This section focuses on the general equations and laws that SWHSNoPCM is based on.
Refname TM:consThermE
Label Conservation of thermal energy
Equation − ∇ ⋅ q + g = ρ C ∂ T ∂ t
Description ∇ is the gradient (Unitless)q is the thermal flux vector (W m 2 )g is the volumetric heat generation per unit volume (W m 3 )ρ is the density (kg m 3 )C is the specific heat capacity (J kg ∘ C )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 ).
Source Fourier Law of Heat Conduction and Heat Equation
RefBy GD:rocTempSimp
Refname TM:sensHtE
Label Sensible heat energy (no state change)
Equation E = C L m Δ T
Description E is the sensible heat (J )C L is the specific heat capacity of a liquid (J kg ∘ C )m is the mass (kg )Δ T 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 .
Source Definition of Sensible Heat
RefBy IM:heatEInWtr
Refname TM:nwtnCooling
Label Newton’s law of cooling
Equation q ( t ) = h Δ T ( t )
Description q is the heat flux (W m 2 )t is the time (s )h is the convective heat transfer coefficient (W m 2 ∘ C )Δ T 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 ).Δ T ( t ) = T ( t ) − T env ( t ) is the time-dependant thermal gradient between the environment and the object.
Source incroperaEtAl2007 (pg. 8)
RefBy GD:htFluxWaterFromCoil