A variety of physical mechanisms acting over a long horizontal cylinder is studied in the present paper. The devotion is to discover some further exact solutions representing the flow and heat under new mechanisms. These include the wall slippage, temperature jump, free convection and asymptotic suction. The expansion or contraction of the cylinder implying that the radius is also changing in time is also taken into consideration. With the help of the presented analytical solutions, the effects of wall slip, temperature jump and wall expansion are easy to visualize, which must be simulated numerically otherwise.