In flow over a surface, velocity and temperature profiles are of the forms: u(y) =ay +by2 - cy3 and t(y) = d+ey+fy2 - gy3 , where the coefficients a through g are constants. Obtain expressions for the friction coefficient c and the convection coefficient h in terms of u, t and appropriate profile coefficients and fluid properties.
Answers
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Explanation:
Answer:
To obtain the expressions for friction coefficient c and convection coefficient h in terms of velocity and temperature profiles, we need to use the equations for shear stress and convective heat transfer coefficient.
Explanation:
The shear stress at the surface of the flow is given by:
τ = μ(dU/dy)
where μ is the dynamic viscosity of the fluid and U is the velocity profile. The friction coefficient c is defined as the ratio of the shear stress to the total pressure:
c = τ / (0.5ρU^2)
where ρ is the density of the fluid.
Substituting the expression for U, we get:
τ = μ[a+2by-3cy^2]
c = 2μ[a+2by-3cy^2] / (ρ[a^2+b^2y^2+c^2y^4])
The convective heat transfer coefficient h at the surface of the flow is given by:
h = -k(dT/dy)
where k is the thermal conductivity of the fluid and T is the temperature profile. The convection coefficient h is defined as the ratio of the convective heat transfer coefficient to the thermal conductivity:
h = -k(dT/dy) / T_s
where T_s is the surface temperature.
Substituting the expression for T, we get:
h = -k[d+ey+fy^2-gy^3] / T_s
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