An analytical study of a free convection boundary layer (BL) for a laminar and steady flow over a vertical flat plate (VFP) having nonuniform thermal conditions has been investigated. The plate is subjected to a variable wall heat flux of where is the distance along the VFP from the leading edge and is a reference heat flux. The boundary layer equations for nonuniform wall heat flux conditions have been formulated. These equations are then solved numerically for the range of exponents and Prandtl numbers () of −0.25 to 1 and 0.01 to 1000 respectively. The effects of two physical parameters and on the characteristic of thermal boundary layer (TBL) and hydrodynamic boundary layer (VBL) are described. Moreover, correlations of TBL and VBL thicknesses have been presented as a function of Pr and The TBL and VBL thickness are more influenced by Pr as compared to These correlations are reasonably accurate for uniform heat flux (n = 0) proposed by A. Bejan using a scale analysis and no other such correlations are available for nonuniform heat flux for a wide range of Prandtl numbers (Pr). It has been found that when both the BL thicknesses decrease with the Pr till a value of is reached. For the growth of VBL and TBL thickness over the VFP increases and decreases respectively. Consequently, the local skin friction coefficient decreases and the local Nusselt number increases with the increase in and at a fixed value of modified Rayleigh number.