COMPACT HEAT EXCHANGERS
CONTENTS INTRODUCTION HUMANS AND ENERGY THERMODYNAMICS ENERGY, HEAT, AND WORK THE FIRST LAW OF THERMODYNAMICS HEAT ENGINES, REFRIGERATORS, AND HEAT PUMPS THE SECOND LAW OF THERMODYNAMICS CARNOT CYCLE HEAT TRANSFER CONDUCTION CONVECTION PARALLEL FLOW ON AN ISOTHERMAL PLATE A CYLINDER IN CROSS FLOW FLOW IN DUCTS FREE CONVECTION RADIATION THERMAL RADIATION VIEW FACTOR RADIATION EXCHANGE BETWEEN DIFFUSE-GRAY SURFACES REFERENCES HEAT SINKS LONGITUDINAL FIN OF RECTANGULAR PRO?LE HEAT TRANSFER FROM FIN FIN EFFECTIVENESS FIN EF?CIENCY CORRECTED PRO?LE LENGTH OPTIMIZATIONS CONSTANT PRO?LE AREA AP CONSTANT HEAT TRANSFER FROM A FIN CONSTANT FIN VOLUME OR MASS MULTIPLE FIN ARRAY I FREE (NATURAL) CONVECTION COOLING SMALL SPACING CHANNEL LARGE SPACING CHANNEL OPTIMUM FIN SPACING FORCED CONVECTION COOLING MULTIPLE FIN ARRAY II NATURAL (FREE) CONVECTION COOLING THERMAL RESISTANCE AND OVERALL SURFACE EF?CIENCY FIN DESIGN WITH THERMAL RADIATION SINGLE LONGITUDINAL FIN WITH RADIATION PROBLEMS THERMOELECTRICS THERMOELECTRIC EFFECT SEEBECK EFFECT PELTIER EFFECT THOMSON EFFECT THOMSON (OR KELVIN) RELATIONSHIPS THERMOELEMENT COUPLE (THERMOCOUPLE) THE FIGURE OF MERIT SIMILAR AND DISSIMILAR MATERIALS SIMILAR MATERIALS DISSIMILAR MATERIALS THERMOELECTRIC GENERATOR (TEG) CONVERSION EF?CIENCY AND CURRENT MAXIMUM CONVERSION EF?CIENCY MAXIMUM POWER EF?CIENCY MAXIMUM PERFORMANCE PARAMETERS MULTICOUPLE MODULES THERMOELECTRIC COOLERS (TEC) THE COEF?CIENT OF PERFORMANCE OPTIMUM CURRENT FOR THE MAXIMUM COOLING RATE OPTIMUM CURRENT FOR THE MAXIMUM COP GENERALIZED CHARTS OPTIMUM GEOMETRY FOR THE MAXIMUM COOLING IN SIMILAR MATERIALS THERMOELECTRIC MODULES COMMERCIAL TEC MULTISTAGE MODULES COMMERCIAL MULTISTAGE PELTIER MODULES DESIGN OPTIONS APPLICATIONS THERMOELECTRIC GENERATORS THERMOELECTRIC COOLERS DESIGN EXAMPLE DESIGN CONCEPT DESIGN OF INTERNAL AND EXTERNAL HEAT SINKS DESIGN OF THERMOELECTRIC COOLER (TEC) FINDING THE EXACT SOLUTION FOR TC AND TH PERFORMANCE CURVES FOR THERMOELECTRIC AIR COOLER THERMOELECTRIC MODULE DESIGN THERMAL AND ELECTRICAL CONTACT RESISTANCES FOR TEG THERMAL AND ELECTRICAL CONTACT RESISTANCES FOR TEC DESIGN EXAMPLE OF TEC MODULE SUMMARY OF DESIGN OF A TEC MODULE HEAT PIPES OPERATION OF HEAT PIPE SURFACE TENSION HEAT TRANSFER LIMITATIONS CAPILLARY LIMITATION MAXIMUM CAPILLARY PRESSURE DIFFERENCE VAPOR PRESSURE DROP LIQUID PRESSURE DROP NORMAL HYDROSTATIC PRESSURE DROP AXIAL HYDROSTATIC PRESSURE DROP APPROXIMATION FOR CAPILLARY PRESSURE DIFFERENCE SONIC LIMITATION ENTRAINMENT LIMITATION BOILING LIMITATION VISCOUS LIMITATION HEAT PIPE THERMAL RESISTANCE CONTACT RESISTANCE VARIABLE CONDUCTANCE HEAT PIPES (VCHP) GAS-LOADED HEAT PIPES CLAYEPYRON-CLAUSIUS EQUATION LOOP HEAT PIPES MICRO HEAT PIPES STEADY-STATE MODELS CONVENTIONAL MODEL COTTER’S MODEL WORKING FLUID FIGURE OF MERIT COMPATIBILITY WICK STRUCTURES SELECTION OF MATERIAL AND WORKING FLUID WORKING FLUID PROPERTIES ESTIMATION OF VAPOR SPACE RADIUS ESTIMATION OF OPERATING LIMITS CAPILLARY LIMITS SONIC LIMITS ENTRAINMENT LIMITS BOILING LIMITS WALL THICKNESS WICK SELECTION MAXIMUM ARTERIAL DEPTH DESIGN OF ARTERIAL WICK LIQUID PRESSURE DROP IN THE ARTERIES LIQUID PRESSURE DROP IN THE CIRCUMFERENTIAL WICK VAPOR PRESSURE DROP IN THE VAPOR SPACE 4 10 10 PERFORMANCE MAP 4 10 11 CHECK THE TEMPERATURE DROP COMPACT HEAT EXCHANGERS FUNDAMENTALS OF HEAT EXCHANGERS COUNTER?OW AND PARALLEL FLOWS OVERALL HEAT TRANSFER COEF?CIENT LOG MEAN TEMPERATURE DIFFERENCE (LMTD) FLOW PROPERTIES NUSSELT NUMBERS EFFECTIVENESS–NTU (?-NTU) METHOD PARALLEL FLOW COUNTER?OW CROSS?OW HEAT EXCHANGER PRESSURE DROP FOULING RESISTANCES (FOULING FACTORS) OVERALL SURFACE (FIN) EF?CIENCY REASONABLE VELOCITIES OF VARIOUS FLUIDS IN PIPE FLOW DOUBLE-PIPE HEAT EXCHANGERS SHELL-AND-TUBE HEAT EXCHANGERS BAF?ES MULTIPLE PASSES DIMENSIONS OF SHELL-AND-TUBE HEAT EXCHANGER SHELL-SIDE TUBE LAYOUT PLATE HEAT EXCHANGERS (PHE) FLOW PASS ARRANGEMENTS GEOMETRIC PROPERTIES FRICTION FACTOR NUSSELT NUMBER PRESSURE DROPS PRESSURE DROPS IN COMPACT HEAT EXCHANGERS FUNDAMENTALS OF CORE PRESSURE DROP CORE ENTRANCE AND EXIT PRESSURE DROPS CONTRACTION AND EXPANSION LOSS COEF?CIENTS CIRCULAR-TUBE CORE SQUARE-TUBE CORE FLAT-TUBE CORE TRIANGULAR-TUBE CORE FINNED-TUBE HEAT EXCHANGERS GEOMETRICAL CHARACTERISTICS THERMAL PROPERTIES CORRELATIONS FOR CIRCULAR FINNED-TUBE GEOMETRY PRESSURE DROP CORRELATIONS FOR LOUVERED PLATE-FIN FLAT-TUBE GEOMETRY PLATE-FIN HEAT EXCHANGERS GEOMETRIC CHARACTERISTICS CORRELATIONS FOR OFFSET STRIP FIN (OSF) GEOMETRY LOUVER-FIN-TYPE FLAT-TUBE PLATE-FIN HEAT EXCHANGERS CORRELATIONS FOR LOUVER FIN GEOMETRY SOLAR CELLS OPERATION OF SOLAR CELLS SOLAR CELLS AND TECHNOLOGY SOLAR IRRADIANCE AIR MASS NATURE OF LIGHT QUANTUM MECHANICS ATOMIC STRUCTURE BOHR’S MODEL LINE SPECTRA DE BROGLIE WAVE HEISENBERG UNCERTAINTY PRINCIPLE SCHR¨ODINGER EQUATION A PARTICLE IN A 1-D BOX QUANTUM NUMBERS ELECTRON CON?GURATIONS VAN DER WAALS FORCES COVALENT BONDING ENERGY BAND PSEUDO-POTENTIAL WELL DENSITY OF STATES NUMBER OF STATES EFFECTIVE MASS EQUILIBRIUM INTRINSIC CARRIER CONCENTRATION FERMI FUNCTION NONDEGENERATE SEMICONDUCTOR EQUILIBRIUM ELECTRON AND HOLE CONCENTRATIONS INTRINSIC SEMICONDUCTORS INTRINSIC CARRIER CONCENTRATION, NI INTRINSIC FERMI ENERGY EXTRINSIC SEMICONDUCTORS IN THERMAL EQUILIBRIUM DOPING, DONORS, AND ACCEPTORS EXTRINSIC CARRIER CONCENTRATION IN EQUILIBRIUM BUILT-IN VOLTAGE PRINCIPLE OF DETAILED BALANCE MAJORITY AND MINORITY CARRIERS IN EQUILIBRIUM GENERATION AND RECOMBINATION DIRECT AND INDIRECT BAND GAP SEMICONDUCTORS ABSORPTION COEF?CIENT PHOTOGENERATION RECOMBINATION RECOMBINATION MECHANISMS BAND ENERGY DIAGRAM UNDER NONEQUILIBRIUM CONDITIONS BACK SURFACE FIELD (BSF) LOW-LEVEL INJECTION BAND-TO-BAND RECOMBINATION TRAP-ASSISTED (SRH) RECOMBINATION SIMPLI?ED EXPRESSION OF THE SRH RECOMBINATION RATE AUGER RECOMBINATION TOTAL RECOMBINATION RATE CARRIER TRANSPORT DRIFT CARRIER MOBILITY DIFFUSION TOTAL CURRENT DENSITIES EINSTEIN RELATIONSHIP SEMICONDUCTOR EQUATIONS MINORITY-CARRIER DIFFUSION EQUATIONS P–N JUNCTION CALCULATION OF DEPLETION WIDTH ENERGY BAND DIAGRAM WITH A REFERENCE POINT QUASI-FERMI ENERGY LEVELS MINORITY CARRIER TRANSPORT BOUNDARY CONDITIONS MINORITY CARRIER LIFETIMES MINORITY CARRIER DIFFUSION LENGTHS MINORITY CARRIER DIFFUSION EQUATION FOR HOLES MINORITY CARRIER DIFFUSION EQUATION FOR ELECTRONS CHARACTERISTICS OF SOLAR CELLS CURRENT DENSITY CURRENT-VOLTAGE CHARACTERISTICS FIGURES OF MERIT EFFECT OF MINORITY ELECTRON LIFETIME ON EF?CIENCY EFFECT OF MINORITY HOLE LIFETIME ON EF?CIENCY EFFECT OF BACK SURFACE RECOMBINATION VELOCITY ON EF?CIENCY EFFECT OF BASE WIDTH ON EF?CIENCY EFFECT OF EMITTER WIDTH WN ON EF?CIENCY EFFECT OF ACCEPTOR CONCENTRATION ON EF?CIENCY 6 10 10 EFFECT OF DONOR CONCENTRATION ON EF?CIENCY 6 10 11 BAND GAP ENERGY WITH TEMPERATURE 6 10 12 EFFECT OF TEMPERATURE ON EF?CIENCY ADDITIONAL TOPICS PARASITIC RESISTANCE EFFECTS (OHMIC LOSSES) QUANTUM EF?CIENCY IDEAL SOLAR CELL EF?CIENCY MODELING MODELING FOR A SILICON SOLAR CELL COMPARISON OF THE SOLAR CELL MODEL WITH A COMMERCIAL PRODUCT DESIGN OF A SOLAR CELL SOLAR CELL GEOMETRY WITH SURFACE RECOMBINATION VELOCITIES DONOR AND ACCEPTOR CONCENTRATIONS MINORITY CARRIER DIFFUSION LIFETIMES GRID SPACING ANTI-RE?ECTION, LIGHT TRAPPING AND PASSIVATION HUMANS AND ENERGY AT THE EARLY STONE AGE (ABOUT 2 MILLIONS YEAR AGO), OUR ANCESTORS WANDERED FROM ONE PLACE TO ANOTHER TO ?ND FOOD AND SHELTER ONE OF THE DISCOVERIES BY HUMANKIND WAS ?RE, WHICH GAVE WARMTH AND LIGHT TO THEIR SHELTERS AND PROTECTED THEM FROM DANGEROUS ANIMALS THIS ?RE WOULD BE THE ?RST USE OF ENERGY BY HUMANKIND AND ALSO A TURNING POINT IN EARLY HUMAN LIFE, PROBABLY COMPARABLE TO THE DISCOVERY OF ELECTRICITY IN THE NINETEENTH CENTURY ABOUT 5,000 YEARS AGO, PEOPLE BEGAN USING THE WIND TO SAIL FROM ONE PLACE TO ANOTHER IT WAS ONLY 2,500 YEAR AGO THAT PEOPLE BEGAN USING WINDMILLS AND WATERWHEELS TO GRIND GRAIN ABOUT 2,300 YEARS AGO, THE ANCIENT GREEK MATHEMATICIAN ARCHIMEDES SUPPOSEDLY BURNED THE SHIPS OF ATTACKING SYRACUSE BY USING MIRRORS TO CONCENTRATE THE SUN’S RAYS ON THEIR SAILS THIS WOULD HAVE BEEN THE ?RST RECORDED USE OF FOCUSED SOLAR ENERGY IN HISTORY MORE RECENTLY, WE LEARNED TO USE RESOURCES SUCH AS FOSSIL FUELS (COALS, OIL, AND NATURAL GAS), RENEWABLE ENERGY (SUNLIGHT, WIND, BIOFUEL, CONTROL VOLUMES AND SIGN CONVENTION FOR (A) CLOSED SYSTEM AND (B) OPEN SYSTEM DURING A PROCESS; IT CAN ONLY CHANGE FORMS THE SIGN CONVENTION IS ILLUSTRATED IN FIGURE 1 1(A) Q > HEAT TRANSFERRED TO SYSTEM (1 1A) Q < HEAT TRANSFERRED FROM SYSTEM (1 1B) W > WORK DONE ON SYSTEM (1 1C) W < WORK DONE BY SYSTEM (1 1D) THE ?RST LAW OF THERMODYNAMICS FOR A CLOSED SYSTEM IN FIGURE 1 1(A) IS GIVEN BY E = Q + W (1 2) WHERE E IS THE TOTAL ENERGY CHANGE IN THE SYSTEM, Q THE HEAT TRANSFERRED, AND W THE WORK DONE CAUTION IS GIVEN TO THE SIGN OF WORK IN EQUATIONS (1 1C) AND (1 1D); SOME BOOKS DE?NE WORK AS POSITIVE WHEN IT IS DONE BY THE SYSTEM THE REASON IS THAT MANY ENGINEERING APPLICATIONS FOCUS ON THE WORK DONE BY A PARTICULAR HEAT ENGINE, AND SO IT IS HELPFUL TO DE?NE THAT AS POSITIVE IN THAT CASE, EQUATION (1 2) BECOMES THAT E = Q ?W TOTAL ENERGY, E, IS THE EXTENSIVE PROPERTY AND PRESENTS ALL THE ENERGY SUCH AS KINETIC, POTENTIAL, THERMAL, LATENT, CHEMICAL, NUCLEAR, AND OTHERS ALL ENERGY EXCEPT KINETIC AND POTENTIAL ENERGY IS CALLED INTERNAL ENERGY, U THE KINETIC ENERGY, KE, IS ASSOCIATED WITH THE MOTION OF THE SYSTEM AS A WHOLE THE POTENTIAL ENERGY, PE, IS ASSOCIATED WITH THE POSITION OF THE SYSTEM AS A WHOLE IN THE CASE OF A STATIONARY SYSTEM, E = U THE POTENTIAL ENERGY MAY BE PRESENT IN A VARIETY OF ?ELDS (GRAVITY, ELECTRIC, OR MAGNETIC) THE TOTAL ENERGY IS EXPRESSED AS E = U + KE + PE (1 3) THE INTERNAL ENERGY IS U = THERMAL + LATENT + CHEMICAL + NUCLEAR + OTHERS (1 4) 2 + GZ (1 7) THIS IS EQUIVALENT TO THE ENERGY BALANCE IN HEAT TRANSFER, WHICH IS EXPRESSED AS ?EST = ?EIN ??EOUT + ?EG (1 7A) WHERE ?EST IS THE ENERGY STORED AND EQUAL TO ?ECV ?EIN IS THE ENERGY ENTERING INTO THE CONTROL VOLUME, ?EOUT THE ENERGY EXITING FROM THE CONTROL VOLUME AND ?EG THE HEAT GENERATION (ELECTRICITY OR NUCLEAR REACTION) THIS EQUATION IS PARTICULARLY USEFUL IN HEAT TRANSFER CALCULATIONS MASS MUST BE CONSERVED HENCE, THE CONSERVATION OF MASS IS EXPRESSED AS DMCV DT = IN ?M ? OUT ?M (1 8) IN THE CASE OF A STEADY ?OW FROM EQUATIONS (1 7) AND (1 8), WE NOTE THAT DECV DT = AND DMCV DT = HEAT ENGINES, REFRIGERATORS, AND HEAT PUMPS DEVICES THAT CAN CONTAIN THE ENERGY OF HEAT AND MAKE IT DO WORK ARE CALLED HEAT ENGINES STEAM AND GAS TURBINE, DIESEL ENGINE, GASOLINE ENGINE, AND OCEAN THERMAL INTRODUCTION ENERGY CONVERSION (OTEC) ARE EXAMPLES OF HEAT ENGINES MOST OF OUR ENERGY COMES FROM THE BURNING OF FOSSIL FUELS AND FROM NUCLEAR REACTIONS: BOTH OF THESE SUPPLY ENERGY AS HEAT HOWEVER, WE NEED MECHANICAL ENERGY TO OPERATE MACHINES OR PROPEL VEHICLES EXERGY TRANSFORMATION FROM A LOW EXERGY (HEAT) TO A HIGH EXERGY (MECHANICAL ENERGY OR ELECTRICITY) IS ALWAYS ACHIEVED IN THE EXPENSE OF THE LOW THERMAL EF?CIENCY OR VICE VERSA FUEL CELLS ARE A GOOD EXAMPLE THAT THE CHEMICAL ENERGY OF A FUEL IS DIRECTLY CONVERTED TO ELECTRICITY WITHOUT THE PROCESS TO HEAT THIS IS A REASON WHY FUEL CELLS HAVE A HIGHER EF?CIENCY THAN CONVENTIONAL COMBUSTION ENGINES A HEAT ENGINE CAN PRODUCE MECHANICAL WORK BETWEEN A HIGH TEMPERATURE SOURCE AND A LOW TEMPERATURE SINK, AS SHOWN IN FIGURE 1 3 IF WE APPLY THE ?RST LAW OF THERMODYNAMICS TO THE HEAT ENGINE IN FIGURE 1 3(A), WE COME UP WITH ?WNET = ?QH ??QL (1 10) WHERE ?WNET IS THE NET WORK, ?QH THE HEAT TRANSFERRED TO THE HEAT ENGINE FROM THE HIGH TEMPERATURE SOURCE, AND ?QL THE HEAT TRANSFERRED TO THE LOW TEMPERATURE SINK FROM THE HEAT ENGINE USING EQUATION (1 10), THE THERMAL EF?CIENCY IN THE HEAT ENGINE IS EXPRESSED AS ?TH = OUTPUT INPUT = ?WNET ?QH = ?QH ??QL ?QH = 1 ? ?QL ?QH (1 11) NOTE THAT THE THERMAL EF?CIENCY IS LESS THAN UNITY IF WE APPLY THE ?RST LAW OF THERMODYNAMICS TO THE REFRIGERATOR IN FIGURE 1 3(B), WE HAVE THE SAME RELATIONSHIP WITH EQUATION (1 10) AS ?WNET = ?QH ??QL (1 12) THE EF?CIENCY OF THE REFRIGERATOR IS EXPRESSED IN TERMS OF COEF?CIENT OF PERFORMANCE (COP), DENOTED BY COPR COPR = OUTPUT INPUT = ?QL ?WNET = ?QL ?QH ??QL = NOTICE THAT THE VALUE OF COPR CAN BE GREATER THAN UNITY THAT IS, THE AMOUNT OF HEAT REMOVED FROM THE LOW-TEMPERATURE ENVIRONMENT CAN BE GREATER THAN THE AMOUNT OF WORK INPUT MOST REFRIGERATORS HAVE COPR OF 2 5 ?3 0 A DEVICE THAT TRANSFERS HEAT FROM A LOW TEMPERATURE BODY TO HIGH TEMPERATURE BODY IS CALLED A HEAT PUMP THE HEAT PUMP CYCLE IS IDENTICAL TO A REFRIGERATOR CYCLE IN PRINCIPLE, BUT DIFFERS IN THAT THE PRIMARY PURPOSE OF THE HEAT PUMP IS TO SUPPLY HEAT RATHER THAN TO REMOVE IT FROM AN ENCLOSED SPACE THE MEASURE OF PERFORMANCE IS ALSO EXPRESSED IN TERMS OF COEF?CIENT OF PERFORMANCE COPHP , DE?NED AS COPHP = OUTPUT INPUT = ?QH ?WNET = ?QH ?QH ??QL = CARNOT CYCLE IF THE EF?CIENCY OF ALL HEAT ENGINES IS LESS THAN 100 PERCENT, WHAT IS THE MOST EF?CIENT CYCLE WE CAN HAVE? THE CARNOT CYCLE IS THE MOST EF?CIENT CYCLE A HEAT ENGINE THAT OPERATES IN THE CARNOT CYCLE WAS PROPOSED IN 1824 BY FRENCH ENGINEER SADI CARNOT HEAT ENGINES ARE CYCLIC DEVICES AND THE WORKING ?UID OF A HEAT ENGINE RETURNS TO ITS INITIAL STATE AT THE END OF EACH CYCLE THE CARNOT CYCLE IS IDEAL, SO THE IDEAL GAS IS USED AS A WORKING ?UID AND THE ENTIRE PROCESS IS REVERSIBLE THERE IS NO FRICTION AND NO HEAT TRANSFER EXCEPT THE ISOTHER- MAL PROCESSES (HEAT TRANSFER) THE MOST EF?CIENT HEAT-TRANSFER PROCESS IS KNOWN TO BE AN ISOTHERMAL PROCESS WHERE THE HIGH- OR LOW-SOURCE TEMPERATURE REMAINS CON- STANT DURING THE PROCESS AND THE MOST EF?CIENT PROCESS BETWEEN TWO-TEMPERATURE INTRODUCTION HEAT SOURCE TH HEAT SINK TL PROCESS EXPANSION PROCESS COMPRESSION PROCESS (1 16) THEN WE COME UP WITH THE FACT THAT THE HEAT TRANSFERRED MUST BE EQUAL TO THE WORK DONE BY THE SYSTEM AS QH = ?1W2 = ? PDV = ? (1 17) SIMILARITY FOR PROCESS 3–4, QL = 3W4 = P DV = (1 18) (1 21) SINCE BOTH PROCESS 2–3 AND PROCESS 4–1 ARE REVERSIBLE AND ADIABATIC (ISENTROPIC), WE CAN APPLY THE POLYTROPIC RELATION WITH K = 1 4 TO THE IDEAL GAS IN THE CYLINDER AS P V K = CONSTANT (1 22) THEREFORE, WE HAVE P2V K 2 = P3V K (1 23) P4V K 4 = P1V K (1 24) MULTIPLYING EQUATIONS (1 20), (1 21), (1 23) AND (1 24) AND CANCELING THE FACTOR P1P2P3P4 GIVES V1V K 2 V3V K 4 = V2V K 3 V4V K INTRODUCTION HEAT TRANSFER IS THERMAL ENERGY IN TRANSIT DUE TO A SPATIAL TEMPERATURE DIFFERENCE THE SECOND LAW OF THERMODYNAMICS TELLS US THAT HEAT IS NATURALLY TRANSFERRED FROM A HIGH-TEMPERATURE BODY TO A LOW-TEMPERATURE BODY HEAT TRANSFER HAS THREE MODES OR MECHANISMS: CONDUCTION, CONVECTION, AND RADIATION THERMAL ENERGY INVOLVES MOTIONS SUCH AS THE ROTATION, TRANSLATION, AND VIBRATION OF MOLECULES TEMPERATURE MEASURES THE AVERAGE KINETIC ENERGY OF MOLECULES MOLECULES IN A WARMER OBJECT HAVE GREATER KINETIC ENERGY THAN MOLECULES IN A COOLER OBJECT WHEN A HOT OBJECT COMES IN CONTACT WITH A COLD ONE, THE MOLECULES IN THE HOT OBJECT TRANSFER SOME OF THEIR KINETIC ENERGY DURING COLLISIONS WITH MOLECULES OF THE COLD OBJECT THIS TRANSFER OF KINETIC ENERGY OF MOLECULES IS THE MECHANISM OF CONDUCTION AND CONVECTION HEAT TRANSFER CONDUCTION USUALLY TAKES PLACE IN A SOLID FOR EXAMPLE, WHEN WE TOUCH A METAL SPOON IN A HOT COFFEE, WE FEEL THE HOTNESS THIS IS DUE TO THE CONDUCTION IN THE SPOON CONVECTION OCCURS ON THE SURFACE OF AN OBJECT WITH ?UID IN MOTION AS ANOTHER EXAMPLE, THINK OF BARE SKIN, WHICH USUALLY EXPERIENCES A HEAT LOSS TO THE AMBIENT AIR BY CONVECTION HEAT TRANSFER SUPPOSE THAT THE SURFACE TEMPERATURE OF OUR SKIN IS GREATER THAN THAT OF THE AMBIENT AIR THEN AIR ADJACENT TO THE SKIN GETS WARM, BECOMING LIGHTER IN DENSITY AND RISING TO INDUCE A ?OW NEAR THE SKIN THIS IS THE MECHANISM OF FREE CONVECTION IF OUR SKIN IS EXPOSED TO WIND, THE MECHANISM OF THE HEAT TRANSFER IS CALLED FORCED CONVECTION RADIATION, OR THERMAL RADIATION, IS SOMEWHAT DIFFERENT FROM CONDUCTION AND CONVEC- TION RADIATION IS ENERGY EMITTED BY MATTER THAT IS AT A NONZERO TEMPERATURE IT IS ELECTROMAGNETIC WAVES (OR PHOTONS) EFFECTIVELY PROPAGATING EVEN IN A VACUUM RADIA- TION IS GENERATED WHEN THE MOVEMENT OF CHARGED PARTICLES (MOLECULES AND ATOMS CAN BE EASILY CHARGED OR IONIZED WHEN THEY LOSE ELECTRONS) IS CONVERTED TO ELECTROMAGNETIC WAVES FOR EXAMPLE, WHY DO WE FEEL THE COLDNESS OF OUTSIDE IN WINTER WHEN WE ARE IN A ROOM WHERE THE AIR TEMPERATURE REMAINS CONSTANT THROUGH THE YEAR? BECAUSE THE WALL’S TEMPERATURE IS LOWER IN WINTER DUE TO CONDUCTION OUR BODY INTERACTS NOT ONLY BY CONVECTION WITH THE AIR BUT ALSO BY THE RADIATION EXCHANGE WITH THE WALLS THERE- FORE, WE HAVE MORE HEAT LOSS IN WINTER THAN IN SUMMER AND FEEL COLDER NOTE THAT HEAT TRANSFER ALWAYS HAS A DIRECTION AND A MAGNITUDE LIKE A VECTOR, WHICH IS VERY IMPORTANT IN ENGINEERING CALCULATIONS CONDUCTION OCCURS AS ENERGY IS TRANSPORTED FROM SUBSTANCE TO SUBSTANCE THE FOURIER LAW OF HEAT CONDUCTION CAN BE EXPRESSED AS QX = ?KADT DX (1 30) WHERE QX IS THE HEAT TRANSFER IN X DIRECTION, K THE THERMAL CONDUCTIVITY (W/MK), A THE HEAT TRANSFER AREA (M2), AND DT /DX THE TEMPERATURE GRADIENT THE MINUS SIGN TAKES THE HEAT ?OW POSITIVE WHERE THE TEMPERATURE GRADIENT IS MATHEMATICALLY NEGATIVE WITH RESPECT TO X COORDINATE CONVECTION OCCURS AS THE ENERGY IS TRANSPORTED BY THE MOTION OF ?UID ALTHOUGH THE CONVECTIVE HEAT TRANSFER APPEARS COMPLICATED BECAUSE OF THE COMPLEX MOTION OF THE ?UID, THE RESULTANT BEHAVIOR CAN BE EXPRESSED IN A SIMPLE WAY Q = HA (TS ?T?) (1 31) INTRODUCTION WHERE H IS THE CONVECTION HEAT TRANSFER COEF?CIENT (W/M2K), A THE HEAT TRANSFER AREA (M2), TS THE SURFACE TEMPERATURE, AND T ?THE ?UID TEMPERATURE THIS EQUATION IS KNOWN AS NEWTON’S LAW OF COOLING NOTE THAT THE SIGN CONVENTION IS SUCH THAT THE HEAT TRANSFER IS POSITIVE WHEN THE HEAT ?OWS OUTWARD FROM THE SURFACE TO THE ?UID RADIATION IS ENERGY EMITTED BY MATTER IN THE FORM OF THE ELECTROMAGNETIC WAVES HENCE, RADIATION BETWEEN TWO OBJECTS EXCHANGES THEIR ENERGIES ONE OF THE TYPICAL RADIATION PROBLEMS IS A RELATIVELY SMALL OBJECT IN LARGE SURROUNDINGS IN THIS CASE, THE RADIATION EXCHANGE CAN BE EXPRESSED AS Q = A?? T S ?T = T?,I ?T 1/HIA = T?,I ?T RCONV,I (1 33) WHERE RCONV,I IS THE CONVECTION THERMAL RESISTANCE THAT IS DE?NED AS T /Q THE CON- VECTION RESISTANCE IN THE INNER CONVECTION COMPONENT, RCONV,I, CAN BE EXPRESSED AS RCONV,I = RCONV,I (1 35) THE CONDUCTION RESISTANCE IN THE WALL IS RCOND = L KA (1 36) THE CONVECTION HEAT TRANSFER EXITING FROM THE WALL IS Q = HOA T2 ?T?,O = T2 ?T?,O 1/HOA = T2 ?T?,O RCONV,O (1 37) THE CONVECTION RESISTANCE IN THE OUTER COMPONENT IS RCONV,O = HOA (1 38) SINCE THE SYSTEM IS COMPOSED OF THREE COMPONENTS IN SERIES, THE THERMAL CIRCUIT CAN BE CONSTRUCTED, WHICH IS SHOWN IN FIGURE 1 6(B) THE TOTAL THERMAL RESISTANCE WILL BE THE SUM OF THE THREE COMPONENTS RTOTAL = HIA + L KA + HOA = T Q (1 39) NOW THE HEAT TRANSFER ACROSS THE WALL CAN BE EXPRESSED USING THE TOTAL THERMAL RESIS- TANCE AS, Q = T?,I ?T?,O HOA = T?,I ?T?,O RTOTAL (1 40) NOTE THAT THE CALCULATION OF THE HEAT TRANSFER ACROSS THE WALL DOES NOT REQUIRE THE INNER AND OUTER SURFACE TEMPERATURES OF THE WALL AN OVERALL HEAT TRANSFER COEF?CIENT IS DE?NED IN THE FOLLOWING EQUATION AS Q = UAT = T 1/UA (1 41) INTRODUCTION THE OVERALL HEAT TRANSFER COEF?CIENT U IS EXPRESSED AS U = RTOTALA (1 42) SOMETIMES A UA VALUE THAT IS THE INVERSE OF THE TOTAL THERMAL RESISTANCE USED IN HEAT EXCHANGER DESIGN UA = RTOTAL (1 43) CONSIDER A THICK TUBE, WHERE THE INNER AND OUTER SURFACES EXPERIENCE THE ?OWS SHOWN IN FIGURE 1 7(A), WE ?ND AN EXPRESSION FOR THE HEAT TRANSFER IN A SIMILAR WAY AS THE PLANE WALL Q = T?,I ?T?,O HI (2?RIL) + LN(RO/RI) 2?KL +