The temperature profile in the boundary layer \(0.1 \mathrm{~m}\) from the leading edge of the plate was measured by a hot-wire anemometer and is shown in Figure P12.30. If the fluid is water, the boundary layer thickness at that location is \(2 \mathrm{~mm}\), the surface temperature is \(T_{s}=350 \mathrm{~K}\), the free-stream temperature is \(T_{\infty}=300 \mathrm{~K}\), and the free-stream velocity is \(v_{\infty}=1 \mathrm{~m} / \mathrm{s}\) :

a. Determine a mathematical expression for the temperature profile.

b. What is the value of the local heat transfer coefficient?

c. What is the value of the friction factor?

d. What is the value of the average heat transfer coefficient at that location?

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Position Temperature Position Temperature 0 1.049 0.5 0.265 0.05 0.795 0.55 0.0692 0.1 0.775 0.6 0.242 0.15 0.393 0.65 0.291 0.2 0.567 0.7 0.022 0.25 0.303 0.75 0.009 0.3 0.322 0.8 0.166 0.35 0.235 0.85 -0.076 0.4 0.189 0.90 0.125 0.45 0.178 0.95 0.047 1.0 -0.017