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Consider the flow of a liquid metal past a flat plate (Pr << 1). We have...

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Mechanical Engineering

Consider the flow of a liquid metal past a flat plate (Pr<< 1). We have shown that for a constant wall teemperature,T_o, the Nusselt number is given by Nu = 0.564*(Re^1/2)*(Pr^1/2).Show that if the surface is not a constant temperature, but isinstead providing a constant heat flux, that the Nusselt numberbecomes Nu = 0.886*(Re^1/2)*(Pr^1/2). Start with the followingexpression for the temperature profile within a semi-infinite bodywith a constant heat flux boundary condition T - T_o = (q_s / k)[((4*alpha*t) / pi)^1/2 * exp(-x^2 / (4*alpha*t)) - x*erfc( x /(4*alpha*t)^1/2 ) ].

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