ESDU AERO 00.03.26
Wall and average gas temperatures for subsonic turbulent flow with heat transfer in ducts of constant circular cross section.
Abstract:
ESDU Aero 00.03.26 provides equations and graphs that allow the determination of the gas or wall temperature distribution along a pipe for subsonic flow of a perfect gas under forced convection heat transfer. Three boundary conditions are considered: uniform heat flux, constant wall temperature, and an arbitrary heat flux distribution. For the gas temperature distribution, under uniform and arbitrary heat flux conditions equations are given, and for the constant wall temperature case curves are given in terms of mean Stanton number which may be obtained from ESDU Aero 00.02.05. For the wall temperature distribution, in the uniform heat flux case an equation for the difference between the wall and gas temperatures is given in terms of the ratio of Stanton number in fullydeveloped flow to the local Stanton number. Equations for that last ratio are also given and involve a number of constants for which values obtained from ESDU Aero 00.02.05 are provided. They apply for Reynolds numbers greater than 20000 and in the thermal entrance region provided the flow is fullydeveloped before heating starts. An equation is derived for an arbitrary heat flux distribution, making use of the principle of superposition to represent that distribution by the sum of a number of uniform heat flux distributions each starting further upstream along the pipe. Graphs giving solutions for that equation are plotted for three special cases: a linear, a sinusoidal and an exponential heat flux distribution. It is noted that the uniform heat flux case can be used as an approximation to an arbitrary heat flux distribution, provided the heat flux gradient along the pipe divided by the heat flux is very small, and the likely errors can be assessed from one of the graphs. For conditions that approach constant wall temperature away from the thermal entrance region, it is suggested that the uniform heat flux equations provide a useful approximation in the thermal entrance region and may therefore be used over the complete heat transfer surface. A worked example illustrates the use of the data.Indexed under:
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