Empirical correlations development for heat transfer and friction factor of a solar rectangular air passage with spherical-shaped turbulence promoters

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A study was conducted to enhance the thermo-hydraulic performance of a rectangular solar air passage with integrated spherical-shaped turbulence promoters. The effects of the flow and geometric parameters on heat transfer along with the friction factor were studied. The experiments were carried out with a relevant range of the Reynolds number from 4500 to 16,500, and geometric parameters consisting of the dimensionless spherical-shaped diameter \((D_{\text{s}} /D_{\text{H}} )\) from 0.130 to 0.217, the stream-wise spacing parameter \((X_{\text{s}} /D_{\text{s}} )\) from 4.04 to 6.47 and the span-wise spacing parameter \((Y_{\text{s}} /D_{\text{s}} )\) from 4.04 to 6.47. An analysis was further carried out to develop empirical correlations for the Nusselt number and the friction factor in terms of geometric parameters and the Reynolds number. Comparisons between results of correlations and the experimental data revealed good agreements. Results showed that, at a specific Reynolds number, the Nusselt number reached a peak at \(D_{\text{s}} /D_{\text{H}}\) and \(Y_{\text{s}} /D_{\text{s}}\) of 0.195 and 4.62, respectively. An increase in the value of \(D_{\text{s}} /D_{\text{H}}\) increases the friction factor, while an increase in \((X_{\text{s}} /D_{\text{s}} )\) and \(Y_{\text{s}} /D_{\text{s}}\) decreased the friction factor. Maximum friction factor for \(D_{\text{s}} /D_{\text{H}}\), \((X_{\text{s}} /D_{\text{s}} )\) and \(Y_{\text{s}} /D_{\text{s}}\) was found at 0.217, 4.04 and 4.04, respectively. In addition, to evaluate the thermo-hydraulic performance, an efficiency parameter called the efficiency factor was calculated. The maximum value of the efficiency factor was 2.98, which occurred at the Reynolds number of 10,500 corresponding to the optimal parameters \(D_{\text{s}} /D_{\text{H}}\) = 0.195, \(X_{\text{s}} /D_{\text{s}}\) = 4.04, and \(Y_{\text{s}} /D_{\text{s}}\) = 4.62.

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\(A_{\text{p}}\) :

Surface area of heated plate (m2)

\(A_{\text{ori}}\) :

Area of the orifice (m2)

\(C_{\text{do}}\) :

Discharge Coefficient

\(c_{\text{p}}\) :

Specific heat of air (J kg−1K−1)

\(D_{\text{H}}\) :

Hydraulic diameter (m)

\(D_{\text{S}}\) :

Obstacle diameter (m)

\({\text{EEC}}\) :

Efficiency evaluation criterion

\(f_{\text{rs}}\) :

Friction factor of the plate with obstacles

\(f_{\text{ss}}\) :

Friction factor of the smooth plate

\(h_{\text{t}}\) :

Convective heat transfer coefficient (W m−2 K−1)

\(H_{\text{P}}\) :

Height of the air passage (m)

\(k_{\text{a}}\) :

Air conductivity (W m−1 K−1)

\(L_{\text{P}}\) :

Length of passage (m)

\(L_{\text{t}}\) :

Length of test segment (m)

\(\dot{m}_{\text{a}}\) :

Mass flow rate of air (kg s−1)

N :

Number of sensors

\(Nu_{\text{rs}}\) :

Nusselt number of the plate with obstacles

\(Nu_{\text{ss}}\) :

Nusselt number of the smooth plate

\((\Delta P)_{\text{d}}\) :

Pressure drop across test segment (Pa)

\((\Delta P)_{\text{o}}\) :

Pressure drop across orifice plate (Pa)

Pr :

Prandtl number

\(\dot{Q}_{\text{u}}\) :

Useful energy gain (W)

\(Re\) :

Reynolds number

\(T_{\text{f}}\) :

Mean air temperature (K)

\(T_{\text{i}}\) :

Mean inlet air temperature (K)

\(T_{\text{p}}\) :

Mean plate temperature (K)

\(T_{\text{o}}\) :

Mean outlet air temperature (K)

\(V\) :

Mean air velocity (m s−1)

\(W_{\text{P}}\) :

Width of air passage (m)

\(\beta_{\text{O}}\) :

Ratio of the open area (%)

\(\beta_{\text{R}}\) :

Ratio of the orifice diameter to the pipe diameter

\(\rho_{\text{a}}\) :

Density of air (kg m−3)

\(\nu_{\text{a}}\) :

Kinematic viscosity of air (m2 s−1)

\(\eta_{\text{p}}\) :

Efficiency factor


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Correspondence to Ehsan Gholamalizadeh.

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Maithani, R., Kumar, A., Gholamali Zadeh, P. et al. Empirical correlations development for heat transfer and friction factor of a solar rectangular air passage with spherical-shaped turbulence promoters. J Therm Anal Calorim 139, 1195–1212 (2020).

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  • Solar air passage
  • Spherical-shaped turbulence promoters
  • Heat transfer
  • Thermo-hydraulic performance