An experimental apparatus is shown in the schematic for measuring the local convection coefficient and the boundary layer temperature distribution for a heated vertical plate immersed in an extensive, quiescent fluid. The plate is maintained at a uniform temperature by circulating a thermostatically controlled fluid through imbedded flow channels. The heat flux and surface temperature are measured at discrete locations along the x-axis by miniature sensors using thin-film thermocouple technology. The fluid temperature in the boundary layer is measured using a micro wire thermocouple probe. The plate is mounted within a room under stable climate control. For the series of observations tabulated below, the quiescent air and room wall temperatures were 296 K. Your task is to process the experimental observations and compare them to results from the similarity solution for laminar free convection (Section 9.4).

The following table provides measurements from the heat flux sensor at six x-locations for the specified plate-air temperature difference. Measurements obtained from the air temperature probe are provided next for three discrete y-locations at two x-locations. The local Grashof numbers corresponding to the x-locations have been calculated to simplify your analysis.

(a) The surfaces of the heat flux sensors experience free convection and radiation exchange with the surroundings. Write an expression for estimating the radiation heat flux from the sensor as a function of the surface emissivity, the temperature of the surroundings, and the temperature difference (Ts – T∞).

(b) Using the expression derived in part (a), apply a correction to the measured total heat flux, q"i, to obtain the convection heat flux, qv, and calculate the convection coefficient. Extend the first table above to include the results of your analysis.

(c) Calculate and plot the local convection coefficient, h/x), as a function of the x-coordinate using the similarity solution, Eqs. 9.19 and 9.20. On the same graph, plot the experimental points. Comment on the comparison between the experimental and analytical results.

(d) For the conditions in the second table, compare the experimental boundary-layer air temperature measurements with those from the similarity solution, Figure 9.4b. Summarize the results of your analysis using the similarity parameter, 71, and the dimensionless temperature, T*. Comment on the comparison between the experimental and analytical results.

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Air probe temperature measurements -Ty = T. Quiescent air T- 296 K etical test pte, T, thermostat- artelled slating th Heat flux gage and thin-film surface L, themocouple, e= 0.05 T,- T = 7.7 K 275 375 x (mm) 25 75 175 475 .(W/m) 41.4 27.2 22.0 20.1 18.3 17.2 T, - T. = 7.3 K x = 200 mm, Gr, = 7.6 x 10 x = 400 mm, Gr, = 6.0 x 10 2.5 5.0 10.0 2.5 5.0 10.0 s(mm) Tx, y) - T(K) 5.5 3.8 5.9 4.5 2.0 1.6