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This chapter delves into the Conservation of Energy, also known as the First Law of Thermodynamics. It discusses various formulations related to heat transfer, including instantaneous and time-interval analyses of control volumes and surfaces. The chapter presents specific applications, such as transient processes in closed systems and surface energy balances. Special cases involving isothermal phase changes and steady-state analysis of open systems are explored. Additionally, problem-solving methodologies for practical applications, including thermal processing of silicon wafers and cooling spherical canisters, are featured.
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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 thebasis for determiningthetemperature • of a system. • Alternative Formulations Time Basis: At an instant or Over a time interval Type of System: Control volume Control surface
(1.11a) Volumetric Phenomena CV at an Instant and over a Time Interval APPLICATION TO ACONTROL VOLUME Note representation of system by a control surface (dashed line)at the boundaries. • At anInstant of Time: Surface Phenomena Conservation of Energy Each term has units of J/s or W. • Over aTime Interval (1.11b) Each term has units of J.
Special Cases (Linkages to Thermodynamics) • Transient Process for aClosed System of Mass (M) Assuming Heat Transfer • to the System (Inflow) and Work Done by the System (Outflow). Over atime interval (1.11c) At aninstant (1.11d) Closed System
Heat transfer is from the conductor (negative ) • Generation may be viewed aselectrical work done on the system (negative ) Example 1.3 Example 1.3: Application to thermal response of a conductor with Ohmic heating (generation): • Involves change inthermal energy and for an incompressible substance
Example 1.4 Example 1.4: Application to isothermal solid-liquid phase change in a container: Latent Heat of Fusion
At anInstant of Time: • Steady Statefor Flow through anOpen System without Phase Change or Generation: (1.11e) Open System
(1.12) Conservation Energy(Instant in Time): Surface Energy Balance THE SURFACE ENERGY BALANCE A special case for which no volume or mass is encompassed by the control surface. • 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 METHODOLOGY OF FIRST LAW ANALYSIS • On aschematicof the system, represent thecontrol surfaceby • dashed line(s). • Choose the appropriatetime basis. • Identify relevant energytransport, generation and/or storageterms • bylabeled arrowson 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 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:
