Thermal Systems • Introduction to Heat Transfer – What and How? – Physical Mechanisms and Rate Equations – Conservation of Energy Requirement • Control Volume • Surface Energy Balance • Thermal Resistance • Thermal Capacitance • Thermal Sources: Temperature and Heat Flow Mechatronics K. Craig Thermal Systems 1 Introduction to Heat Transfer • Energy can be transferred by interactions of a system with its surroundings: – Heat – Work • Thermodynamics deals with equilibrium end states of the process during which an interaction occurs. It provides no information concerning the nature of the interaction or the time rate at which it occurs. • Heat Transfer is inherently a non-equilibrium process and we study the modes of heat transfer and heat transfer rates. Mechatronics K. Craig Thermal Systems 2 • What is heat transfer? – Heat transfer (or heat) is energy in transit due to a temperature difference. – Whenever there exists a temperature difference in a medium or between media, heat transfer must occur. – Different types of heat transfer processes are called modes: • Conduction: When a temperature gradient exists in a stationary medium (solid or fluid), heat transfer occurs across the medium. • Convection: Heat transfer occurs between a surface and a moving fluid when they are at different temperatures. • Radiation: All surfaces of finite temperature emit energy in the form of electromagnetic waves. In the absence of an intervening medium, there is heat transfer by radiation between two surfaces at different temperatures. Mechatronics K. Craig Thermal Systems 3 Heat Transfer Modes: Conduction, Convection, and Radiation Mechatronics K. Craig Thermal Systems 4 • Physical Mechanisms and Rate Equations – Conduction • Processes at the atomic and molecular level sustain this mode of heat transfer. • Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interaction between the particles. • Consider a gas with no bulk motion in which there exists a temperature gradient. We associate the temperature at any point with the energy of the gas molecules in the vicinity of the point: random translational motion as well as internal rotational and vibrational motions of the molecules. Higher temperatures are associated with higher molecular energies. When particles collide, a transfer of energy from the more energetic to the less energetic particles must occur. When a temperature gradient is present, energy transfer by conduction must occur in the direction of decreasing temperature. Mechatronics K. Craig Thermal Systems 5 Association of Conduction Heat Transfer with Diffusion of Energy due to Molecular Activity Mechatronics K. Craig Thermal Systems 6 • The situation is much the same in liquids, although in liquids molecules are more closely spaced and the molecular interactions are stronger and more frequent. • In a solid, conduction may be attributed to atomic activity in the form of lattice vibrations (exclusively for a non-conductor), as well as translational motion of free electrons when the material is a conductor. – Conduction Rate Equation • For heat conduction, the rate equation is known as Fourier’s Law. • For a one-dimensional plane wall having a temperature distribution T(x), the rate equation is: dT qk¢¢ =- Heat flux is the heat transfer rate in x dx the x direction per unit area q¢¢ = heat flux (W/m)2 perpendicular to the direction of x transfer k=× thermal conductivity (W/mK) Mechatronics K. Craig Thermal Systems 7 – Convection • Convection heat transfer mode is comprised of two mechanisms: – Energy transfer due to random molecular motion (diffusion) – Energy transferred by the bulk (macroscopic) motion of the fluid. Large numbers of molecules moving collectively in the presence of a temperature gradient gives rise to heat transfer. • Total heat transfer is due to a superposition of energy transport by the random motion of molecules and by the bulk motion of the fluid. The term convection is used to refer to this cumulative transport, while the term advection is used to refer to transport due to bulk fluid motion. • We are especially interested in convection heat transfer between a fluid in motion and a bounding surface when the two are at different temperatures. Mechatronics K. Craig Thermal Systems 8 Boundary Layer Development in Convection Heat Transfer Mechatronics K. Craig Thermal Systems 9 • Hydrodynamic, or velocity, boundary layer: region in the fluid through which the velocity varies from zero at the surface to a finite value u¥ associated with the flow. • If the surface and flow temperatures differ, there will be a region of the fluid through which the temperature varies from Ts at the surface to T¥ in the outer flow. This region is called the thermal boundary layer and it may be smaller, larger, or the same size as that through which the velocity varies. • The contribution to heat transfer due to random molecular motion (diffusion) generally dominates near the surface where the fluid velocity is low. • The contribution to heat transfer due to bulk fluid motion originates from the fact that boundary layers grow as the flow progresses in the x direction. • Nature of the Flow: – Forced Convection: flow is caused by some external means, e.g., fan, pump, wind. Mechatronics K. Craig Thermal Systems 10 – Free Convection: flow is induced by buoyancy forces in the fluid, which arise from density variations caused by temperature variations in the fluid. • Convection heat transfer is then energy transfer occurring within a fluid due to the combined effects of conduction and bulk fluid motion. In general, the energy that is being transferred is the internal thermal energy of the fluid. • However, there are convection processes for which there is, in addition, latent heat exchange. This latent heat exchange is generally associated with a phase change between the liquid and vapor states of the fluid, e.g., boiling and condensation. – Convection Rate Equation • Regardless of the particular nature of the convection heat transfer mode, the rate equation is of the form: q¢¢ =-h(TT) s ¥ Newton’s Law of Cooling 2 q¢¢x = convective heat flux (W/m) h=× convection heat transfer, or film, coefficient (W/m2 K) Mechatronics K. Craig Thermal Systems 11 • The film coefficient, h, encompasses all the effects that influence the convection mode, e.g., boundary layer conditions, surface geometry, nature of fluid motion, fluid thermodynamic and transport properties. • Range of Values for h (W/m2K): – Free Convection: 5 – 25 – Forced Convection: 25 – 250 (Gases), 50 – 20,000 (Liquids) – Convection with Phase Change (boiling or condensation): 2500 – 100,000 – Radiation • Thermal radiation is energy emitted by matter (solid, fluid, or gas) that is at a finite temperature, attributable to changes in the electron configurations of the constituent atoms or molecules. • The energy of the radiation field is transported by electromagnetic waves and does not require the presence of a material medium, in fact, it occurs most efficiently in a vacuum. Mechatronics K. Craig Thermal Systems 12 – Radiation Rate Equation • The maximum flux (W/m2) at which radiation may be emitted from a surface is given by the Stefan-Boltzmann Law: 4 qT¢¢ =s s Ts = absolute surface temperature (K) s=× Stefan-Boltzmann Constant = 5.67E-8 (W/m24K) • Such a surface is called an ideal radiator. The heat flux emitted by a real surface is less than that of the ideal radiator and is given by: 4 qT¢¢ =es s e= emissivity (radiative property of the surface) • Determination of the net rate at which radiation is exchanged between surfaces is quite complicated. Mechatronics K. Craig Thermal Systems 13 • Special Case: net exchange between a small surface and a much larger surface that completely surrounds the smaller one. The surface and surroundings are separated by a gas that has no effect on the radiation transfer. The net rate of radiation heat exchange between the surface and its surroundings is: q 4422 q¢¢ ==es(Ts-Tsurr) =es(Ts+Tsurr)(Ts+Tsurrs)(T-Tsurr) =-hr(TTssurr ) A • Note that the area and emissivity of the surroundings do not influence the net heat exchange rate in this case. Radiation Exchange between a Surface and its Surroundings Mechatronics K. Craig Thermal Systems 14 • Conservation of Energy Requirement – In the application of the conservation laws, we first need to identify the control volume, a fixed region of space bounded by a control surface through which energy and matter pass. – Energy Conservation Law: • The rate at which thermal and mechanical energy enters a control volume through the control surface minus the rate at which this energy leaves the control volume through the control surface (surface phenomena) plus the rate at which energy is generated in the control volume due to conversion from other energy forms, e.g., chemical, electrical, electromagnetic, or nuclear, (volumetric phenomena) must equal the rate at which this energy is stored in the control volume. E&ing+E&-=EE&&outst Mechatronics K. Craig Thermal Systems 15 • The inflow and outflow rate terms usually involve energy flow due to heat transfer by the conduction, convection, and/or radiation modes. In a situation involving fluid flow across the control surface, these terms also include energy transported by the fluid into and out of the control volume in the form of potential, kinetic, and thermal energy. – Example Problem • A long conducting rod of diameter D and electrical resistance ¢ per unit length R e is initially in thermal equilibrium with the ambient air and its surroundings. This equilibrium is disturbed when an electrical current I is passed through the rod. Develop an equation that could be used to compute the variation of the rod temperature with time during passage of the current. Mechatronics K. Craig Thermal Systems 16 – Surface Energy Balance • We frequently apply the conservation of energy requirement at the surface of a medium. In this case, the control surface includes no mass or volume. The generation and storage terms of the conservation expression are no longer relevant.