1. Discuss image formation in schlieren and shadowgraph measurements when the test section is a region of non-isothermal fluid. Compare images to be expected in schlieren when the knife edge is moved to change the initial intensity falling on the screen. Compare images obtained in shadowgraph when the screen position is moved away from the test cell. Consider various possibilities such as side heated cavity, differentially heated horizontal fluid layer with stable and unstable stratification, and a heat generating fluid layer.
2. Beam deflection and displacement are sources of errors in interferometry. Beam displacement is a source of error in schlieren. In this respect, shadowgraph is the most general optical method available transport phenomena. Examine beam displacement errors during schlieren as a function of the length of the apparatus and the temperature gradient. Evaluate these errors numerically for assumed values of lengths and temperature differences. Would refraction errors be greater in liquids as compared to gases? Discuss removal of these errors from schlieren data.
3. Examine the validity of linearizing approximations in shadowgraph analysis.
4. A layer of common salt starts to dissolve in water contained in a circular beaker. It is required to image concentration field (and its gradients) as a function of time. It is proposed that schlieren and shadowgraph techniques be used for this purpose. Develop the optical configurations required for this purpose and the steps involved in image analysis. Sketch expected images when the knife edge position is changed (schlieren) and the screen is moved away from the exit plane of the apparatus (shadowgraph).
5. Discuss design principles for monochrome and color filters. Discuss analysis of color schlieren images in the context of question 4.
6. Discuss image processing techniques suitable for schlieren and shadowgraph. Develop computer programs for methods such as Fourier filtering, contrast improvement, and histogram equalization. These programs can be applied to synthetic (analytically generated) images created by suitably defined intensity functions. 
7. Discuss evaluation of temperature from schlieren images when the wall boundary condition is one of prescribed temperature. Repeat this calculation for a wall boundary condition of constant heat flux.
8. A rectangular region is fully insulated and carries a heat generating fluid. Discuss appearance of schlieren and shadowgraph patterns as a function of time.
9. Develop computer programs for tomographic inversion of schlieren and shadowgraph data using convolution back projection and algebraic reconstruction techniques. Here, the test data can be generated from a synthetic three dimensional steady temperature field. Given this function T(x,y,z), projections of the derivative fields can be obtained by numerically integrating temperature in the viewing direction over the chosen physical domain. With the projection data combined with the tomographic inversion algorithm, the original temperature field can be reconstructed. Inversion errors can be estimated by comparing the original field against the reconstructed.
10. Self-study: Review related methods such as schlieren interferometry (article 3), and schlieren tomography applied to unsteady heat and mass transfer (article 4).