Abstract
Since the ducts are important parts of the engineering facilities and entropy generation decreases the performance of such facilities, it is necessary to study the amount of entropy generation in these geometries in order to reach to maximum efficiency. In addition, the study of turbulent boundary layer flow in curved diffuser has significant importance. Therefore, the current work investigates the effects of curvature and adverse pressure gradient parameter on efficiency and entropy generation due to turbulent and viscosity dissipations in three curved diffusers with curvature ratios of 0.0113, 0.0161 and 0.023 for different adverse pressure gradient parameters of 0.48, 0.56, 0.62, 0.86 and 0.994. Results show that in order to design the curved diffusers to reach the maximum efficiency and minimum total entropy generation in airconditioning systems, the lowest value of adverse pressure gradient parameter and the highest value of curvature radius should be considered, respectively. The total entropy generation on concave and convex walls decreases with increasing the adverse pressure gradient parameter, while by increasing the curvature radius, it decreases on convex wall and increases on concave wall. Moreover, the rate of increasing the total entropy on convex wall is more than concave wall at constant adverse pressure gradient parameter. Finally, it was found that with decreasing the adverse pressure gradient parameter and increasing the curvature radius, the efficiency increases.
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Abbreviations
 A _{1} :

The crosssectional area at inlet region (m^{2})
 A _{2} :

The crosssectional area at outlet region (m^{2})
 C1:

The flow on the convex wall of the curved diffuser
 C2:

The flow on the concave wall of the curved diffuser
 k :

Turbulent kinetic energy (m^{2} s^{−2})
 p :

Pressure (kg m^{−1} s^{−2})
 p _{ k } :

Constant
 R :

Centerline radius (mm)
 S _{g,T} :

Entropy generation due to fluctuation velocity (Wm^{−3} K^{−1})
 S _{g,v} :

Entropy generation due to mean flow dissipation (Wm^{−3} K^{−1})
 S _{ g } :

Entropy generation (Wm^{−3} K^{−1})
 T _{0} :

Reference temperature (K)
 t :

Time (s)
 \( \overline{{u_{i}}}, \) \( \overline{{u_{j}}} \) :

Mean velocity (ms^{−1})
 \( u_{i}^{\prime} \), \( u_{i}^{\prime} \),:

Fluctuation velocity (ms^{−1})
 \( \bar{u} \),\( \bar{v} \),\( \bar{w} \) :

Mean velocity components (ms^{−1})
 \( u^{\prime},v^{\prime},w^{\prime} \) :

Fluctuation velocity components (ms^{−1})
 \( \overline{{u^{\prime} v^{\prime}}} \) :

Turbulent shear stress (m^{2} s^{−2})
 Α_{1}, α_{2}, α_{3} :

Constant
 Β_{1}, β_{2}, β_{3}, β^{*} :

Constant
 β :

Adverse pressure gradient parameter
 ɛ :

Turbulent dissipation (m^{2} s^{−2})
 η :

Efficiency
 θ :

Turning angle (°)
 μ :

Dynamic viscosity (kg m^{−1} s^{−1})
 μ _{ t } :

Turbulent viscosity (kg m^{−1} s^{−1})
 μ _{eff} :

Effective viscosity (kg m^{−1} s^{−1})
 ϑ :

Kinematic viscosity (m^{2} s^{−1})
 ρ :

Density (kg m^{−3})
 \( \sigma_{\omega 1},\sigma_{\omega 2},\sigma_{k1},\sigma_{k2} \) :

Constant
 \( \bar{\varphi} \) :

Entropy generation due to viscosity (wm^{−3})
 \( \overline{{\varphi_{\theta}}} \) :

Entropy generation due to heat transfer (w km^{−3})
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Yadegari, M., Bak Khoshnevis, A. Entropy generation analysis of turbulent boundary layer flow in different curved diffusers in airconditioning systems. Eur. Phys. J. Plus 135, 534 (2020). https://doi.org/10.1140/epjp/s1336002000545y
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