Conductors

Conductors are used to represent heat flow paths from node to node. Two basic types of conductors may be defined by the user: linear and radiation.

Linear Conductors

The conductance of a linear conductor is input in units of energy per unit time per unit degree, and the heat rate through such a conductor is calculated in the network solution routines as:

Q = G * (Ti - Tj)

where:

Q       Heat rate (energy/time)  
G       Conductance (note G = 1 / R ) 
T       Temperature

Conduction

Conduction is the process by which heat flows within a material or between different materials in direct contact. For heat transfer by conduction, the conductance is computed as:

G = k * A / L

where:

k       thermal conductivity (energy / length-time-degree) 
A       cross-sectional area of the conduction path (length2) 
L       length of the conductance path (length)

Mass Flow

Mass flow conductors are actually a special type of linear conductor. The use of a mass flow conductor in a thermal network is a convenient method for the transfer of energy from one point to another due to the actual movement (flow) of a fluid from one point to another. The mass flow conductor simply accounts for the internal energy term of a mass moving from one location to another. Such a conductor is defined by prefixing the up stream node number with a minus sign. The node so designated will not be allowed to lose or gain heat through the conductor, even though its temperature will be used to calculate a heat flow to the downstream node. Mass flow conductors are computed from the equation:

G = Mdot * Cp

where;

G       the flow conductor (energy/time-deg) 
Mdot    is the mass flow rate (mass/time) 
Cp      is the specific heat of the fluid (energy/mass-deg)

Radiation Conductors

The value of a radiation conductor is input in units of energy per unit time per degree**4. It is be computed as:

G = A * e(eff) * F(i-j) * s
or
G = A * F(i-j) * s

where;

G       value of the conductor 
A       area of the surface i 
e(eff)  emittance (dimensionless)
s       Stefan-Boltzmann Constant (energy/length2-time-deg4) 1.714E-09 BTU/ft2-hr-R4    or   
        5.6677E-09 mW/cm2-K4  
F(i-j)  black body view factor from surface i to j (dimensionless) 
F(i-j)  gray body view factor from surface i to j (dimensionless

The emittance e, is a measure of how well a body can radiate energy as compared with a black body. Emittance is the ratio of total emissive power of a real surface at temperature T to the total emissive power of a black surface at the same temperature. The emittance of surfaces is a function of several things including the material, surface condition, and temperature. The emittance may be altered by polishing, roughing, painting, etc.

The view factor F(i-j) is a function of the geometry of the system only. Many computer programs have been developed to compute the view factors between complex geometries; however view factors between some surfaces with simple geometries can be hand calculated. The methods and equations are found in several heat transfer texts.

The gray body view factor F(i-j) is the product of the geometric shape factor F(i-j) and a factor which allows for departures from black body conditions (i.e. reflections). For example, for two parallel flat plates:

F(1-2) = F(2-1) = 1

F(1-2) = [ 1 / ( 1/e1 + 1/e2 -1) ] x F(1-2)

The effective emittance e* between two surfaces may be used to compute the gray body view factor with the following equation;

F(i-j) = e* x F(i-j)

The error induced by the use of e* is the result of neglecting secondary reflections from surfaces other than the two for which the effective emittance was determined.

MAIN