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The main feature of thermodynamic diagrams is the equivalence between the area in the diagram and energy. When air changes pressure and temperature during a process and prescribes a closed curve within the diagram the area enclosed by this curve is proportional to the energy which has been gained or released by the air.
One can often quickly calculate this using the PV diagram as it is simply the area enclosed by the cycle. [citation needed] Note that in some cases specific volume will be plotted on the x-axis instead of volume, in which case the area under the curve represents work per unit mass of the working fluid (i.e. J/kg). [citation needed]
The "dryness fraction", x, gives the fraction by mass of gaseous water in the wet region, the remainder being droplets of liquid. An enthalpy–entropy chart, also known as the H–S chart or Mollier diagram, plots the total heat against entropy, [1] describing the enthalpy of a thermodynamic system. [2]
In thermodynamics, a temperature–entropy (T–s) diagram is a thermodynamic diagram used to visualize changes to temperature (T ) and specific entropy (s) during a thermodynamic process or cycle as the graph of a curve. It is a useful and common tool, particularly because it helps to visualize the heat transfer during a process.
The volume rate of flow of liquid through a source or sink (with the flow through a sink given a negative sign) is equal to the divergence of the velocity field at the pipe mouth, so adding up (integrating) the divergence of the liquid throughout the volume enclosed by S equals the volume rate of flux through S. This is the divergence theorem. [2]
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. [1] In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then ...
Given any curve c : (a, b) → S, one may consider the composition X ∘ c : (a, b) → ℝ 3. As a map between Euclidean spaces, it can be differentiated at any input value to get an element (X ∘ c)′(t) of ℝ 3. The orthogonal projection of this vector onto T c(t) S defines the covariant derivative ∇ c ′(t) X.