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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
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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**Title: Analysis of Airflow Over a Flat Plate** **Introduction:** This study involves analyzing airflow over a flat plate with a length \( L = 1 \, \text{m} \). **Problem Statement:** 1. **Evaluating Air Velocity:** Determine the air velocity at which boundary layer (B.L.) flow transitions from laminar to turbulent at \( x_c = 0.3 \, \text{m} \) from the leading edge of the plate. 2. **Local Convection Coefficients:** The local convection coefficients in the laminar and turbulent boundary layers are given by: - Laminar: \( h_{\text{lam}}(x) = C_{\text{lam}} x^{-0.5} \) - Turbulent: \( h_{\text{turb}}(x) = C_{\text{turb}} x^{-0.2} \) Where: - \( C_{\text{lam}} = 9.002 \, \text{W/m}^{3/2} \cdot \text{K} \) - \( C_{\text{turb}} = 52.55 \, \text{W/m}^{1.8} \cdot \text{K} \) - \( x \) is in meters. 3. **Average Convection Coefficient - Laminar Region:** Develop an expression for the average convection coefficient \( \overline{h}_{\text{lam}}(x) \) as a function of \( x \) for the laminar region, \( 0 \leq x \leq x_c \). 4. **Average Convection Coefficient - Turbulent Region:** Develop an expression for the average convection coefficient \( \overline{h}_{\text{turb}}(x) \) as a function of \( x \) for the turbulent region, \( x_c \leq x \leq L \). 5. **Graphical Analysis:** Using a software tool, plot the local and average convection coefficients, \( h_x \) and \( \overline{h}_x \), respectively, as functions of \( x \) for \( 0 \leq x \leq L \). 6. **Heat Transfer Rate Calculation:** If the plate has a depth of \( 0.5 \,
Transcribed Image Text:**Title: Analysis of Airflow Over a Flat Plate** **Introduction:** This study involves analyzing airflow over a flat plate with a length \( L = 1 \, \text{m} \). **Problem Statement:** 1. **Evaluating Air Velocity:** Determine the air velocity at which boundary layer (B.L.) flow transitions from laminar to turbulent at \( x_c = 0.3 \, \text{m} \) from the leading edge of the plate. 2. **Local Convection Coefficients:** The local convection coefficients in the laminar and turbulent boundary layers are given by: - Laminar: \( h_{\text{lam}}(x) = C_{\text{lam}} x^{-0.5} \) - Turbulent: \( h_{\text{turb}}(x) = C_{\text{turb}} x^{-0.2} \) Where: - \( C_{\text{lam}} = 9.002 \, \text{W/m}^{3/2} \cdot \text{K} \) - \( C_{\text{turb}} = 52.55 \, \text{W/m}^{1.8} \cdot \text{K} \) - \( x \) is in meters. 3. **Average Convection Coefficient - Laminar Region:** Develop an expression for the average convection coefficient \( \overline{h}_{\text{lam}}(x) \) as a function of \( x \) for the laminar region, \( 0 \leq x \leq x_c \). 4. **Average Convection Coefficient - Turbulent Region:** Develop an expression for the average convection coefficient \( \overline{h}_{\text{turb}}(x) \) as a function of \( x \) for the turbulent region, \( x_c \leq x \leq L \). 5. **Graphical Analysis:** Using a software tool, plot the local and average convection coefficients, \( h_x \) and \( \overline{h}_x \), respectively, as functions of \( x \) for \( 0 \leq x \leq L \). 6. **Heat Transfer Rate Calculation:** If the plate has a depth of \( 0.5 \,
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