Experimental study of natural convection heat transfer from horizontal cam tubes in a vertical array under constant heat flux

Abstract

In the present study, natural convection heat transfer from a single horizontal cam cross-section tube and a vertical array of three cam tubes under constant heat flux submerged in water is investigated, experimentally. The experiment is carried out for modified Rayleigh number range of $6.5 \times 10^{8}$ to $2.6 \times 10^{9}$, and a dimensionless tube spacing range of 1.5, 2.0, and 2.5. The effects of modified Rayleigh number, cam tube orientation, and dimensionless spacing on the heat transfer rate from the individual tube and tube array are studied. Based on the results, the effect of thermal plume on the rate of heat transfer from the second and third cam tubes in the vertical array is strongly dependent on the dimensionless spacing. Under fixed conditions, the mean Nusselt number of the single horizontal cam tube with upward facing orientation is higher than that of the downward facing and rightward facing orientations for all the modified Rayleigh numbers.

Appendix: Uncertainly analysis

The uncertainty in the local heat transfer coefficient was obtained using the method presented in Reference [30].

$$h_{\uptheta } = \frac{Q}{{\pi D_{{\text{h}}} L\left( {T_{{\text{b}}} - T_{{\text{s}}} } \right)}}f\left( {T_{{\text{s}}} ,T_{{\text{b}}} ,\frac{Q}{{A_{{\text{s}}} }}} \right) = f\left( {T_{{\text{s}}} ,T_{{\text{b}}} ,V,I,D_{{\text{h}}} ,L} \right)$$

$$w_{{\text{h}}} = f\left( {w_{{{\text{T}}_{{\text{s}}} }} ,w_{{{\text{T}}_{{\text{b}}} }} ,w_{{\text{V}}} ,w_{{\text{I}}} ,w_{{{\text{D}}_{{\text{h}}} }} ,w_{{\text{L}}} } \right)$$

$$w_{{\text{h}}} = \left[ {\left( {\frac{\delta h}{{\delta V}}w_{{\text{V}}} } \right)^{2} + \left( {\frac{\delta h}{{\delta I}}w_{{\text{I}}} } \right)^{2} + \left( {\frac{\delta h}{{\delta I}}w_{{{\text{D}}_{{\text{h}}} }} } \right)^{2} + \left( {\frac{\delta h}{{\delta I}}w_{{\text{L}}} } \right)^{2} + \left( {\frac{\delta h}{{\delta T_{s} }}w_{{{\text{T}}_{{\text{s}}} }} } \right)^{2} + \left( {\frac{\delta h}{{\delta T_{{\text{b}}} }}w_{{{\text{T}}_{{\text{b}}} }} } \right)^{2} } \right]^{\frac{1}{2}} \times 100$$

$$\begin{aligned} \frac{{w_{{\text{h}}} }}{h} & = \left[ {\left( {\frac{{w_{{\text{V}}} }}{V}} \right)^{2} + \left( {\frac{{w_{{\text{I}}} }}{I}} \right)^{2} + \left( {\frac{{w_{{{\text{D}}_{{\text{h}}} }} }}{{D_{{\text{h}}} }}} \right)^{2} + \left( {\frac{{w_{{\text{L}}} }}{L}} \right)^{2} + \left( {\frac{{w_{{{\text{T}}_{{\text{s}}} }} }}{{T_{{\text{s}}} - T_{{\text{b}}} }}} \right)^{2} + \left( {\frac{{w_{{{\text{T}}_{{\text{b}}} }} }}{{T_{{\text{s}}} - T_{{\text{b}}} }}} \right)^{2} } \right]^{\frac{1}{2}} \\ & = \left[ {\left( {0.0090^{2} } \right) + \left( {0.0735^{2} } \right) + \left( {0.0209^{2} } \right) + \left( {0.05^{2} } \right) + \left( {0.0148^{2} } \right) + \left( {0.0148^{2} } \right)} \right]^{\frac{1}{2}} = 9.3\% \\ \end{aligned}$$