GATE ME 2014 Set 1 — Question 56
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Heat Transfer → Convection → Thermal Boundary Layer
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Question
The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by , where is measured perpendicular to the plate, is the plate length, and , and are arbitrary constants. and are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is and the wall heat flux is , the Nusselt number is equal to
Correct answer
(B) b
Solution
The wall heat flux is given by Fourier's Law at the surface ():Let the non-dimensional temperature profile be :At the wall (), , so . Substituting into the profile equation:Differentiating with respect to :At :Substituting this into the expression for :The Nusselt number is defined as:Thus, the Nusselt number is equal to .
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