How alcohol dissolves a non-polar solutes like alkane ? Is it the dispersion force done the work ?

By definition, alcohols have the OH group (polar) and this is why short alkyl (low number of carbons) alcohols are miscible in water. However, alcohols have an alkyl moiety as well. This is non-polar and interacts with the non-polar nature of the alkane, thus dissolving it. A given alkane solute will be more soluble in n-butyl alcohol than it will be in methanol since the n-butyl alcohol has a larger non-polar group than does the methanol.