Encyclopaedia Index

### TEM1

------------Character flag; group 7----

TEM1... character name recognised by SATELLITE as denoting the solved-for first-phase temperature. The command SOLVE(TEM1) activates the solution of the temperature equation and selects the first unallocated store to be found, working from variable NPHI backwards.

In GROUND, the integer index ITEM1 should be used in calls to FN routines or as the argument of L0F.

TEM2 and ITEM2 perform the same services for the second phase.

(See TEMP for background information and the difference between TEM1 and TMP1.)

### TEM1, the temperature of the first phase.

(Note that all that is written here about TEM1 applies also to TEM2, the temperature of the second phase, if the 1's are replaced by 2's.)

### The energy equation in terms of temperature

When the variable TEM1 is a solved-for variable, EARTH formulates the energy equation in terms of temperature rather than enthalpy. This practice is much to be preferred when several materials, having differing enthalpy-temperature relations, are present, as is true of conjugate-heat-transfer problems for example.

The temperature TEM1 enters three terms of the energy-conservation equation, namely those for convection, time-dependence and heat conduction.

The first two involve the specific heat, as follows:

• The convection contribution to the energy equation is:
normal velocity * phase density * volume fraction * area * specific heat * temperature
• The time-dependence contribution to the energy equation is:
phase density * volume fraction * (volume/time interval) * specific heat * temperature
The thermal conductivity enters as a multiplier of the temperature gradient.

The energy equation (in one dimension only, to avoid needless repetition) can thus be expressed symbolically as:

M.(<Cp>".T" - <Cp>.T)/dt
+ m(+).(<Cp>(+).T(+) - <Cp>.T) + m(-).(<Cp>(-).T(-) - <Cp>.T)
- (A(+).k(+)/dX(+))(T-T(+)) - (A(-).k(-)/dX(-))(T-T(-)) - So(h)
= 0

wherein:

(+/-) refer to the + and - direction neighbour cells, " refers to values at the previous time-step, M is the mass of fluid in the cell at the previous time-step, m is a mass-inflow rate which is either positive or zero, A is a cell-face area, dX is the distance between cell centres, k is the conductivity,

So, in the energy source term, <Cp> is an effective specific heat capacity, and obedience to M/dt + m(+) + m(-) = 0, the mass-balance equation, is implied.

A, dX and k are defined on the cell faces, while all other quantities are defined at cell centres. "Upwinding" is presumed.

The effective specific heat-capacity must be defined in a such a way as to yield the correct enthalpy-conservation equation,i.e.so that the first two terms of the above equation are equivalent to:

M.(h" - h)/dt m(+).(h(+) - h) + m(-).(h(-) - h)

It follows that the effective specific heat capacity must be defined as;
<Cp>= (h - Habs)/Tabs where Tabs is the temperature on an absolute scale (i.e. degrees Kelvin or Rankine) and Habs is the enthalpy of the material at the absolute zero.

See PHENC entry: SPECIFIC HEATS.

### Mass-inflow boundary conditions

When a mass-inflow patch has a temperature condition expressed via:

COVAL(patchname,TEM1,ONLYMS,Tin),

EARTH automatically multiplies the inflow temperature Tin by the specific heat which prevails in the cells into which the mass is flowing in order to create an energy source. This is adequate only if the specific heat of the inflowing material is the same as that in these cells, which is probable only if the specific heat is a constant for the fluid.

If the multiplication is not desired, for whatever reason, the internal multiplication by specific heat can be deactivated by starting the PATCH name with the characters NOCP. It then becomes the task of the user to insert Tabs_in*CPin, i.e. the enthalpy, as the VALue in the COVAL command, which thus appears as:

COVAL(NOCP....,TEM1,ONLYMS,Tabs_in*CPin).

### Other matters

If the domain is occupied by solids and fluids, both of which are participating in the heat-exchange process, it is necessary to activate harmonic averaging of the diffusion coefficients for TEM1. This is controlled by the last argument of SOLUTN and is activated automatically by the Satellite when TEM1 is SOLVEd.

If the z direction is involved,i.e.the case has been set up y-z, x-z or x-y-z, convergence may be accelerated by activating whole field solution for TEM1. This is controlled by the fourth argument of SOLUTN.

See the PATCH entry in Group 13 for radiation and free-convection boundary conditions for TEM1. See the PATCH entry in Group 12 for the introduction of 'contact resistances'.

### TEM2

See PHENC entry: TEM1