| Summary: | Turbulent heat transfer in channel flows is an important area of research due to its simple geometry and diverse industrial applications. Reynolds-Averaged Navier–Stokes (RANS) models are the most-affordable simulation methodology and are often the only viable choice for investigating industrial flows. However, accurate modelling of wall-bounded flows is challenging in RANS, and the assessment of the performance of RANS models for heated turbulent channel flow has not been sufficiently investigated for a wide range of Reynolds and Prandtl numbers. In this study, five RANS models are assessed for their ability to predict heat transfer in channel flows across a wide range of Reynolds and Prandtl numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula>) by comparing the RANS results with respect to the corresponding Direct Numerical Simulation data. The models include three Eddy Viscosity Models (EVMs): standard <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="0.222222em"></mspace><mi>k</mi><mo>−</mo><mi>ϵ</mi></mrow></semantics></math></inline-formula>, low Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ϵ</mi><mspace width="0.222222em"></mspace><mi>L</mi><mi>S</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ω</mi><mspace width="0.222222em"></mspace><mi>S</mi><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula>, as well as two Reynolds Stress Models (RSMs): Launder–Reece–Rodi and Speziale–Sarkar–Gatski models. The study analyses the Reynolds number effects on turbulent heat transfer in a channel flow at a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> of 0.71 for friction Reynolds number values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>180</mn><mo>,</mo><mspace width="0.222222em"></mspace><mn>395</mn><mo>,</mo><mspace width="0.222222em"></mspace><mn>640</mn><mo>,</mo></mrow></semantics></math></inline-formula> and 1020. The results show that all models accurately predict velocity across all Reynolds numbers, but the accuracy of mean temperature prediction drops with increasing Reynolds number for all models, except for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ω</mi><mspace width="0.222222em"></mspace><mi>S</mi><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula> model. The study also analyses the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> effects on turbulent heat transfer in a channel flow with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> values between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.025</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>10.0</mn></mrow></semantics></math></inline-formula>. An error analysis is performed on the results obtained from different turbulence models, and it is shown that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ω</mi><mspace width="0.222222em"></mspace><mi>S</mi><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula> model has the smallest error for the predictions of the mean temperature and Nusselt number for high-Prandtl-number flows, while the low Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ϵ</mi><mspace width="0.222222em"></mspace><mi>L</mi><mi>S</mi></mrow></semantics></math></inline-formula> model shows the smallest errors for low-Prandtl-number flows at different Reynolds numbers. An analytical solution is utilised to identify <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula> effects on forced convection in a channel flow into three different regimes: analytical region, transitional region, and turbulent diffusion-dominated region. These regimes are helpful to discuss the validity of the models in relation to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula>. The findings of this paper provide insights into the performance of different RANS models for heat transfer predictions in a channel flow.
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