Afr. Mat. DOI 10.1007/s13370-014-0277-4 Mathematical modelling and exact solution of steady fully developed mixed convection flow in a vertical micro-porous-annulus Basant K. Jha · Babatunde Aina Received: 17 March 2014 / Accepted: 4 July 2014 © African Mathematical Union and Springer-Verlag Berlin Heidelberg 2014 Abstract This work analyzes the behaviors of fully developed mixed convection flow of an incompressible and viscous fluid in a vertical micro-porous-annulus (MPA) taking into account the velocity slip and temperature jump at the outer surface of inner porous cylinder and inner surface of outer porous cylinder. The present study explores the effects of the suction/injection, mixed convection, the Knudsen number, Prandtl number and the radius ratio on the MPA hydrodynamic and thermal behaviours. It is interesting to remark that as suction/injection on the MPA increases, the fluid velocity and temperature is enhanced. In addition, the rate of heat transfer at outer surface of inner porous cylinder decrease with increase in Knudsen number for suction at the inner porous cylinder and simultaneous injec- tion at the outer porous cylinder while the result is just contrast at inner surface of outer porous cylinder. Keywords Micro-porous-annulus (MPA) · Mixed convection · Suction/injection · Velocity slip · Temperature jump Mathematics Subject Classification 80A20 List of symbols C p = Specific heat at constant pressure D h = Hdraulic diameter [2(r 2 - r 1 )] F v = Tangential momentum accommodation coefficient F t = Thermal accommodation coefficient g = Gravitational acceleratioin B. K. Jha · B. Aina (B ) Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria e-mail: ainavicdydx@yahoo.com B. K. Jha e-mail: basant777@yahoo.co.uk 123