core showing the straight fins and tubes with air and water flowing at right angles to each other.