ME 353 Heat Transfer 1

M.M. Yovanovich

AIRPROPS.MWS

Dry air properties at one atmosphere pressure.

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Reference: F. P. Incropera and DeWitt, 4th edition, 1996,

Fundamentals of Heat and Mass Transfer.

Uinits are: rho[kg/m^3], cp[kJ/kg K], mu[N s/m^2], nu[m^2/s],

alpha[m^2/s], kf[W/m K], Pr[-].

Temperature range: 200 <= T(K) <= 600.

Create quadratic fits for the data. Show the data in a table.

Check the property values against the tabulated data at

T = 300 K.

Show how to plot the data and the correlation for density.

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> restart:

> with(stats):with(plots):

Temperature list.

> temps:= [200, 250, 300, 350, 400, 450, 500, 550, 600];

Properties lists for mass density, specific heat, dynamic and kinematic

viscosities, thermal diffusivity, thermal conductivity, and Prandtl number.

> rhos:=
[1.7458, 1.3947, 1.1614, 0.9950, 0.8711, 0.7740,
0.6964, 0.6329, 0.5804];

> cps:=
[1.007, 1.006, 1.007, 1.009, 1.014, 1.021,
1.030, 1.040, 1.051];

> mus:=
[132.5e-7, 159.6e-7, 184.6e-7, 208.2e-7, 230.1e-7,
250.7e-7, 270.1e-7,288.4e-7, 305.8e-7];

> nus:=
[7.590e-6, 11.44e-6, 15.89e-6, 20.92e-6, 26.41e-6,
32.39e-6, 38.79e-6, 45.57e-6, 52.69e-6];

> alphas:=
[10.3e-6, 15.9e-6, 22.5e-6, 29.9e-6, 38.3e-6, 47.2e-6,
56.7e-6, 66.7e-6, 76.9e-6];

> kfs:=
[18.1e-3, 22.3e-3, 26.3e-3, 30.0e-3, 33.8e-3, 37.3e-3,
40.7e-3, 43.9e-3,46.9e-3];

> Prs:=
[0.737, 0.720, 0.707, 0.700, 0.690, 0.686, 0.684, 0.683, 0.685];

Create quadratic and linear fits for the dry air properties.

> density:=
fit[leastsquare[[T, rho], rho = a*T^2 + b*T + c,
{a, b, c}]]([temps, rhos]);

> subs(T = 300, density);

> rho1:= evalf(subs(T = 300, rhs(density)), 4);

> specific_heat:=
fit[leastsquare[[T, cp], cp = a*T^2 + b*T + c,
{a, b, c}]]([temps, cps]);

> dynamic_viscosity:=
fit[leastsquare[[T, mu], mu = a*T^2 + b*T + c,
{a, b, c}]]([temps, mus]);

> kinematic_viscosity:=
fit[leastsquare[[T, nu], nu = a*T^2 + b*T + c,
{a, b, c}]]([temps, nus]);

> diffusivity:=
fit[leastsquare[[T, alpha], alpha = a*T^2 + b*T + c,
{a, b, c}]]([temps, alphas]);

> conductivity:=
fit[leastsquare[[T, kf], kf = a*T^2 + b*T + c,
{a, b, c}]]([temps, kfs]);

> Prandtl:=
fit[leastsquare[[T, Pr], Pr = a*T + b,
{a, b}]]([temps, Prs]);

Check the fits against the property values at T = 300.

> testT300:=
evalf(subs(T = 300,
[density, specific_heat, dynamic_viscosity,
kinematic_viscosity, diffusivity, conductivity, Prandtl]), 4);

Tabular display of the data.

> rhodata:=
[seq([temps[j], rhos[j]], j = 1..9)]:
`density_values` = convert(%, matrix);

> cpdata:=
[seq([temps[j], cps[j]], j = 1..9)]:
`specific_heat_values` = convert(%, matrix);

> mudata:=
[seq([temps[j], mus[j]], j = 1..9)]:
`dynamic_viscosity_values` = convert(%, matrix);

> nudata:=
[seq([temps[j], nus[j]], j = 1..9)]:
`kinematic_viscosity_values` = convert(%, matrix);

> alphadata:=
[seq([temps[j], alphas[j]], j = 1..9)]:
`diffusivity_values` = convert(%, matrix);

> kfdata:=
[seq([temps[j], kfs[j]], j = 1..9)]:
`conductivity_values` = convert(%, matrix);

> Prdata:=
[seq([temps[j], Prs[j]], j = 1..9)]:
`Prandtl_number_values` = convert(%, matrix);

Show the correlation and the data plots for the mass density.

> plot1:= plot(rhs(density), T = 200..600):
plot2:= plot(rhodata, style = POINT):
plot[display]({plot1, plot2});

>