Experimental investigations on thermal performance of solar air heater with wavy fin absorbers

Abstract

In this paper, the thermal performance of wavy finned solar air heater are investigated experimentally. Experiments were performed under Jamshedpur (22° 48’ N, 86° 11′ E) prevailing weather conditions. The effect of mass flow rate, fin spacing and insolation on thermal efficiency and air temperature rise of wavy fin solar air heaters are investigated. The results showed that the maximum efficiency of 69.55% has been found for the mass flow rate 0.0158 kg/s and fin spacing of 2 cm. Further, for the same fin spacing, maximum air temperature rise has been obtained as 64.33°C at the mass flow rate of 0.00312 kg/s. For the range of mass flow rate (0.00312–0.0158 kg/s) and fin spacing (2–6 cm), the wavy fin absorber solar air heater has been found to be 67.44 to 121.43% thermally efficient. These experimental results would be reliable and useful for optimum design in practical applications.

Appendices

Appendix 1: Error analysis

Although extreme care has been taken to perform experiment but there is always a chance of error in experimental measurements. So, it is necessary to determine maximum possible error in the experimental measurements. The error analysis was done for the error interval associated with experimental results. The methodology suggested by cline and Mc clintock [19] has been used to measure the error.

If the value of any parameter is calculated using certain measured quantities then error in measurement of ‘φ’ (parameters) is given as:

$$ \frac{\delta \varphi}{\varphi }={\left[{\left(\frac{\delta \varphi}{\partial {x}_1}\delta {x}_1\right)}^2+{\left(\frac{\delta \varphi}{\partial {x}_2}\delta {x}_2\right)}^2+.............+{\left(\frac{\delta \varphi}{\partial {x}_n}\delta {x}^n\right)}^2\right]}^{0.5} $$

Where δx₁, δx₂, δx₃......δx_n are the possible errors in measurements x₁, x₂, x₃....x_n andδφ is called as absolute uncertainty and δφ/φ is known as relative uncertainty. Table 6 shows the accuracy of measuring instruments.

Table 6 Accuracy of measuring instruments

Area of absorber plate

$$ {\displaystyle \begin{array}{c}{A}_p=\left(W\times L\right)\\ {}\delta Ap=\left[{\left(\frac{\delta {A}_p}{\delta L}\times \delta L\right)}^2+{\left(\frac{\delta {A}_p}{\delta W}\times \delta W\right)}^2\right]\\ {}\delta {A}_p={\left[W\times \delta l\right]}^2+{\left[L\times \delta W\right]}^2\\ {}\delta {A}_p={\left[{\left(\frac{W\ x\ \delta L}{W\ x\ L}\right)}^2+{\left(\frac{Lx\delta W}{WxL}\right)}^2\right]}^{0.5}\\ {}\delta {A}_p={\left[{\left(\frac{1}{1200}\right)}^2+{\left(\frac{1}{400}\right)}^2\right]}^{0.5}\\ {}=2.63x\ {10}^{-3}=0.263\%\end{array}} $$

Area of Flow

$$ {\displaystyle \begin{array}{c}{A}_f=\left(W\times {L}_{act}\right)+n\left({L}_f\times {L}_{act}\right)\\ {}\delta {A}_f=\left[{\left(\frac{\delta A}{\delta L}\times \delta L\right)}^2+{\left(\frac{\delta A}{\delta W}\times \delta W\right)}^2+n{\left(\frac{\delta \left({L}_f{L}_{act}\right)}{\delta {L}_{act}}\right)}^2+{\left(\frac{\delta \left({L}_f{L}_{act}\right)}{\delta {L}_{act}}\times {L}_f\right)}^2\right]\\ {}\delta {A}_f={\left[W\times \delta l\right]}^2+{\left[{L}_{act}\times \delta W\right]}^2+\eta {\left({L}_f\times \delta {L}_{act}\right)}^2+{\left({L}_f{L}_{act}\right)}^2\\ {}\delta {A}_f={\left(\frac{\delta {L}_{act}}{L_{act}}\right)}^2+{\left(\frac{\delta W}{W}\right)}^2+7{\left[{\left(\frac{\delta {L}_{act}}{L_{act}}\right)}^2+{\left(\frac{\delta {L}_f}{\delta {L}_f}\right)}^2\right]}^{0.5}\\ {}\delta {A}_f={\left[{\left(\frac{1}{1390}\right)}^2+{\left(\frac{1}{400}\right)}^2+7\left[{\left(\frac{1}{45}\right)}^2+{\left(\frac{1}{1390}\right)}^2\right]\right]}^{0.5}\\ {}\delta {A}_f=0.05888\\ {}\delta {A}_f=5.888\%\end{array}} $$

Area of orifice meter (A _o)

$$ {\displaystyle \begin{array}{c}{A}_0=\frac{\pi }{4}{d}_2^2\\ {}\frac{\delta {A}_o}{\delta {d}_2}=\frac{2\pi {d}_2}{4}=\frac{\pi {d}_2}{2}\\ {}\delta {A}_o=\left(\frac{\pi {d}_2}{2}\right)\delta {d}_2\\ {}\frac{\delta {A}_o}{A_o}=\frac{\pi {d}_2\delta {d}_2\times 4}{2\times \pi \times {d}_2^2}=\frac{2\delta {d}_2}{d_2}=\frac{2\times (0.05)}{19}=0.526\%\end{array}} $$

Mass flow rate ($\dot{m}$)

$$ {\displaystyle \begin{array}{c}\dot{m}={C}_d{A}_0{\left[\frac{2\rho \varDelta P}{1-{\beta}^4}\right]}^{0.5}\\ {}\frac{\delta \dot{m}}{\dot{m}}={\left[{\left(\frac{\delta {C}_d}{C_d}\right)}^2+{\left(\frac{\delta {A}_0}{A_0}\right)}^2+\frac{1}{4}{\left(\frac{\delta \rho}{\rho}\right)}^2+\frac{1}{4}{\left(\frac{\delta \left(\varDelta P\right)}{\left(\varDelta P\right)}\right)}^2+\frac{1}{4}{\left(\frac{\delta \beta}{\beta}\right)}^2\right]}^{0.5}\\ {}={\left[{(0.016)}^2+{(0.00526)}^2+\frac{1}{4}{(0.0083)}^2+\frac{1}{4}{\left(\frac{1}{25}\right)}^2+\frac{1}{4}{(0.00121)}^2\right]}^{0.5}\\ {}=0.0437\ or\ 4.37\%\end{array}} $$

Useful heat gain (Q_u)

$$ {\displaystyle \begin{array}{c}{Q}_u=\dot{m}{C}_p\left({T}_o-{T}_i\right)\\ {}\frac{\delta {Q}_u}{Q_u}={\left[{\left(\frac{\delta \dot{m}}{\dot{m}}\right)}^2+{\left(\frac{\delta Cp}{Cp}\right)}^2+{\left(\frac{\delta \left(\varDelta T\right)}{\left(\varDelta T\right)}\right)}^2\right]}^{0.5}\\ {}={\left[{(0.0437)}^2+{\left(1/1005\right)}^2+{\left(0.5/15.2\right)}^2\right]}^{0.5}\\ {}=0.0547\ or\ 5.47\%\end{array}} $$

Heat transfer coefficient ⁽ $\overline{h}$ ⁾

$$ {\displaystyle \begin{array}{c}\overline{h}=\frac{Q_u}{A_p\left({T}_{pm}-{T}_{fm}\right)}\\ {}\frac{\delta \overline{h}}{\overline{h}}={\left[{\left(\frac{\delta {Q}_u}{Q_u}\right)}^2+{\left(\frac{\delta {A}_p}{A_p}\right)}^2+{\left(\frac{\delta {T}_{pf}}{T_{pf}}\right)}^2\right]}^{0.5}\\ {}={\left[{(0.0547)}^2+{(0.00358)}^2+{\left(\frac{1}{12}\right)}^2\right]}^{0.5}\\ {}=0.09974\ \mathrm{or}\ 9.974\%\end{array}} $$