Example 9.5

M.M. Yovanovich

EX9P5.MWS

Example 9.5 of Incropera and DeWitt.

> restart:

Air properties and system parameters.

> airprops:=
(g = 9.81, kf = 0.030, nu = 20.92e-6, alpha = 29.9e-6,
Pr = 0.70, beta = 0.00285);

> syspar:=
(Di = 100/1000, Do = 120/1000, Ti = 120 + 273, To = 35 + 273);

Raithby-Hollands correlation equations.

> Q_per_length:= 2*Pi*keff/(ln(Do/Di))*(Ti - To);
#Eq.(9.58)

> keff:= 0.386*kf*(Pr/(0.861 + Pr))^(1/4)*Racstar^(1/4);
#Eq. (9.59)

> Racstar:= (ln(Do/Di))^4/L^3/(Di^(-3/5) + Do^(-3/5))^5*RaL;
#Eq. (9.60)

> RaL:= g*beta*(Ti - To)*L^3/(alpha*nu);

This relation is not defined in the 4th edition

> L:= (Do - Di)/2; #See Fig. 9.14

> RaDi:= g*beta*(Ti - To)*Di^3/(alpha*nu);

Calculations.

> RaL1:=
evalf(subs(airprops, syspar, RaL), 5);

> Racstar2:=
evalf(subs(airprops, syspar, Racstar), 6);

> RaDi2:=
evalf(subs(airprops, syspar, RaDi), 6);

> keff2:=
evalf(subs(airprops, syspar, airprops, keff), 6);

> Q_per_length2:=
evalf(subs(airprops, syspar, Q_per_length), 6);

The calculated values agree with the values reported in the text.

The heat transfer rate per unit length with fiber-glass is obtained from the conduction relationship.

> Q_per_length3:=
evalf(subs(Di = 100/1000, Do = 120/1000, k = 0.0380,
Ti = 120, To = 35, 2*Pi*k/ln(Do/Di)*(Ti - To)), 4);

The calculated value agrees with the text value.