The similarity equations based on correct scaling as described in the reference book 'Convection Heat Transfer' by Adrian Bejan. The equations are given as:
(3/4)*F*theta' = theta"
(1/Pr)*(0.5*F'^2 - (3/4)*F*F") = - F"' + theta
The pdf file explains the correct scaling and also describes the derivation and the results of the numerical solution in detail.
Hope this helps!
Rohan Kokate (2021). Similarity solution of laminar natural convection BL flow (https://www.mathworks.com/matlabcentral/fileexchange/83588-similarity-solution-of-laminar-natural-convection-bl-flow), MATLAB Central File Exchange. Retrieved .
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