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Different Coordinate Systems

Different Coordinate Systems. cartesian. cylindrical. spherical. Work Examples. [1] Sliding Block. Δ x. F. CM. work done to the control mass so it is energy gained. [2] Shear Work on a Fluid. Belt. shear stress × speed × area. v x. W. t. CM. Liquid Bath.

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Different Coordinate Systems

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  1. Different Coordinate Systems cartesian cylindrical spherical

  2. Work Examples [1] Sliding Block Δx F CM work done tothe control mass so it is energy gained [2] Shear Work on a Fluid Belt shear stress × speed × area vx W t CM Liquid Bath work done tothe control mass so it is energy gained

  3. Work Examples [3] Boundary Displacement Gas Expansion W p0 boundary work Δz CM p1 work done by the control mass so it is energy lost Strain (Compression/Expansion) F boundary work (constant area) Δz CM1 work done to the control mass so it is energy gained

  4. Work Examples [4] Shaft/Propeller CM torque × angular speed work done tothe control mass so it is energy gained W [5] Electrical Work (Heat Generation) CM Joule (or resistive or Ohmic) heating R work done tothe control mass so it is energy gained W + - V

  5. Work Examples [6] Surface Tension CM Soap bubble air surface tension × area change straw CM work done tothe control mass so it is energy gained Soap film inside a wire movable wire ΔA

  6. Work Examples [7] Spring Compression F Δx

  7. Enthalpy We can literally define a new specific property enthalpy as the summation of the internal energy and the pressure × volume (flow work) Porter, 1922 Thus for open systems, the first law is frequently written as

  8. Heat Transfer • Heat Transfer is the transport of thermal energy due to a temperature difference across a medium(s) • mediums: gas, liquid, solid, liquid-gas, solid-gas, solid-liquid, solid-solid, etc. • Thermal Energy is simply the kinetic energy (i.e. motion) of atoms and molecules in the medium(s) • Atoms/molecules in matter occupy different states • translation, rotation, vibration, electronic • the statistics of these individual molecular-level activities will give us the thermal energy which is approximated by temperature • Heat Transfer, Thermal Energy, and Temperature are DIFFERENT. DO NOT confuse them. • Heat generation (electrical, chemical, nuclear, etc.) are not forms of heat transfer Q but forms of work W • Q is the transfer of heat across the boundary of the system due to a temperature difference

  9. Definitions Symbol/Units Quantity Meaning Energy associated with molecular behavior of matter U [J] – extensive property u[J/kg] – intensive property Thermal Energy Means of indirectly assessing the amount of thermal energy stored in matter T[K] or [°C] Temperature Thermal energy transport due to a temperature gradient (difference) Heat Transfer various Thermal energy transferred over a time interval (Δt > 0) Heat Heat Transfer Thermal energy transferred per unit time Heat Rate/Heat Flow Thermal energy transferred per unit time per unit surface area Heat Flux

  10. Modes of Heat Transfer Conduction & convection require a temperature difference across a medium (the interactions of atoms/molecules) Radiation transport can occur across a vacuum

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