Heat Transfer: Physical Origins and Rate Equations Chapter One Sections 1.1 and 1.
Heat Transfer and Thermal Energy What is heat transfer? Heat transfer is thermal energy in transit due to a temperature difference. What is thermal energy? Thermal energy is associated with the translation, rotation, vibration and electronic states of the atoms and molecules that comprise matter. It represents the cumulative effect of microscopic activities and is directly linked to the temperature of matter.
Heat Transfer and Thermal Energy (cont.) DO NOT confuse or interchange the meanings of Thermal Energy, Temperature and Heat Transfer Quantity Meaning Symbol Units Thermal Energy + Energy associated with microscopic behavior of matter U or u J or J/kg Temperature A means of indirectly assessing the amount of thermal energy stored in matter T K or C Heat Transfer Thermal energy transport due to temperature gradients Heat Amount of thermal energy transferred over a time interval t 0 Q J Heat Rate Thermal energy transfer per unit time q W Heat Flux Thermal energy transfer per unit time and surface area q W/m + U u Thermal energy of system Thermal energy per unit mass of system
Modes of Heat Transfer Modes of Heat Transfer Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to the random motion of its constituent atoms, molecules and /or electrons. Convection: Heat transfer due to the combined influence of bulk and random motion for fluid flow over a surface. Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported as electromagnetic waves (or photons). Conduction and convection require the presence of temperature variations in a material medium. Although radiation originates from matter, its transport does not require a material medium and occurs most efficiently in a vacuum.
Heat Transfer Rates: Conduction Conduction: Heat Transfer Rates General (vector) form of Fourier s Law: Heat flux W/m q = k T Thermal conductivity W/m K Temperature gradient C/m or K/m Application to one-dimensional, steady conduction across a plane wall of constant thermal conductivity: dt T T1 q x = k = k dx L T1 T q x = k (1.) L Heat rate (W): qx = q x A
Heat Transfer Rates: Convection Convection Heat Transfer Rates Relation of convection to flow over a surface and development of velocity and thermal boundary layers: Newton s law of cooling: ( ) = (1.3a) q h Ts T h : Convection heat transfer coeffici (W/m ent K)
Heat Transfer Rates: Radiation Radiation Heat Transfer Rates Heat transfer at a gas/surface interface involves radiation emission from the surface and may also involve the absorption of radiation incident from the surroundings G if T. (irradiation, ), as well as convection ( ) s T Energy outflow due to emission: 4 E = Eb = Ts (1.5) E : Emissive power ( W/m ) : Surface emissivity ( 0 1) : Emissive power of a blackbody (the perfect emitter) E b -8 4 ( ) : Stefan-Boltzmann constant 5.67 10 W/m K Energy absorption due to irradiation: Gabs = G G : Absorbed incid radiation abs ent (W/m ) : Surface absorptivity ( 0 1) G : Irradiation W/m ( ) (1.6)
Heat Transfer Rates: Radiation (cont.) Heat Transfer Rates Irradiation: Special case of surface exposed to large surroundings of uniform temperature, T sur G = G = T sur 4 sur If =, the net radiation heat flux from the surface due to exchange with the surroundings is: 4 4 ( ) ( sur ) rad = b s = s (1.7) q E T G T T
Heat Transfer Rates: Radiation (cont.) Heat Transfer Rates Alternatively, rad r r ( ) q = h T T s sur ( sur )( sur ) r s s ( K) h : Radiation heat transfer coefficient W/m h = T + T T + T (1.8) (1.9) For combined convection and radiation, ( ) ( ) q = q + q = h T T + h T T (1.10) conv rad s r s sur
Process Identification Problem 1.87(a): Process identification for single-and double-pane windows Schematic: q conv,1 q rad,1 q cond,1 q conv,s q rad,s q cond, q conv, q rad, q s Convection from room air to inner surface of first pane Net radiation exchange between room walls and inner surface of first pane Conduction through first pane Convection across airspace between panes Net radiation exchange between outer surface of first pane and inner surface of second pane (across airspace) Conduction through a second pane Convection from outer surface of single (or second) pane to ambient air Net radiation exchange between outer surface of single (or second) pane and surroundings such as the ground Incident solar radiation during day; fraction transmitted to room is smaller for double pane
Problem: Electronic Cooling Problem 1.40: Power dissipation from chips operating at a surface temperature of 85 C and in an enclosure whose walls and air are at 5 C for (a) free convection and (b) forced convection. Schematic: Assumptions: (1) Steady-state conditions, () Radiation exchange between a small surface and a large enclosure, (3) Negligible heat transfer from sides of chip or from back of chip by conduction through the substrate. Analysis: Pelec = qconv + qrad A= L = ( ) = (a) If heat transfer is by natural convection, 5/4 5/4-4 5/4 q = CA T T = 4.W/m K.5 10 m 60K = 0.158W q P conv rad elec ( ) ( )( ) s ( ) ( ) = -4-8 4 4 4 4 0.60.5 10 m 5.67 10 W/m K 358 98 K = 0.065W = 0.158W + 0.065W = 0.3W (b) If heat transfer is by forced convection, conv elec 4-4 ( ) ( )( ) q = ha T T = 50W/m K.5 10 m 60K = 3.375W P 0.015m.5 10 m -4 s = 3.375W + 0.065W = 3.44W 4 4 ( s ) ( s sur ) = ha T T + A T T