solids meshing issue

Hello

 I'm going to mesh one cylinder in which the element size is supposed to be reduced across the axial direction. In other words, the cylinder  solid is should be mapped followed to top and bottom sides of cylinder as shown in the first figure. I have tried to mesh the solid adopting multi solid mapping method by dividing the main solid to several solids in axial direction however the not ''mappable face along the surface'' error is noticed. the second figure is my target sample.

Kindly consider this issue.

Thank you  

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