Fig. 1 Wall function mean velocity profiles compared to DNS reference data [ 13 – 16 ] and previously documented algebraic wall function formulations [ 1 , 2 ] at Re τ  = 1000 and 2000. MSE over the range y δ < 0.1 is shown for each case. The datasets shown here were used to ... More about this image found in Wall function mean velocity profiles compared to DNS reference data [ 13 – ...

Fig. 2 Mean velocity profiles comparing new wall function formula to DNS data from: ( a ) Refs. [ 13 – 16 ] and ( b ) Refs. [ 17 – 20 ]. MSE over the range y δ < 0.1 is shown for each case. More about this image found in Mean velocity profiles comparing new wall function formula to DNS data from...

Fig. 3 Estimated values of the additive constant F ( Pr ) in Eq. (20) , based on comparison with DNS data [ 13 – 16 ] at Re τ  = 1000 and 2000. The empirically determined curve fit for F ( Pr ) used in the new wall function is shown (Eq. (22) ). More about this image found in Estimated values of the additive constant F ( Pr ) in Eq. (20) ...

Fig. 4 Mean temperature profiles for Re τ  = 1000 ( a ) and Re τ  = 2000 ( b ), for different values of Pr, comparing new wall function formula to DNS reference data [ 13 – 16 ]. MSE over the range y δ < 0.1 is shown for each case. More about this image found in Mean temperature profiles for Re τ  = 1000 ( a ) and Re τ  = 2000 ( b )...

Fig. 5 Wall function mean temperature profiles for Re τ  = 2000, compared to DNS reference data [ 13 – 16 ] and in the log-law region to the model of Jayatilleke [ 6 ] More about this image found in Wall function mean temperature profiles for Re τ  = 2000, compared to DNS...

Fig. 6 Mean temperature profiles for Re τ  = 500 and different values of Pr, comparing new wall function formula to DNS reference data [ 13 – 16 ]. MSE over the range y δ < 0.1 is shown for each case. More about this image found in Mean temperature profiles for Re τ  = 500 and different values of Pr, com...

Fig. 7 Mean temperature profiles for Re τ  = 395 and different values of Pr, comparing new wall function formula to DNS data from [ 17 – 20 ]. MSE over the range y δ < 0.1 is shown for each case. More about this image found in Mean temperature profiles for Re τ  = 395 and different values of Pr, com...

Fig. 1 T-tube structure: ( a ) T-tube used in simulation and ( b ) T-tube for experiments (with thermal insulation foam) More about this image found in T-tube structure: ( a ) T-tube used in simulation and ( b ) T-tube for expe...

Fig. 2 Layout of monitoring points More about this image found in Layout of monitoring points

Fig. 3 Comparison between experimental results and numerical simulation results: ( a ) FB1 plane, ( b ) B3 plane, and ( c ) PB2 plane More about this image found in Comparison between experimental results and numerical simulation results: (...

Fig. 4 Numerical simulation of T-tube model More about this image found in Numerical simulation of T-tube model

Fig. 5 Schematic diagram of monitoring point layout of T-tube calculated by numerical simulation More about this image found in Schematic diagram of monitoring point layout of T-tube calculated by numeri...

Fig. 6 Results of grid independence verification for numerical simulation More about this image found in Results of grid independence verification for numerical simulation

Fig. 7 Temperature cloud atlas of pipeline center section after fluid mixing reaches stability under different momentum ratios. ( a )–( e ) represent cases 1–5, respectively. More about this image found in Temperature cloud atlas of pipeline center section after fluid mixing reach...

Fig. 8 Temperature cloud atlas of pipe wall after fluid mixing reaches stability under different momentum ratios. ( a )–( e ) represent cases 1–5, respectively. More about this image found in Temperature cloud atlas of pipe wall after fluid mixing reaches stability u...