However, there are many problems, particularly in practical processes and systems, where the desired result is known or prescribed, but the conditions needed for achieving this result are unknown. The boundary conditions may also be undefined or unknown. Such problems are known as inverse problems since we seek to determine the conditions that would lead to the known desired outcome. The solution of inverse problems is of interest in many different areas such as biology, medicine, and economics. But this is of particular interest in thermal processes and systems. For instance, in manufacturing and advanced materials processing, the time-dependent temperature, shear, or pressure variation which a component must undergo to obtain desired characteristics is often prescribed from material property considerations. An example of this circumstance is the heat treatment of materials. However, the boundary and initial conditions, in terms of heat input, pressure, flow rate and temperature, are not known and must be determined by solving the inverse problem. Similarly, in environmental problems, we may be interested in determining the location and energy discharged by a source such as a fire. But, because of hazardous conditions, we are only able to measure temperature, flow, and concentration far downstream from the source. We can then use an inverse solution to locate the source and obtain its input.

This paper focuses on inverse problems in thermal convection and considers a few fundamental and practical circumstances. The inverse problems resulting from a thermal plume or jet in cross flow and from a heat source on a vertical flat surface are of particular interest in environmental problems and in fire safety. The inverse problem involves determining the strength and location of the heat source or the jet by employing a few selected data points downstream, since an extensive collection of data is often expensive and time consuming. A major concern in inverse solutions is the non-uniqueness of the results obtained. Therefore, optimization techniques are needed to reduce the uncertainty in the results. A predictor-corrector strategy is outlined, along with optimization to minimize the data points needed and to ensure uniqueness of the solution. Another approach based on search and optimization is also developed to solve the inverse natural convection flow due to a finite heat source, such as an electronic component or a fire, on a wall.

Similarly, another problem considered here is an optical fiber drawing furnace whose wall temperature distribution is not known. But a few selected data points on a rod at the center of the furnace are used to solve the inverse problem to determine the wall temperature to a high level of accuracy and uniqueness. Again, optimization of the process is used to enhance the efficiency of the solution strategy and obtain an essentially unique solution. These basic approaches can be extended to other inverse convection transport problems. A few examples are given to demonstrate the importance of inverse solutions and the versatility of the presented solution strategies.