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i want to develop an equation for temperature distribution of a car exhaust pipe, i’m not...

i want to develop an equation for temperature distribution of a car exhaust pipe, i’m not looking for an answer but for the way to find it. take any needed values from internet for diameter..etc or assume logical values. Thank you
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The exhaust system is responsible by about 30% of the energy loss from an internal combustion engine. The energy carried by the exhaust gas can be evaluated from the analysis of the internal fluid flow. The heat transfer and fluid flow is analyzed taking the duct as a straight pipe, as shown by the attached photo...

In order to determine the temperature profiles it has been proposed a model based on FDM. The implemented model solve the energy equation from fundamental assumptions: (1) steady state; (2) fully developed turbulent flow; (3) turbulent velocity profile 1/7; (4) variable properties; (5) fluid modelled as air.

The results of this model are compared with results obtained from the Ansys CFX® software, in which the governing equations of turbulent flow are resolved. The governing equations are the continuity equation (Eq. 1), momentum equation (Eq. 2) and energy equation (Eq. 3).

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