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Today, The industry looking for A new solutions to optimize energy. Industries release a large amount of water vapor into the atmosphere through gas stacks. The flue gas can be a potential source for obtaining much needed cooling water for industries. In this paper, numerical study to investigate the mass and heat transfer by condensing vapors by condensation waste heat recovery and water from the membrane to the flue gas is used, has been. The tube wall is made of a specially designed porous material which is capable to extract condensate liquid from the flue gas. Ceramic membrane capture water via capillary condensation, Recover, and reuse the sensible and latent waste heat. Comparison among the model findings with experimental data showed the validity and precision of the model with a deviation of less than 6%. The results indicated that Membrane condenser exchanger heat and mass transfer coefficients, respectively, 70 and 55 percent greater than the heat exchanger can be.