Air at a free stream temperature of T 20 C is in parallel

Chapter , Problem 6.12

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QUESTION:

Air at a free stream temperature of T 20 C is in parallel flow over a flat plate of length L 5 m and temperature Ts 90 C. However, obstacles placed in the flow intensify mixing with increasing distance x from the leading edge, and the spatial variation of temperatures measured in the boundary layer is correlated by an expression of the form T( C) 20 70 exp (600xy), where x and y are in meters. Determine and plot the manner in which the local convection coefficient h varies with x. Evaluate the average convection coefficient for the plate.

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QUESTION:

Air at a free stream temperature of T 20 C is in parallel flow over a flat plate of length L 5 m and temperature Ts 90 C. However, obstacles placed in the flow intensify mixing with increasing distance x from the leading edge, and the spatial variation of temperatures measured in the boundary layer is correlated by an expression of the form T( C) 20 70 exp (600xy), where x and y are in meters. Determine and plot the manner in which the local convection coefficient h varies with x. Evaluate the average convection coefficient for the plate.

ANSWER:


The local convection coefficient h(x) is given by:

h(x) = (T(x) - T_f)/(Ts - T_f) * Nu

where Nu is the Nusselt number (which is typically assumed to be constant in this flow regime).

Substituting the expression for T(x) in the equation for h(x

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