Mathematical Model-Based Optimization of Thermal Performance in Heat Exchangers Using PDE-Constrained Methods

Abstract

Heat exchangers are an important element seen inNULL power generation, chemical processing and HVAC lines, wherein the efficient thermal management concludes directly on the energy consumption, system life and the operational cost. One of the common traditional design approaches is empirical correlations with iterative experimentation, which is time consuming and suboptimal for complex geometries or changing operating condition. This article reports on a comprehensive and mathematically rigorus optimization framework for heat exchanger thermal performance using partial differential equation (PDE) constrained optimization. The model couples the incompressible Navier–Stokes equations for fluid flow with the convection–diffusion energy equation for heat transfer, which allows details in coupling of the thermal and fluid domains of the heat exchanger. A physical and geometric constrained approach is then used to formulate the objective functional that minimizes temperature non uniformity, pressure losses and thermodynamics irreversibility. Finite element discretization with a Galerkin formulation is used for numerical implementation while adjoint based sensitivity analysis is used for efficient gradient computation which make gradient based optimization algorithms scalable. The proposed method is shown to effectively improve the heat transfer rate, reduce pressure drop post heat transfer, and minimize entropy in a shell and tube heat exchanger using a case study. Predictions from this modeling agree with experimental data, hence verifying the applicability of PDE-constrained optimization to enable them to become the next generation of thermal systems through high fidelity, physics informed and computationally efficient pathway.