ME 353 Heat Transfer 1

M.M. Yovanovich

FCEXP2.MWS

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Forced convection heat transfer from an isothermal finite circular cylinder.

Consider both axial and cross flow

The fluid is dry air at one atmosphere.

Use the Yovanovich (1988) general correlation equation.

Compute the Reynolds number, 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:=
SsqrtAstar + (0.15*(P/sqrt(A))^(1/2)*Reynolds^(1/2) + 0.35*Reynolds^(0.566))*Pr^(1/3);

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

> SsqrtAstar1:=
sqrt(A)/D*4/Pi*(1 + 0.869*(L/D)^(0.76))/(0.5 + L/D);

> SsqrtAstar2:=
sqrt(S)/D*4/sqrt(Pi)/sqrt(1 + 0.5*D/L)/ln(2*L/D);

> cylinder:=
(Tw = 360, Tinfinity = 300, Uinfinity = 2.5,
D = 30/1000, L = 100/1000);

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

Calculate the Reynolds number for the finite cylinder.

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

Calculate the Nusselt numbers for the cylinder in axial and cross flow

arrangements.

The blockage parameter accounts for the orientation of the cylinder axis

with respect to the velocity vector.

> PoversqrtA:= (P/sqrt(A))^(1/2);

> Paxial:= Pi*D; Pcrossflow:= 2*(D + L);

> PoversqrtA1:= evalf(subs(cylinder, Paxial), 4);

> PoversqrtA2:= evalf(subs(cylinder, Pcrossflow), 4);

> Nu_cyl_axial:=
evalf(subs(airprops, A = Acylinder, P = Paxial, cylinder,
Nusselt), 5);

> Nu_cyl_crossflow:=
evalf(subs(airprops, A = Acylinder, P = Pcrossflow, cylinder,
Nusselt), 5);

> LoverD:= evalf(subs(cylinder, L/D), 4);

Since L/D < 8, use the first correlation equation for the dimensionless

diffusive limit.

> SsqrtAstar:=
evalf(subs(cylinder, A = Acylinder, SsqrtAstar1), 4);

The Nusselt numbers for axial and crossflow.

> Nu_axial:= Nu_cyl_axial;

> Nu_crossflow:= Nu_cyl_crossflow;

Calculate the area-average heat transfer coefficient.

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

> h_axial:=
evalf(subs(airprops, cylinder, A = Acylinder,
NusqrtA = Nu_axial, h), 5);

> h_crossflow:=
evalf(subs(airprops, cylinder, A = Acylinder,
NusqrtA = Nu_crossflow, h), 5);

Calculate the heat transfer rates.

> Q_axial:=
evalf(subs(airprops, cylinder, A = Acylinder,
NusqrtA = Nu_axial, Q), 5);

> Q_crossflow:=
evalf(subs(airprops, cylinder, A = Acylinder,
NusqrtA = Nu_crossflow, Q), 5);

The heat transfer from the cylinder is approximately 11.3% greater in the

crossflow arrangement.

Summary of calculations.

> `case`:= cylinder;

> `Reynolds number` = Re_cyl;

> `P over A^(1/2) axial`:= PoversqrtA1;

> `P over A^(1/2) cross flow`:= PoversqrtA2;

> `SsqrtA`:= SsqrtAstar;

> `Nu axial flow`:= Nu_axial;

> `Nu cross flow`:= Nu_crossflow;

> `h axial flow`:= h_axial;

> `h cross flow`:= h_crossflow;

> `Q axial flow`:= Q_axial;

> `Q cross flow`:= Q_crossflow;

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