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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 ofwhereis the distance along the VFP from the leading edge andis 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 exponentsand Prandtl numbers () of −0.25 to 1 and 0.01 to 1000 respectively. The effects of two physical parametersandon 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  andThe TBL and VBL thickness are more influenced by  Pr  as compared toThese 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 whenboth the BL thicknesses decrease with the  Pr  till a value ofis reached. Forthe 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 inandat a fixed value of modified Rayleigh number.

Free convection boundary layer correlations for a vertical plate with nonuniform heating