ME 353 Heat Transfer 1

M.M. Yovanovich

FCEXP1.MWS

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Forced convection heat transfer from an isothermal cube and an

isothermal finite circular cylinder. The fluid is dry air at one atmosphere.

Use the Pasternak and Gavin correlation equation.

Compute the Reynolds numbers, the Nusselt numbers, the heat transfer

coefficients, and the heat transfer rates.

Use the properties calculator on the ME 353 Web site.

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> restart:

Air properties at Tfilm = 330 K.

Tfilm = (Tw + Tinfinity)/2 = Tinfinity + deltaT/2.

Properties calculator on ME 353 Web site.

> airprops:=
(Pr = 0.71, rho = 1.07, cp = 1.01, mu = 1.99*10^(-5),
kf = 0.0283, nu = 1.86*10^(-5), alpha = 2.63*10^(-5),
beta = 3.03*10^(-3));

Forced convection relationships.

> Q:= h*A*(Tw - Tinfinity);
h:= kf/sqrt(A)*Nusselt;
Nusselt:= C*Reynolds^m*Pr^(1/3);
Reynolds:= Uinfinity*sqrt(A)/nu;
coefficients_PasternakGavin:= (C = 0.914, m = 0.514);

> cube:= (Tw = 360, Tinfinity = 300, Uinfinity = 1.5, s = 50/1000);

> cylinder:=
(Tw = 360, Tinfinity = 300, Uinfinity = 1.5,
D = 50/1000, L = 100/1000);

> Acube:= evalf(subs(cube, 6*s^2), 4);

> Acylinder:= evalf(subs(cylinder, Pi*D*L + 2*Pi/4*D^2), 4);

Check the Reynolds numbers for the cube and finite cylinder.

> ResqrtA:= Uinfinity*sqrt(A)/nu;

> Re_cube:= evalf(subs(airprops, cube, A = Acube, ResqrtA), 6);

> Re_cyl:= evalf(subs(airprops, cylinder, A = Acylinder, ResqrtA), 6);

Nusselt number correlation of Pasternak and Gauvin (1960).

The Reynolds numbers lie outside the range. We will use this

correlation to estimate the magnitude of h.

> NusqrtA:= 0.914*ResqrtA^(0.514)*Pr^(1/3);

> Nu_cube:=
evalf(subs(airprops, cube, A = Acube, NusqrtA), 5);

> Nu_cyl:=
evalf(subs(airprops, cylinder, A = Acylinder, NusqrtA), 5);

Calculate the area-average heat transfer coefficient.

> h:= kf/sqrt(A)*NusqrtA;

> h_cube:= evalf(subs(airprops, cube, A = Acube, h), 5);

> h_cyl:= evalf(subs(airprops, cylinder, A = Acylinder, h), 5);

Calculate the heat transfer rates.

> Q:= `h A (Tw - Tinfinty)`;

> Q:= h*A*(Tw - Tinfinity);

> Qcube:= evalf(subs(airprops, cube, A = Acube, Q), 5);

> Qcylinder:= evalf(subs(airprops, cylinder, A = Acylinder, Q), 5);

Summary of calculations.

> areas:= [Acube, Acylinder];

> Reynolds:= [Re_cube, Re_cyl];

> Nusselt:= [Nu_cube, Nu_cyl];

> heat_transfer_coeff:= [h_cube, h_cyl];

> heat_transfer_rate:= [Qcube, Qcylinder];

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