(Solution) - For liquid metals with Prandtl numbers much less the unity -(2025 Original AI-Free Solution)

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For liquid metals with Prandtl numbers much less the unity, the hydrodynamic boundary layer is much thinner than the thermal boundary layer. As a result, one may assume that the velocity in the boundary layer is uniform [u = U? and v = 0]. Starting with equation (4.7b), show that the energy equation and its boundary condition are analogous to those for a semi-infinite slab with a sudden change in surface temperature (see Equation (2.105)). Then show that the local Nusselt number is given by
Nux = 0.565 (Rex Pr)0.5
Compare this relation with the equation for liquid metals in Table 4.5.
GIVEN
Liquid metal flowing over a flat plate
ASSUMPTIONS
Steady state
Uniform velocity in the boundary layer: u = U?, v = 0
Mercury is at room temperature(20°C)