<jupyter_start><jupyter_text>Forced Convection For A Cylinder in Cross FlowExperiments have been conducted on a metallic cylinder 12.7 mm in diameter and 94 mm long. Thecylinder is heated internally by an electrical heater and is subjected to a cross flow of air ina low-speed wind tunnel. Under a specific set of operating conditions for which the upstream airvelocity and temperature were maintained at V = 10 m/s and 26.2oC, respectively, theheater power dissipation was measured to be P =46 W, while the average cylinder surfacetemperature was determined to be Ts = 128.4oC. It is estimated that 15% of the powerdissipation is lost through the cumulative effect of surface radiation and conduction through the endpieces.  Convection heat transfer coefficient by experimentDetermine the convection heat transfer coefficient from the experimental observations.  Given<jupyter_code>import numpy as np
from thermal_system_calculation import FluidState, Fluid

diameter_cylinder = 0.0127 # m
length_cylinder = 0.094 # m
velocity_air = 10 # m/s
temp_air = 26.2 # degC
q_heater = 46 # W
temp_surface = 128.4
ratio_heat_lost_endpieces = 0.15<jupyter_output><empty_output><jupyter_text>Findconvection heat transfer coefficient from the experimental observations, $h_\mathrm{exp}$  Schematics![Schematic](images/forced_convection_cylinder_cross_flow.png)  Assumptions1. Steady state conditions2. Uniform and constant surface temperature and properties for air  Properties<jupyter_code>temp_fluid = np.mean([temp_air, temp_surface]) + 273.15 # K
fluid_state_air = FluidState(
    fluid=Fluid.AIR,
    temp_k=temp_fluid,
    characteristic_length=diameter_cylinder
)
k_air = fluid_state_air.k
cp_air = fluid_state_air.cp
density_air = fluid_state_air.density
dynamic_viscosity_air = fluid_state_air.dynamic_viscosity
print(f"The properties for air at {temp_fluid} K are:")
print(f"\t- Thermal conductivity: {k_air:.3f} W/mK")
print(f"\t- Specific heat capacity: {cp_air:.3f} J/kgK")
print(f"\t- density_air: {density_air:.3f} kg/m3")
print(f"\t- dynamic viscosity: {dynamic_viscosity_air:.3e} Pa s")<jupyter_output>The properties for air at 350.45 K are:
	- Thermal conductivity: 0.030 W/mK
	- Specific heat capacity: 1009.246 J/kgK
	- density_air: 1.007 kg/m3
	- dynamic viscosity: 2.089e-05 Pa s<jupyter_text>AnalysisFrom the Newton's cooling law and energy balance,$$q_\mathrm{conv} = hA\left(T_s - T_\infty\right)$$$$q_\mathrm{conv} = q_\mathrm{heater} - q_\mathrm{endpiece}$$$$q_\mathrm{endpiece} = 0.15 q_\mathrm{heater}$$<jupyter_code>area_cylinder = np.pi * diameter_cylinder * length_cylinder
q_conv = (1 - ratio_heat_lost_endpieces) * q_heater
h_exp = q_conv / (area_cylinder * (temp_surface - temp_air))

print(f"Convection heat transfer coefficient from the experiment is {h_exp:.3f} W/m2K.")<jupyter_output>Convection heat transfer coefficient from the experiment is 102.010 W/m2K.<jupyter_text>Compare the experiment with the empirical calculationCompare the experiment result with the convection coefficient computed from an appropriatecorrelation. AnalysisWe will use Churchill and Bernstein equation$$Nu_L = 0.3 + \frac{0.62Re_D^0.5 Pr^{1/3}}{\left[1 + 0.4 / Pr)^{2/3}\right]^0.25}        \left[1 + \left(\frac{Re_D}{282000}\right)^{5/8}\right]^{4/5}$$<jupyter_code># Define a function for the Churchill and Bernstein equation
def get_nusselt_number_circular_cylinder_cross_flow(pr, re):
    return 0.3 + (0.62 * re**0.5 * pr**(1/3)) / \
           (1 + (0.4/pr)**(2/3))**0.25 *\
           (1 + (re/282000)**(5/8))**0.8
pr = cp_air * dynamic_viscosity_air / k_air
re = density_air * velocity_air * diameter_cylinder / dynamic_viscosity_air
nu = get_nusselt_number_circular_cylinder_cross_flow(pr, re)
h_emp = nu * k_air / diameter_cylinder

print(f"Convection heat transfer coefficient from the empirical equation is {h_emp:.3f} W/m2K.")<jupyter_output>Convection heat transfer coefficient from the empirical equation is 96.659 W/m2K.
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