(b) Heat transfer to surroundings.

Natural convection to pipe surroundings in the test-bench needs to be included. Wall temperatures along the exhaust pipe were measured using thermography. Figure 4 shows, as an example, views of the external surface of the pipe and the DOC.

**Figure 4.** Example of infrared images of the exhaust line in (**a**) the exhaust pipe and (**b**) the DOC. Temperatures in the scale are in ◦C. Squares seen in (**a**) are wall temperature measurement points.

An average skin temperature was used to calculate an effective convection heat transfer coefficient. This skin temperature simplification is considered as reasonable, since calculation of heat transfer rates is not very sensitive in the values of pipe wall temperatures [5].

Total transferred heat from pipe wall to surroundings is *Q* (W) (Equation (6)):

$$\dot{Q} = \overline{h}\_{\infty} \pi d \left( T\_{\text{wall}} - T\_{\infty} \right) + \varepsilon \pi dL \sigma \left( T\_{\text{wall}}^4 - T\_{\text{amb}}^4 \right) \tag{6}$$

.

Here, all terms in the right side of Equation (6) are grouped in one single equivalent convection term (Equation (7)):

$$
\dot{Q} = \overline{h}\_{eff} \pi dL (T\_{\text{wall}} - T\_{\infty}) \tag{7}
$$

The effective convection coefficient accounts for convection and radiation heat losses, although radiation heat transfer to the environment is expected to be low, since wall temperature is below 400 ◦C [4]. A similar approach is explained in Kapparos et al. [8].

Based on the measured exhaust gas and pipe wall temperatures, an energy balance for the exhaust gas is employed for the calculation of the heat flux. The resulting heat fluxes are employed in the estimation of a mean gas-to-wall convection coefficient.

Since temperature at both ends of the exhaust pipe are measured, total heat losses *Q* (W) can be obtained as Equation (8):

$$\mathcal{Q} = \dot{m}\_{\mathcal{K}} c\_{p\prime\mathcal{K}} \left( T\_{\mathcal{K}^{\dot{m}}} - T\_{\mathcal{K}^{\prime}\text{out}} \right) \tag{8}$$

.

Equaling Equations (7) and (8), *heff* can be derived as Equation (9):

.

*heff* = . *mgcp*,*<sup>g</sup> Tg*,*in* − *Tg*, *out πd*(*Twall* − *<sup>T</sup>*∞) (9)
