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In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformationsdoi:10.11648/j.acm.20170601.15 fatcat:c7wngy4vufaqxnytp5jj257e5i