Can beta D-glucose be present hydrolysate after hydrolysis of cellulose and how can it be converted into alpha D-glucose? When we perform the hydrolysis of cellulose by acid, we already knew that it can convert cellulose into glucose. As we know, cellulose is composed of beta glucose units linked by beta 1,4-glucosidic bonds. So I would like to know, resulting glucose after hydrolysis is beta or alpha glucose? If beta glucose is present, how can it be converted to alpha?
In aqueous solution, $\alpha$-D-glucose and $\beta$-D-glucose equilibrate. So glucose derived from aqueous acid hydrolysis of cellulose will eventually become an equilibrium mixture of α and β. 

A 2006 paper goes into great detail on the kinetics and thermodynamics of the interconversion (in water).  They say: 


  At 30 °C, the rate constants for ring closing toward α-pyranose and β-pyranose are 0.044 s−1 and 0.072 s−1, respectively.


Keep in mind those figures don't include the effect of acid catalysis, and are incomplete without rate constants for the formation of the ring-open aldehyde from the two different pyranoses.  But they should give you a rough sense of how quickly the process occurs.  A later figure in the same paper shows that it takes roughly 12,000 seconds or 3.3 hrs for nearly complete (~90%) relaxation to equilibrium.

Also see chemistry.stackexchange.com/a/7311/13184 for more information.