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The linear stability of a thin film of volatile liquid flowing over a surface with embedded, regularly spaced heaters is investigated. The temperature gradients at the upstream edges of the heaters induce gradients in surface tension that create a pronounced non-uniformity in the film profile due to the formation of capillary ridges. The Governing equations for the evolution of the film thickness are derived within the lubrication approximation, and three important parameters that affect the dynamics and stability of the film are identified. The computed two-dimensional, steady solutions for the local film thickness reveal that due to evaporation there is a slight change in the height of capillary ridge at subsequent heaters downstream. Using a linear stability analysis, it is shown that, as for a single heater, the film is susceptible to two types of instabilities. A rivulet instability leads to spanwise-periodic rivulets, and an oscillating thermocapillary instability leads to streamwise, time-periodic oscillations in the film thickness. The critical Marangoni number is calculated for both types of instability for a range of parameter values. The effect of the number of heaters, heater width, and gap between the heaters on the critical Marangoni number is computed and analyzed. For small evaporation rates and less volatile films, the presence of multiple heaters has almost no noticeable effect on the film stability. For larger evaporation rates and more volatile films, additional heaters decrease the Marangoni number at instability onset. The destabilizing effect of multiple heaters is sensitive to the heater geometry and spacing. Furthermore, the limitations of streamwise periodic boundary conditions for analyzing the stability of such flows are discussed. Computations on the transient and nonlinear growth of perturbations are also presented and indicate that the results of eigenanalysis are physically determinant.

Watermarking software is one of the most important methods for protecting copyrights, certifying ownership, and combating software piracy. The advancement of communication technology has resulted in an enormous amount of digital data that needs to be protected. Watermarking is a technique for concealing private information in an original signal while improving its overall performance. Multipleiwatermarking, which involves inserting more than oneiwatermark into a singleimultimedia product, is another hot topic in the world of digital picture watermarking. Using simply a digital watermarking approach, a trademark or copyrightmessage is discreetly inserted in the medical image. Many academics have collaborated to create ANFIS, which includes a watermark in the principal (cover) image. Watermarking embedding locations can be chosen based on regions of interest (ROIs). We first deconstruct the cover image into four sub-bands with 3-L LWT, then modify the singular values inside each band with SVD. Following various attacks on the watermarked image, such as blurring, addinginoise, pixelation, rotation, rescaling,icontrast adjustment, gammaicorrection, histogram equalisation, cropping,isharpening, lossy compression, and so on, the original insertediwatermark image is extracted from allibands and compared using MSE and PSNR values. The trials reveal that changing all frequencies makes our watermarked image more resistant to a wide range of image processing attacks (including standard geometric attacks), i.e. we can effectively recover the watermark from some of the four sub-bands using ANFIS.