The hot-film heat flux gage shown schematically may be used to determine the convection coefficient of an adjoining fluid stream by measuring the electric power dissipation per unit area, P"_e (W/m²), and the average surface temperature, T_s,f' of the film, The power dissipated in the film is transferred directly to the fluid by convection, as well as by conduction into the substrate. If substrate conduction is negligible, the gage measurements can be used to determine the convection coefficient without application of a correction factor. Your assignment is to perform a two-dimensional, steady-state conduction analysis to estimate the fraction of the power dissipation that is conducted into a 2-mm-thick quartz substrate of width W = 40 mm and thermal conductivity k = 1.4 W/m ∙ K. The thin, hot-film gage has a width of w = 4 mm and operates at a uniform power dissipation of 5000 W/m². Consider cases for which the fluid temperature is 25°C and the convection coefficient is 500, 1000 and 2000 W/m² ∙ K.

Use the finite-element method of FEHT to analyze a symmetrical half-section of the gage and the quartz substrate. Assume that the lower and end surfaces of the substrate are perfectly insulated, while the upper surface experiences convection with the fluid.

(a) Determine the temperature distribution and the conduction heat rate into the region below the hot film for the three values of h. Calculate the fractions of electric power dissipation represented by these rates. Him: Use the View/Heat Flow command to find the heat rate across the boundary elements.

(b) Use the View/Temperature Contours command to view the isotherms and heat flow patterns. Describe the heat flow paths, and comment on features of the gage design that influence the paths. What limitations on applicability of the gage have been revealed by your analysis?

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Ts.f Hot-thin film, P" = 5000 W/m2 Fluid Quartz substrate k = 1.4 W/m•K Teo, h Ew = 4 mm 2 mm P". -W = 40 mm %3D +w/2 W/2