This section focuses on the general equations and laws that SWHSNoPCM is based on.
Refname TM:consThermE
Label Conservation of thermal energy
Equation -∇\cdot{}\boldsymbol{q}+g=ρ\,C\,\frac{\,\partial{}T}{\,\partial{}t}
Description ∇ is the gradient (Unitless)\boldsymbol{q} is the thermal flux vector (\frac{\text{W}}{\text{m}^{2}} )g is the volumetric heat generation per unit volume (\frac{\text{W}}{\text{m}^{3}} )ρ is the density (\frac{\text{kg}}{\text{m}^{3}} )C is the specific heat capacity (\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}} )t is the time ({\text{s}} )T is the temperature ({{}^{\circ}\text{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^{\text{L}}}\,m\,ΔT
Description E is the sensible heat ({\text{J}} ){C^{\text{L}}} is the specific heat capacity of a liquid (\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}} )m is the mass ({\text{kg}} )ΔT is the change in temperature ({{}^{\circ}\text{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\left(t\right)=h\,ΔT\left(t\right)
Description q is the heat flux (\frac{\text{W}}{\text{m}^{2}} )t is the time ({\text{s}} )h is the convective heat transfer coefficient (\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}} )ΔT is the change in temperature ({{}^{\circ}\text{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\left(t\right)=T\left(t\right)-{T_{\text{env}}}\left(t\right) is the time-dependant thermal gradient between the environment and the object.
Source incroperaEtAl2007 (pg. 8)
RefBy GD:htFluxWaterFromCoil