A Genetic Algorithm Based Optimization Scheme To Find The Best Set Of Design Parameters To Enhance The Performance Of An Automobile Radiator

A R T I C L E I N F O Radiator, Overall Heat transfer rate, Genetic Algorithm, Spacing ratio Received July 2013 Accepted July 2013 Available online December 2013 The present work aims at maximizing the overall heat transfer rate of an automobile radiator using Genetic Algorithm approach. The design specifications and empirical data pertaining to a rally car radiator obtained from literature are considered in the present work. The mathematical function describing the objective for the problem is formulated using the radiator core design equations and heat transfer relations governing the radiator. The overall heat transfer rate obtained from the present optimization technique is found to be 9.48 percent higher compared to the empirical value present in the literature. Also, the enhancement in the overall heat transfer rate is achieved with a marginal reduction in the radiator dimensions indicating better spacing ratio compared to the existing design. ________________________________ * Corresponding Author G.Chaitanya, B.Ravi Sankar / International Journal of Lean Thinking, Volume 4, Issue 2( December 2013) 34 probability of flux brazed aluminum radiators in automobiles. The radiators used in cars whose service life exceeded 10 years were tested after adequate flux removal treatment and routine maintenance. The results were satisfactory indicating high probability of reutilization of aluminum radiators. Kyoung suk park et al (2002) developed a theoretical model to analyze the heat transfer phenomenon of automotive cooling systems. The heat release phenomenon from combustion gas to coolant through the cylinder wall was simulated using the engine cycle simulation program. Shires et al (1994) presented very exhaustive and lucid information on the of mechanism heat transfer in various types of heat exchangers such as shell and tube, double pipe exchangers and re boilers. The information showed greater emphasis on process heat transfer which is very significant from the automotive domain point of view. Chiou (1975) applied the unit core heat transfer method to obtain the necessary correction factor when the tube length of the radiator varies from the basic core length. The correlation data required for generating the necessary correction factor were obtained from the wind tunnel tests. Brace et al (2001) studied the applicability of electrically controlled cooling systems for automotive engines. The work described a system whose coolant flow rate could be strategically controlled by a micro-processor resulting in optimal flow rate of coolant for effective heat transfer. Robinson et al (2003) developed novel heat transfer correlations for IC Engine radiators based on the data obtained from a specially designed test rig. The test rig was operated under wide variety of conditions. The factors such as surface roughness, fluid viscosity variations at different temperatures and dynamically under developed flow were considered in the new correlations. Kodandaraman and Subhramanyan (2004) presented a comprehensive collection of various material property data and formulae in the field of heat and mass transfer covering all modes of heat transfer, both steady state and transient. With the advent of various mathematical programming techniques, many researchers applied various algorithms to determine the optimal design parameter set that maximizes the overall heat transfer rate of the radiator. Optimization of complex nonlinear functions of higher order such as the overall heat transfer rate function of radiator is an uphill task. The conventional optimization schemes often result in getting trapped at local optimum or may take impracticably high number of iterations due to a poor starting design vector. Genetic Algorithms provide an efficient solution to such problems. Genetic algorithms are highly unlikely to get trapped at a local optimum as they work with a population of design vectors instead of a single starting vector. Andrey Popov (2005), developed mat lab codes for both single and multi-variable function optimization using genetic algorithm. Both conventional and blending cross over mechanisms were extensively utilized in arriving at function optimal. David Goldberg (2006) presented detailed and in depth information on different genetic operators and on some advanced concepts like sharing parameters, principle of dominance etc with supporting programs and a wide variety of examples. Puneet Saxena et al (2001) applied the genetic algorithm technique on an automobile radiator for achieving a cost effective solution. Uniform spread cross over mechanism was adopted for generating the offspring population of design vectors from the mating pool. Rajasekharan and Vijayalakshmi pai (2003) gave a comprehensive introduction to genetic algorithm technique through lucid examples along with other evolutionary techniques such as fuzzy logic and neural networks. The operation of various genetic operators and various selection mechanisms such as roulette wheel, tournament and rank based techniques were explained in detail through simple hand calculations and simply written codes. Deb (2004) introduced various techniques for handling maximization type functions and minimization type functions using genetic algorithms. Various constrained handling techniques were also discussed in detail as genetic algorithms are usually known to handle unconstrained G.Chaitanya, B.Ravi Sankar / International Journal of Lean Thinking, Volume 4, Issue 2( December 2013) 35 optimization functions. In this work, the objective function (Overall heat transfer rate) is modeled using 4 design parameters which in turn are represented as functions of 6 design variables (tube corner radius, tube width, tube wall thickness, length of the tube, no of tubes and fin width.). The range or spread of each design variable i.e. upper and lower bounds are defined from the experimental data present in the literature. The optimization process is carried out using roulette wheel selection technique and by implementing the uniform cross over mechanism for generating off spring design vectors. 2. STATEMENT OF THE OPTIMIZATION PROBLEM In devices such as radiators, where the usual process of heat transfer takes place through more than one mode, the overall heat transfer coefficient is estimated. The overall heat transfer coefficient U is a function of local heat transfer coefficients. The local heat transfer coefficients are in turn functions of Reynold’s number, Prandtl number, thermal conductivity and air flow passage diameter. The overall heat transfer rate is obtained as the product of overall heat transfer coefficient and total heat transfer area. Based on the test results, the following empirical relation representing the overall heat transfer rate of the rally car radiator was presented by Franciscus Xavierus Laubscher (6) and is represented as equation [1]. Where, Dhw: Hydraulic diameter of water tubes in meters Dha: Hydraulic diameter of air flow passages in meters Aw: Total heat transfer area on the water side of heat exchanger in square meters. Aa: Total heat transfer area on the air side of heat exchanger in square meters. are the design parameters that are in turn functions of the design variables (tube corner radius rt , tube width xtw , tube wall thickness xtwt , length of the tube L, no of tubes n and fin width xfw). The design parameters Dhw, Dha, Aw and Aa are estimates as shown in equations 2 to 5 respectively. The values of Reynolds number, Prandtl number, thermal conductivity on water side and air side of the radiator as well as the values of constants C4 , C5, a and d from literature (Franciscus Xavierus Laubscher (6) ) are tabulated in tables 1 to 2. The coefficients of dynamic viscosity are chosen from C.P kodandaraman data book (4). C4 0.0225082 Reynolds number (water side), Rew 8686.99 a 0.6491463 Thermal Conductivity (Water), Kw 0.6575 w/m c Prandtl number. Prw 2.55 Table 1: Design parameters on water side of radiator C5 1.0365971 Reynolds number (air side), Rea 1786.736 d 0.4860783 G.Chaitanya, B.Ravi Sankar / International Journal of Lean Thinking, Volume 4, Issue 2( December 2013) 36 Thermal Conductivity (Air), Ka 0.02653 w/m c Prandtl number Pra 0.693 Table 2: Design parameters on air side of radiator                  