Since Mandelbrot founded the fractal geometry theory in early 1980’s, the theory and technique have received steady attention in many disciplines such as in physics, mathematics, and engineering. etc. In this talk, a brief history about Euclid geometry and fractal ge-ometry is reviewed, and then the research progresses on fractal ge-ometry theory and technique are reviewed including exactly self-similar fractals and statistically self-similar fractals. Follow on is a brief review on research progresses on transport properties in the areas of modern science and engineering including material science and engineering, fiber science and engineering, energy engineering, and transport in porous media, etc. by fractal geometry theory and technique. Finally, a few of comments are made on future possible research directions regarding the fractal geometry theory and their applications.
Keywords: Fractal, Material science and engineering, Fiber science and engineering, Porous media, Review.
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