Theory

The outer surface is treated as a cylinder of diameter $D_{out}$ in cross flow at speed $V$ ; the Churchill and Bernstein correlation (Churchill and Bernstein, 1977) gives the Nusselt number from the Reynolds number, equation (1), with air properties at the film temperature (see Outer environment). Faster air gives a larger $h$ , roughly as $V^{1/2}$ to $V^{0.8}$ over the usual range.

Equations

Re = \frac{V D_{out}}{\nu}, \qquad Nu = 0.3 + \frac{0.62\,Re^{1/2}Pr^{1/3}}{\left(1 + (0.4/Pr)^{2/3}\right)^{1/4}}\left[1 + \left(\frac{Re}{282000}\right)^{5/8}\right]^{4/5}, \qquad h = \frac{Nu\,k}{D_{out}}

(1)

where	meaning	unit
$V$	Air speed past the muffler (this setting)	m/s
$D_{out}$	Outer characteristic diameter	m
$\nu, k$	Kinematic viscosity and conductivity of air at the film temperature	m²/s, W/(m K)
$Pr$	Prandtl number	-
$h$	Outer convective coefficient	W/(m² K)

Default and rule

Default: 15 m/s in the box (environment 'Vehicle moving' only)
Rule: 15 m/s in the box (54 km/h); required for this environment.
Source: Churchill and Bernstein (Churchill and Bernstein, 1977).

Valid range > 0

Effective speed

Under a vehicle the local air speed is lower than the driving speed and not perpendicular to the muffler; use an effective value.

References 1

Churchill, S. W. and Bernstein, M. (1977). A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. Journal of Heat Transfer, 99(2), 300-306. DOI 10.1115/1.3450685

Theory

Equations

Default and rule

Valid range > 0

Related 3

References 1