A 1/12 inch diameter metal wire is placed in still air at 66 deg F. Determine the rate of heat generation required to maintain the surface temperature of the wire at 1734 deg F. The heat loss due to radiation may be neglected.

> restart;

The mean film temperature at the air wire interface is given below.

> To:=1734*F; Tinf:=66*F; Tf:=(To+Tinf)/2; beta:=1/Tf;

Other fluid properties of air at 900 deg F

> mu:=0.0846*lbm/hr/ft; k:=0.0320*Btu/hr/ft/F; Cp:=0.260*Btu/lbm/F; rho:=0.02374*lbm/ft^3;

Other parameters

> dia:=1/12/12*ft; deltaT:=To-Tinf; g:=4.17*10^8*ft/hr^2;

Compute Prandtl number

> Pr:=Cp*mu/k;

Compute Grashof number

> Gr:=(rho^2*beta*g*dia^3*deltaT)/mu^2;

Compute Gr x Pr. If greater than 10^4 can use Eq. 13.5-3 to Approximate Nusselt number.

> GrPr:=Gr*Pr;

GrPr is much smaller than 10^4. Must use experimental data and polynomial fit to determine Nusselt number.

> readlib(log10):

> log(GP):=log10(GrPr);

> log(Nu):=-5E-5*(log(GP))^4+.0003*(log(GP))^3+.012*(log(GP))^2+.124*(log(GP))+.0285;

> Nu_m:=10^log(Nu);

From the definition of the Nusselt number we can determine the mean Heat Transfer Coefficient: (hm).

> hm:=Nu_m*k/dia;

The rate of heat loss can be determined from Eq. 13.1-1. Q = hm * Area * deltaT.

> Q = hm*3.14159*dia*deltaT;