Article [11] Unsteady Heat Transfer Of A Monatomic Gas Between Two Coaxial Circular Cylinders Abstract: We consider a kinetic-theory treatment of the cylindrical unsteady heat transfer. A model kinetic equation of the BGK(Bhatnager-Gross-Krook) type is solved using the method of moments with two-sided distribution function. We study the relations between the different macroscopic properties of the gas as the temperature, density, and heat flux with both the radial distance r and time t. Also we study the problem from the viewpoint of irreversible thermodynamics and estimate the entropy, entropy production, entropy flux, thermodynamic forces, kinetic coefficients, the change in internal energy, and the verification of the positive sign of the kinetic inequality stemmed from the Onsager , relation for nonequilibrium thermodynamic nature of the system. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jam/1049075017