Inverse solutions of convective heat transfer problems

Inverse problems are well known in nearly every discipline of science and engineering. In mechanical engineering, in particular, inverse heat transfer problems have always been a major focus for research and improvement. Inverse heat transfer solutions are usually needed when direct measurement of a boundary condition, commonly in the form of temperature, or a thermophysical property of a material, is not feasible. Estimating the aerodynamic heating on a reentering shuttle heat shields or approximating the temperature dependence of thermal conductivity of a cooled ingot during steel tempering are examples of inverse heat transfer applications in engineering. A new inverse methodology to tackle the inverse heat convection problem of a wall plume is studied and presented here. A detailed study of the forward problem is developed, and the results are used to build the inverse solution methodology. Through studying the forward problem, unique interpolating functions relating plume heat source strength and location to various flow features such as steady-state temperature on the wall downstream of the plume, are developed. These functions would form up a system of equations through which plume source strength and location are estimated. A search-based optimization method, particle swarm optimization (PSO), is used to minimize the estimation error through improving the system of equations. In the first study, numerically simulated steady-state laminar and turbulent wall plume flows are considered. Temperature variations on the wall prove to have a unique correlation with the heat input and location of the plume. Our proposed method formulates these relations into mathematical functions for distinct locations on the wall, downstream of the plume. PSO would choose the best pair, or more, of locations on the wall to read the temperatures and form up a system of equations to solve for plume heat source strength and location. Results demonstrate high accuracy in estimating both unknowns. The second study focuses on the transient behavior of the laminar wall plume flow. It is shown that the time it takes for the temperature, at any given location downstream of the flow, to reach a maximum across the boundary layer is related to plume heat input and location. The methodology formulates these functions and PSO would find the optimal data points on the wall to form up the system of equations. The results of this study also demonstrate high accuracy in estimating both plume strength and location. The third study is about testing the methodology against experimental data. An experiment setup of the wall plume problem was built and temperatures on the wall downstream of the plume were measured. To test the robustness of the methodology, the same relative functions derived in the first study are applied to the experimental data to great success. The inverse solution produces accurate estimations of the heat input and source location with the experiment data as well. The ultimate goal of this project is to provide an inverse solution to rapidly and accurately respond in applications that include free convection heat transfer, such as overheating of electronic devices and small fires in data centers and small rooms. To that end, the proposed methodology could be considered as the first step towards a more complex and general inverse heat convection solution.Ph.D.Includes bibliographical reference