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The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter  r  = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter  S  arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 &lt;  n  &lt; 1) flows from the shear-thickening fluid ( n  &gt; 1) flows while the Newtonian fluid ( n  = 1) flows remain unaffected by this parameter no matter what be the value of  S .

Natural Convection Flow of Power-Law Fluids over a Heated Horizontal Plate Surface