Transport Phenomena · Momentum transport and viscous flow
Hot water flows turbulently over one face of a flat plate
Problem
Hot water flows turbulently over one face of a flat plate. Between y_0 = 0.20 mm and δ = 25.0 mm, use the prescribed velocity u(y) = U(y/δ)^(1/7), with U = 3.00 m/s, and the mixing length l_m = 0.40y(1 - y/δ). The eddy thermal diffusivity is α_t = l_m^2|du/dy|/Pr_t with Pr_t = 0.85. Take the molecular thermal diffusivity as α = 1.45×10^-7 m^2/s, density as 995 kg/m^3, and heat capacity as 4180 J/(kg·K). The temperature is 355 K at y_0 and 315 K at δ. Assuming steady one-dimensional heat transport and a constant heat flux q_y = -ρc_p(α + α_t)dT/dy, determine q_y and T(y) throughout y_0 ≤ y ≤ δ.
Hint
Differentiate the one-seventh-power velocity law before forming α_t.
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