## 1 Introduction  
Around a third of the fuel energy in a light-duty diesel engine is wasted through the exhaust system [1]. Rising awareness of environmental issues together with the fuel economy have encouraged research on energy recovery [1, 2] from exhaust gas. An obvious first step for energy recovery is evaluating the heat source. The nature of exhaust flow changes during engine operation. Hence, there is a need for models that allow evaluating exhaust gas in a cost- and time-efficient manner under different engine conditions. Computational fluid dynamics (CFD) is becoming a very popular tool for numerical predictions in the automotive industry. CFD models are employed in five major areas: vehicle aerodynamics, thermal management (cooling and climate control), cylinder combustion, engine lubrication and exhaust system performance. The main applications of CFD in exhaust systems are: flow distribution in the front of the monolith, pressure loss through exhaust system, skin temperature prediction, heat loss analyses and emission-related studies [3]. High levels of energy lost through engine exhaust have brought attention to heat transfer in exhaust systems and how to model associated phenomena. In [PERSON] et al. [4], the status of knowledge regarding heat transfer phenomena in automotive exhaust systems was summarized, and a transient model covering diverse exhaust piping configurations was presented. Using this model, [PERSON] et al. [5] studied heat transfer in automotive exhaust pipes for steady and transient conditions. It is stated that the code is suitable to support a complete and efficient methodology for design optimization. Not only are exhaust heat transfer and temperature models important for energy recovery, but also for on-board control and diagnosis of the after-treatment system. In the work of [PERSON] et al. [6], diesel oxidation catalyst (DOC) inlet temperature was modelled depending on fuel mass flow and engine speed using an engine map look-up table. Traditionally, one-dimensional (1D) simulations using in-house or commercial codes have been used to study exhaust flow. In [PERSON] et al. [7], a 1D model of system thermal behavior was developed. The exhaust system is modelled as connected pipe and junction elements with lumped thermal capacities. Heat transfer correlations for quasi-steady and transient conditions were investigated. The computational model supports studies of exhaust and after-treatment system design, the investigation of thermal conditions, and performance characteristics. Model predictions and experimental data were in good agreement. In [PERSON] et al. [8], a 1D heat transfer model in an automotive diesel exhaust is presented. The external natural convective heat transfer coefficient was given by [PERSON] and [PERSON]'s correlation. A sensitivity analysis of the main variables (heat transfer coefficient, external pipe emissivity and others) affecting heat transfer in exhaust pipes was carried out. [PERSON] et al. [9] developed a 1D model of an exhaust pipe (without the catalytic converter). Apart from typical variables studied, effects of pipe geometry and flow regime were investigated. One-dimensional tools have the advantage of shorter computational time, but the accuracy of the results is limited by their inability to simulate 3D flow effects in regions such as the inlet and outlet cone. Usually strong turbulent flow exists when angled and asymmetrical cones are presented [3]. Three different approaches were used in [PERSON] et al. [10] to simulate the exhaust and underbody of the car: 1D, 3D finite elements and 3D complete thermo-fluid-dynamics. Both 3D models allowed to detect the most critical points in terms of higher temperatures  
In [PERSON] et al. [11], temperature distribution and heat flow analyses on the exhaust system of a mining diesel engine to determine technical parameters of a heat recuperation system are presented. Three-dimensional numerical simulations show it is possible to develop a suitable design of an energy recovery device.