Parameters Retrieval of Heat Transfer systems using Inverse Optimization

Abstract

This thesis is dealing with the numerical and experimental analysis of heat transfer systems to minimize the loss of heat transfer and maintaining the temperature as per our requirement. Fins are the one of the heat transfer system employed to dissipate the heat from the heating equipment. The race of maintaining the high efficiency from the least inputs tends to originate new technology in the field of heat transfer. Different types of configuration of fins are used for the purpose of heat transfer. Our body is also behave like a heat transfer system considered as bioheat system. Present work marked at applying the theory of parameter estimation by optimization techniques to a few engineering and bioheat problems involving heat transfer. For this, two heat transfer problems involving cylindrical pin fin and brain tissue have been considered. In addition, experimental data based parameter retrieval on a cylindrical pin fin is also undertaken. The work successfully reveals the application of one non-evolutionary optimization algorithms Golden Section Search Method (GSSM) for single parameter retrieval and one evolutionary optimization algorithms Differential Evolution (DE) for unknown multi-parameter retrievals. At first pdepe pin fin involving all temperature-dependent modes of heat transfer and discrete boundary conditions and finite element method is employed to solve the Pennes bioheat transfer equation as forward problem in cancerous brain. Furthermore, experiments are also done to get forward results on the pin fin of brass. Then, the GSSM and the DE are applied on these fin problems to inversely predict critical parameters such as heat flux, heat transfer coefficient, and perfusion rate. After estimating various parameters, the amount of satisfactory simulated measurement errors/noise are also evaluate. Based on the literature survey, the research work initiates with the formulation and the solution of the recognized parabolic heat transfer problems on fins and bioheat transfer involving different levels of nonlinearities, for which either forward and/or inverse analyses were not found or less work done. Under this gaps are identified, two parabolic heat transfer problems are assumed. Initially, for the forward solution, the pdepe is applied for the cylindrical pin fin of brass involving all temperature-dependent modes of heat transfer and discrete boundary conditions. Furthermore, a comparative experimental study is also conducted on a solid brass pin fin. The experimental values are used for the theoretical analysis in MATLAB. Later, the GSSM and the DE, are applied on these bioheat and fin problems to inversely guess critical parameters such as the heat flux, heat transfer coefficient, perfusion rate. Due to the incompatibility of the GSSM for multi-parameter estimation, the DE is used as optimization technique for the multiple parameter retrievals. After estimating various parameters, the amount of satisfactory simulated measurement errors/noise are also evaluated. Different cases of heat input in the fin is studied like constant heat flux, variable heat flux, static heat flux in triangular manner and static heat flux in realistic form. For constant heat flux under static conditions, a tolerance level of 5% is acceptable for temperature with a maximum error of 3.72% in reconstruction. Linear triangular heat flux with on-off conditions under static conditions, a tolerance level of 3% is acceptable for temperature with a maximum error of 6% in reconstruction. Non-linear realistic heat flux under static conditions, a tolerance level of 4% is acceptable for temperature with a maximum error of 4% in reconstruction. The retrieved heat flux is well in agreement with the actual heat flux as confirmed by experiments. The maximum uncertainties in reconstructed heat flux are 5%, 6% and 2% for different voltage and current. It is also found that the present retrieval procedure is a real approach to estimate unknown regulatory parameters for practically filling a wanted output from a given system. The concept of heat transfer analysis is also applied to retrieve parameters such as perfusion rate to estimate the presence, size, and location in parabolic bioheat transfer problems of brain tissue. The Pennes model is used for the heat transfer and solved by the Finite Element Method as forward problem. The gradient free Differential Evolution is used as the optimization method. The code is run for three times, and each time different combinations of the unknown parameters are found. It is observed that the maximum deviation of temperature field obtained from estimated value of (P1, P2, P3, P4, P5, P6 and P7) from exact ones is found to be 0.008 %.