Consider airflow over a flat plate of length L = 1 m. a) Evaluating the thermophysical properties of air at 400 K, determine the air velocity if the B.L. flow is observed to transition from laminar to turbulent at x = 0.3 m from the leading edge of the plate. b) The local convection coefficients in the laminar and turbulent boundary layers are, respectively, hlam(x) = Clamx-0.5 and hurb (x) = Cturb-x-0.2 where, Clam = 9.002 W/m³/2. Kand Cturb = 52.55 W/m¹.8 - K, and x has units of m. Develop an expression for the average convection coefficient, hlam (x), as a function of distance from the leading edge, x, for the laminar region, 0≤ x ≤ xc- c) Develop an expression for the average convection coefficient, turb (x), as a function of distance from the leading edge, x, for the turbulent region, xe ≤ x ≤ L.. d) Using the programming software of your choice, plot the local and average convection coefficients, hy and hx, respectively, as a function of x for 0 ≤ x ≤ L. e) If the plate has a depth into the page of 0.5 m and the surface and free stream temperatures are T₁ = 300 K and T∞ = 500 K, respectively, calculate the total heat transfer rate from the plate surface. f) Calculate the ratio of the heat transfer rates from the laminar and turbulent boundary layers, lam aturb
Consider airflow over a flat plate of length L = 1 m. a) Evaluating the thermophysical properties of air at 400 K, determine the air velocity if the B.L. flow is observed to transition from laminar to turbulent at x = 0.3 m from the leading edge of the plate. b) The local convection coefficients in the laminar and turbulent boundary layers are, respectively, hlam(x) = Clamx-0.5 and hurb (x) = Cturb-x-0.2 where, Clam = 9.002 W/m³/2. Kand Cturb = 52.55 W/m¹.8 - K, and x has units of m. Develop an expression for the average convection coefficient, hlam (x), as a function of distance from the leading edge, x, for the laminar region, 0≤ x ≤ xc- c) Develop an expression for the average convection coefficient, turb (x), as a function of distance from the leading edge, x, for the turbulent region, xe ≤ x ≤ L.. d) Using the programming software of your choice, plot the local and average convection coefficients, hy and hx, respectively, as a function of x for 0 ≤ x ≤ L. e) If the plate has a depth into the page of 0.5 m and the surface and free stream temperatures are T₁ = 300 K and T∞ = 500 K, respectively, calculate the total heat transfer rate from the plate surface. f) Calculate the ratio of the heat transfer rates from the laminar and turbulent boundary layers, lam aturb
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Consider airflow over a flat plate of length L = 1 m.
a) Evaluating the thermophysical properties of air at 400 k, determine the air velocity
if the B.L. flow is observed to transition from laminar to turbulent at x = 0.3 m from
the leading edge of the plate.
b) The local convection coefficients in the laminar and turbulent boundary layers are,
respectively,
hlam(x) = Clam-x-0.5 and hurb(x) = Cturb-x-0.2
where, Clam = 9.002 W/m³/2. K and Cturb 52.55 W/m¹-8. K, and x has units of m.
Develop an expression for the average convection coefficient, hlam (x), as a function
of distance from the leading edge, x, for the laminar region, 0 ≤ x ≤ xc.
c) Develop an expression for the average convection coefficient, turb (x), as a function
of distance from the leading edge, x, for the turbulent region, xc ≤ x ≤ L..
d) Using the programming software of your choice, plot the local and average
convection coefficients, hx and hx, respectively, as a function of x for 0 ≤ x ≤ L.
e) If the plate has a depth into the page of 0.5 m and the surface and free stream
temperatures are T, = 300 K and T∞ = 500 K, respectively, calculate the total heat
transfer rate from the plate surface.
f) Calculate the ratio of the heat transfer rates from the laminar and turbulent
boundary layers,
qlam
qturb
=
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