Experimental study of heat transfer enhancement in a rectangular duct distributed by multi V-perforated baffle of different relative baffle width

Abstract

The current research deals with the experimental investigation of the heat transfer behavior and optimum relative width parameter of the multi V-down pattern perforated baffle rectangular duct. The 60° angled multi V-down perforated pattern baffle are attached on the lower duct wall having an aspect ratio (W _D /H _D ) of 10.0 and a Reynolds number (Re) ranging from 4000 to 9000. The experiment was conducted by varying the relative baffle width (W _D /W _B ) ranging from 1.0 to 6.0, relative baffle height (H _B /H _D ) was 0.5, relative baffle pitch (P _B /H _B ) was 10.0, relative hole position (O _B /H _B ) was 0.44, open area ratio (β _O ) was 12 %. The experimental investigation shows that at a relative baffle width of 5.0 the thermal performance was maximized. Thermo-hydraulic performance (η _p ) comparison shows that multi V-down pattern perforated baffle has better outcomes as compared to other baffles shaped rectangular duct.

Appendix: Uncertainty analysis

During experimentation, lots of factors come into play which causes deviation in the values of the measured parameters from the actual value. It is essential to investigate this deviation which might occur due to carelessness during experimentation. Uncertainty analysis provides the maximum possible error in numerical digits. It is based on the random sampling during the experimentation. The uncertainty analysis tells us expected accuracy, not the exact accuracy of the system. To evaluate uncertainty involve in this experiment method suggested by Kline and McClintock [40] is used. If the value of any parameter is calculated using certain measured quantities then error in measurement of “y” (parameter) is given as follows.

$$\frac{\delta y}{y} = \left[ {\left( {\frac{\delta y}{{\delta x_{1} }}\delta x_{1} } \right)^{2} + \left( {\frac{\delta y}{{\delta x_{2} }}\delta x_{2} } \right)^{2} + \left( {\frac{\delta y}{{\delta x_{3} }}\delta x_{3} } \right)^{2} + \cdots + \left( {\frac{\delta y}{{\delta x_{n} }}\delta x_{n} } \right)^{2} } \right]^{0.5}$$

where, $\delta x_{1} ,\delta x_{2} ,\delta x_{3} , \ldots ,\delta x_{n}$ are possible error in measurement of x ₁, x ₂, x ₃, …, x _n , δ _y is known as absolute uncertainty and $\frac{{\delta_{y} }}{y}$ is known as relative uncertainty.

In the present experiment, important parameters considered for uncertainty analysis are Reynolds number, Heat transfer coefficient, Nusselt number, and friction factor. The values of measured parameters are given in Table 3.

Table 3 Measured parameters and their respective values

The thermo-physical properties of air have been determined by following standard correlations:

$$\mu = 1.81 \times 10^{ - 5} \times \left( {\frac{{T_{f} }}{293}} \right)^{0.735} \quad C_{p} = 1006 \times \left( {\frac{{T_{f} }}{293}} \right)^{0.0155}$$

$$K_{a} = 0.0257 \times \left( {\frac{{T_{f} }}{293}} \right)^{0.86} \quad \rho_{a} = \frac{97500}{287.045} \times T_{f}$$

Uncertainty associated with instruments used in various measurements of parameters in the experiment is given in Table 4.

Table 4 Uncertainty intervals of various measurements

• 1. Uncertainty in Area of absorber plate

$$A_{p} = W_{D} \times L_{t}$$

$$\frac{{\delta A_{p} }}{{A_{p} }} = \left[ {\left( {\frac{{\delta L_{t} }}{{L_{t} }}} \right)^{2} + \left( {\frac{{\delta W_{D} }}{{W_{D} }}} \right)^{2} } \right]^{0.5}$$

• 2. Uncertainty in Area of flow

$$A_{p} = W_{D} \times H_{B}$$

$$\frac{{\delta A_{p} }}{{A_{p} }} = \left[ {\left( {\frac{{\delta H_{B} }}{{H_{B} }}} \right)^{2} + \left( {\frac{{\delta W_{D} }}{{W_{D} }}} \right)^{2} } \right]^{0.5}$$

• 3. Uncertainty in measurement of Hydraulic diameter

$$D_{hd} = \frac{{4 \times \left( {W_{D} \times H_{B} } \right)}}{{2 \times \left( {W_{D} \times H_{B} } \right)}} = 2\left( {W_{D} H_{B} } \right)\left( {W_{D} + H_{B} } \right)^{ - 2}$$

$$\frac{{\delta D_{hd} }}{{D_{hd} }} = \frac{{\left[ {\left( {\frac{{\delta D_{hd} }}{{\delta W_{D} }}\delta W_{D} } \right)^{2} + \left( {\frac{{\delta D_{hd} }}{{\delta H_{B} }}\delta H_{B} } \right)^{2} } \right]^{0.5} }}{{2\left( {W_{D} \times H_{B} } \right)\left( {W_{D} + H_{B} } \right)^{ - 1} }}$$

• 4. Uncertainty in Area of orifice meter

$$A_{o} = \frac{\pi }{4}D_{o}^{2}$$

$$\frac{{A_{o} }}{{\delta A_{o} }} = \frac{{\frac{{\pi D_{o} \times \delta D_{o} }}{2}}}{{\frac{\pi }{4}D_{o}^{2} }} = \frac{{2 \times \delta D_{o} }}{{D_{o} }} = \frac{2 \times 0.1}{42.96}$$

• 5. Uncertainty in density measurement

$$\rho_{a} = \frac{{P_{a} }}{{R \times T_{o} }}$$

$$\frac{{\delta \rho_{a} }}{{\rho_{a} }} = \left[ {\left( {\frac{{\delta P_{a} }}{{P_{a} }}} \right)^{2} + \left( {\frac{{\delta T_{o} }}{{T_{o} }}} \right)^{2} } \right]^{0.5}$$

• 6. Uncertainty in mass flow rate measurement

$$m_{a} = C_{do} A_{o} \left[ {\frac{{2\rho_{a} \left( {\Delta p} \right)_{0} }}{{1 - \beta^{4} }}} \right]^{0.5}$$

$$\frac{{\delta m_{a} }}{m} = \left[ {\left( {\frac{{\delta C_{do} }}{{C_{do} }}} \right)^{2} + \left( {\frac{{\delta A_{o} }}{{A_{o} }}} \right)^{2} + \left( {\frac{{\delta \rho_{a} }}{{\rho_{a} }}} \right)^{2} + \left( {\frac{{\delta \left( {\Delta p} \right)_{0} }}{{\left( {\Delta p} \right)_{0} }}} \right)^{2} } \right]^{0.5}$$

• 7. Uncertainty in measurement of air velocity in channel

$$V = \frac{{m_{a} }}{{\rho_{a} \times W_{D} \times H_{B} }}$$

$$\frac{\delta V}{V} = \left[ {\left( {\frac{{\delta m_{a} }}{{m_{a} }}} \right)^{2} + \left( {\frac{{\delta \rho_{a} }}{{\rho_{a} }}} \right)^{2} + \left( {\frac{{\delta W_{D} }}{{W_{D} }}} \right)^{2} + \left( {\frac{{\delta H_{B} }}{{H_{B} }}} \right)^{2} } \right]^{0.5}$$

• 8. Uncertainty in useful heat gain

$$Q_{u} = m_{a} c_{p} \left( {T_{0} - T_{i} } \right) = m_{a} c_{p}\Delta T$$

$$\frac{{\delta Q_{u} }}{{Q_{u} }} = \left[ {\left( {\frac{{\delta m_{a} }}{{m_{a} }}} \right)^{2} + \left( {\frac{{\delta c_{p} }}{{c_{p} }}} \right)^{2} + \left( {\frac{{\delta\Delta T}}{{\Delta T}}} \right)^{2} } \right]^{0.5}$$

• 9. Uncertainty in heat transfer coefficient

$$h_{t} = \frac{{Q_{u} }}{{A_{p} \times \left( {T_{p} - T_{f} } \right)}} = \frac{{Q_{u} }}{{A_{p} \times\Delta T_{f} }}$$

$$\frac{{\delta h_{t} }}{{h_{t} }} = \left[ {\left( {\frac{{\delta Q_{u} }}{{Q_{u} }}} \right)^{2} + \left( {\frac{{\delta A_{p} }}{{A_{p} }}} \right)^{2} + \left( {\frac{{\delta\Delta T_{f} }}{{\Delta T_{f} }}} \right)^{2} } \right]^{0.5}$$

• 10. Uncertainty in Nusselt number

$$Nu_{rs} = \frac{{h_{t} D_{hd} }}{{K_{a} }}$$

$$\frac{{\delta Nu_{rs} }}{{Nu_{rs} }} = \left[ {\left( {\frac{{\delta D_{hd} }}{{D_{hd} }}} \right)^{2} + \left( {\frac{{\delta h_{t} }}{{h_{t} }}} \right)^{2} + \left( {\frac{{\delta K_{a} }}{{K_{a} }}} \right)^{2} } \right]^{0.5}$$

• 11. Uncertainty in Reynolds Number

$$Re = \frac{{V \cdot D_{hd} }}{\nu } = \frac{{\rho_{a} VD_{hd} }}{\mu }$$

$$\frac{\delta Re}{Re} = \left[ {\left( {\frac{{\delta D_{hd} }}{{D_{hd} }}} \right)^{2} + \left( {\frac{\delta V}{V}} \right)^{2} + \left( {\frac{{\delta \rho_{a} }}{{\rho_{a} }}} \right)^{2} + \left( {\frac{\delta \mu }{\mu }} \right)^{2} } \right]^{0.5}$$

• 12. Uncertainty in friction factor

$$f_{rs} = \frac{{2\left( {\Delta _{p} } \right)_{d} D_{hd} }}{{4\rho_{a} L_{t} V^{2} }}$$

$$\frac{{\delta f_{rs} }}{{f_{rs} }} = \left[ {\left( {\frac{{\delta D_{hd} }}{{D_{hd} }}} \right)^{2} + \left( {\frac{\delta V}{V}} \right)^{2} + \left( {\frac{{\delta L_{t} }}{{L_{t} }}} \right)^{2} + \left( {\frac{{\delta \rho_{a} }}{{\rho_{a} }}} \right)^{2} + \left( {\frac{{\delta \left( {\Delta _{p} } \right)_{d} }}{{\left( {\Delta _{p} } \right)_{d} }}} \right)^{2} } \right]^{0.5}$$

The uncertainty calculation has been done on a single test run (constant Reynolds number), the uncertainty analysis for complete test run for single geometry (complete set of Reynolds number) is carried out and results are presented in Table 5 for the experimental data.

Table 5 Range of uncertainty in the measurement of essential parameters