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Theoretical Models

This section focuses on the general equations and laws that SWHSNoPCM is based on.

RefnameTM:consThermE
LabelConservation of thermal energy
Equationq+g=ρCTt
Description
  • is the gradient (Unitless)
  • q is the thermal flux vector (Wm2)
  • g is the volumetric heat generation per unit volume (Wm3)
  • ρ is the density (kgm3)
  • C is the specific heat capacity (JkgC)
  • t is the time (s)
  • T is the temperature (C)
Notes
  • The above equation gives the law of conservation of energy for transient heat transfer in a given material.
  • For this equation to apply, other forms of energy, such as mechanical energy, are assumed to be negligible in the system (A:Thermal-Energy-Only).
SourceFourier Law of Heat Conduction and Heat Equation
RefByGD:rocTempSimp
RefnameTM:sensHtE
LabelSensible heat energy (no state change)
EquationE=CLmΔT
Description
  • E is the sensible heat (J)
  • CL is the specific heat capacity of a liquid (JkgC)
  • m is the mass (kg)
  • ΔT is the change in temperature (C)
Notes
  • E occurs as long as the material does not reach a temperature where a phase change occurs, as assumed in A:Water-Always-Liquid.
SourceDefinition of Sensible Heat
RefByIM:heatEInWtr
RefnameTM:nwtnCooling
LabelNewton’s law of cooling
Equationq(t)=hΔT(t)
Description
  • q is the heat flux (Wm2)
  • t is the time (s)
  • h is the convective heat transfer coefficient (Wm2C)
  • ΔT is the change in temperature (C)
Notes
  • Newton’s law of cooling describes convective cooling from a surface. The law is stated as: the rate of heat loss from a body is proportional to the difference in temperatures between the body and its surroundings.
  • h is assumed to be independent of T (from A:Heat-Transfer-Coeffs-Constant).
  • ΔT(t)=T(t)Tenv(t) is the time-dependant thermal gradient between the environment and the object.
SourceincroperaEtAl2007 (pg. 8)
RefByGD:htFluxWaterFromCoil