An air flow with velocity u∞ = 2m/s and T∞ = 300K is used to cool the surface of a flat metal plate that is L = 0.5m long, W = 0.5m wide, and H = 0.1m thick. The plate receives a uniform heat flux input of q′′ = 500W/m^2 from the bottom. Assume the plate reaches the steady state and has a uniform surface temperature Ts and bottom temperature Tb. Assume one-dimensional conduction across the plate. For the air flow, the Prandtl number is Pr = 0.7, the kinematic viscosity is ν = 2 × 10^(−5) m^2/s, and
An air flow with velocity u∞ = 2m/s and T∞ = 300K is used to cool the surface of a flat metal plate that is L = 0.5m long, W = 0.5m wide, and H = 0.1m thick. The plate receives a uniform heat flux input of q′′ = 500W/m^2 from the bottom. Assume the plate reaches the steady state and has a uniform surface temperature Ts and bottom temperature Tb. Assume one-dimensional conduction across the plate. For the air flow, the Prandtl number is Pr = 0.7, the kinematic viscosity is ν = 2 × 10^(−5) m^2/s, and the thermal conductivity is kf = 0.03 W/m · K. The solid material of the plate has a uniform thermal conductivity ks = 10 W/m · K.
Given correlations for convection heat transfer over flat plate:
• For the laminar flow region, the local Nusselt number is Nu = 0.332Re^(1/2)*Pr(1/3)
• For the turbulent flow region, the local Nusselt number is Nu = 0.0296Re^(4/5)*Pr(1/3)
Questions:
(1) Determine the local convection heat transfer coefficient h(x) and the averaged con- vection heat transfer coefficient hL for the entire plate surface. Need to show the details of the integration.
(2) Determine the plate surface temperature Ts.
(3) Determine the plate bottom temperature Tb.
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