Heat Transfer Today

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Heat and Mass Transfer

Visual Studio Executables

Natural Convection next to a Heated, Vertical Flat Plate

UPDATED: 01/08/2024

This module solves the governing equations for natural convection next to a heated vertical flat plate in their similarity form.  We convert the continuity, vertical momentum (simplified using the Boussinesq approximation) and thermal energy equations into a pair of non-linear, coupled ordinary differential equations.  We specify the needed boundary conditions at both the surface of the plate and out at a distance from the plate.  We discretize the two equations and solve the resulting linear system iteratively.

Module Description


The only fluid input for the similarity solution is the Prandtl number of the fluid.  In addition, the user selects the extent of the computing region (ηmax) and the spatial increment (Δη) to be used.  Results in similarity form for vertical velocity and temperature are plotted in the left window.  The user supplies the plate length and its temperature temperature and ambient temperature to compute results in dimensional form.   In addition the kinematic viscosity of the fluid and the acceleration of gravity are input.


With that data, the right hand window shows vertical velocity profile in dimensional form at four stations along the plate.  The velocity profiles  are shown superimposed on the temperature field.  The user can explore the effects of the Prandtl number of the fluid  (and compare with results for forced convection over a flat plate). The value of existing analytical solutions covering extreme Prandtl numbers (Pr<<1 (liquid metals) and Pr>>1 (oils)) is evident from these calculations.   The traditional way of solving this problem is matched asymptotic expansions.

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