Conservation of Energy

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Presentation transcript:

Conservation of Energy Chapter One Section 1.3

Alternative Formulations CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS) An important tool in heat transfer analysis, often providing the basis for determining the temperature of a system. Alternative Formulations Time Basis: At an instant or Over a time interval Type of System: Control volume Control surface

CV at an Instant and over a Time Interval APPLICATION TO A CONTROL VOLUME At an Instant of Time: Note representation of system by a control surface (dashed line) at the boundaries. Surface Phenomena Volumetric Phenomena Conservation of Energy (1.11a) Each term has units of J/s or W. Over a Time Interval (1.11b) Each term has units of J.

Special Cases (Linkages to Thermodynamics) Closed System Special Cases (Linkages to Thermodynamics) Transient Process for a Closed System of Mass (M) Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow). Over a time interval (1.11c) At an instant (1.11d)

Example 1.3: Application to thermal response of a conductor with Ohmic heating (generation): Involves change in thermal energy and for an incompressible substance Heat transfer is from the conductor (negative ) Generation may be viewed as electrical work done on the system (negative )

Example 1.4 Example 1.4: Application to isothermal solid-liquid phase change in a container: Latent Heat of Fusion

Open System Steady State for Flow through an Open System without Phase Change or Generation: At an Instant of Time: (1.11e)

Surface Energy Balance THE SURFACE ENERGY BALANCE A special case for which no volume or mass is encompassed by the control surface. Conservation Energy (Instant in Time): (1.12) Applies for steady-state and transient conditions With no mass and volume, energy storage and generation are not pertinent to the energy balance, even if they occur in the medium bounded by the surface. Consider surface of wall with heat transfer by conduction, convection and radiation.

METHODOLOGY OF FIRST LAW ANALYSIS On a schematic of the system, represent the control surface by dashed line(s). Choose the appropriate time basis. Identify relevant energy transport, generation and/or storage terms by labeled arrows on the schematic. Write the governing form of the Conservation of Energy requirement. Substitute appropriate expressions for terms of the energy equation. Solve for the unknown quantity.

Problem: Silicon Wafer Problem 1.43: Thermal processing of silicon wafers in a two-zone furnace. Determine (a) the initial rate of change of the wafer temperature and (b) the steady-state temperature. SCHEMATIC

Problem: Silicon Wafer (cont.) or, per unit surface area

Problem: Silicon Wafer (cont.)

Problem Cooling of Spherical Canister Problem 1.48: Cooling of spherical canister used to store reacting chemicals. Determine (a) the initial rate of change of the canister temperature, (b) the steady-state temperature, and (c) the effect of convection on the steady-state temperature.

Problem Cooling of Spherical Canister SCHEMATIC:

Problem Cooling of Spherical Canister

Problem Cooling of Spherical Canister