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In the present work, carbon black (CB) works as a pore-forming agent in the preparation of alumina porous ceramics. The pore structures ( i.e. mean pore size, pore size distribution and various pores size proportions) were characterized by means of Micro-image Analysis and Process System (MIAPS) software and mercury intrusion porosimetry. Then their correlation and thermal conductivity as well as strength were determined using grey relation theory. The results showed that the porosity and mean pore size increased against the amount of CB, whereas the thermal conductivity, cold crushing strength and cold modulus of rupture reduced. The <2 μm pores were helpful for enhancing the strength and decreasing the thermal conductivity whereas the >14 μm pores had the opposite effects. [ABSTRACT FROM AUTHOR]