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Free Convection Past a Vertical Flat Plate

version (18.7 KB) by Housam Binous
computes velocity and temperature profiles


Updated 27 Nov 2007

No License

The program computes the velocity and temperature profiles for free convection past an isothermal vertical plate. Results are obtained after solving two coupled nonlinear differential equations. The shooting method is used to obtain the boundary conditions, required to solve the coupled ODEs, which match the conditions in the outer fluid. We plot velocity and temperature profiles versus a similarity variable for different Prandtl numbers (Pr=0.01, 1, 10 and 100). The figures obtained are in agreement with those given in Analysis of Transport Phenomena, William M. Deen, OUP, 1998 (figures 12-5 and 12-6 pages 500-501). This problem was solved originally by Ostrach, 'An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force', NACA Tech. Rept. No 1111, 1953. Derivation of the governing equations can be found in Deen's book.

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Cite As

Housam Binous (2020). Free Convection Past a Vertical Flat Plate (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (9)

Sopan Das


works with matlab2009 but not with the newer version of matlab i tried.


good thinks

r. rajesh

verry good e book


John D'Errico

This is getting better. There are now useful comments to follow what was done and references to pursue the subject further. I'd have wished for an extra line or two that explained why a stiff solver was necessary for this problem. In a perfect world, I'd ask for a couple of paragraphs of intuitive explanation to draw in the student who might be interested in the subject, but lacks a complete background. These comments might, for example, explain what a Prandtl number is, and how it impacts the solution.

urs (us) schwarz

no help; not a clean function; no enhancement for ML programmers, be, eg, a sleek new syntax or novel vectorization engine; no usable output for common users nor a generalizable function; altogether, no real value or enhancement for the ML community at large

Duane Hanselman

No help text whatsoever. Not a function. No inputs. No identified outputs. No value to users.


added link to Wolfram Library Archive

added comments and improved the method of resolution of this split boundary problem

typo in description

MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
Platform Compatibility
Windows macOS Linux