Heat Transport

Heat transport is completely analogous to mass transport. Hence, heat can be simulated as a species The chemical (or non-chemical, such as bacterial or viral) constituents that are stored and transported through an environmental system in a contaminant transport model. In GoldSim, the Species element defines all of the contaminant species being simulated (and their properties). in GoldSim. Note, however, that GoldSim treats all species in terms of mass. In order to simulate heat transport, therefore, you will need to enter data which reference heat (e.g., calories) as if it were mass (e.g., grams). The easiest way to do this is to assume, for the purpose of data entry and calculations, that 1 gram is equivalent to 1 calorie. At the end of your calculations, you can then multiply results by 1 cal/g so that they display in the proper units.

When simulating heat, the following points should be noted:

• The molecular diffusivity must be replaced by the thermal diffusivity (typically denoted as κ). The thermal diffusivity is computed as follows:
  
  κ = K/(ρ c_p)
  
  where:
  
  κ is the thermal diffusivity [m²/sec];
  K is the thermal conductivity [cal/(sec m °C)];
  ρ is the density [kg/m³]; and
  c_p is the specific heat [cal/(kg °C)].
  

• To convert computed "heat concentrations" in a fluid (in cal/m³) to temperature, it is necessary to divide the "heat concentration" by the product ρ c_p.

• To convert computed "heat concentrations" in a solid (in cal/kg) to temperature, it is necessary to divide the "heat concentration" by c_p.

• Partition coefficients The ratio of the species’ concentration in a medium to its concentration in the Reference Fluid at equilibrium. Partition coefficients are inputs to Solid and Fluid elements. between media Materials (such as water, sand, clay, air) that constitute (are contained within) transport pathways. GoldSim provides two types of elements for defining media: Fluids and Solids. for heat can be computed by assuming that at equilibrium, the temperature in all media is the same. The partition coefficient (which simply represents the ratio of concentrations) between solid A and fluid B is then:
  
  K_AB = c_p,A / (c_p,B ρ_B)
  
  where:
  
  K_AB is the partition coefficient between solid A and fluid B [m³/kg];
  ρ_B is the density of fluid B [kg/m³];
  c_p,A is the specific heat of solid A [cal/(kg °C)]; and
  c_p,B is the specific heat of fluid B [cal/(kg °C)].
  
  Similarly, the partition coefficient between fluid C and fluid B is:
  
  K_CB = (c_p,C ρ_C) / (c_p,B ρ_B)
  
  where:
  
  K_CB is the partition coefficient between fluid C and fluid B [m³/m³];
  ρ_C is the density of fluid C [kg/m³]; and
  c_p,C is the specific heat of fluid C [cal/(kg °C)].
  

• Note that the species heat could be produced by a reaction:
  
  A + B ⇒ 2C + n HEAT
  
  where n is the number of calories of heat produced per mole of A reacted.

If you also had to simulate heat conduction through a solid (e.g., conduction through the wall of pipeline), you could do so as follows:

• Give the solid (e.g., representing the pipeline material) an arbitrarily small fictitious porosity value.

• Define the tortuosity for the solid in such a way that it produces the correct heat flow (since in GoldSim, all of the transport is through the fluid phase):