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CHE/ME 109 Heat Transfer in Electronics

CHE/ME 109 Heat Transfer in Electronics. LECTURE 20 – SPECIFIC NATURAL CONVECTION MODELS. SPECIFIC NATURAL CONVECTION MODELS. EXTENDED SURFACES THE NUSSELT NUMBER FOR FINNED SYSTEMS IS BASED ON THE SPACING BETWEEN FINS, S, AND THE FIN HEIGHT, L: FOR CONSTANT SURFACE TEMPERATURE.

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CHE/ME 109 Heat Transfer in Electronics

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  1. CHE/ME 109 Heat Transfer in Electronics LECTURE 20 – SPECIFIC NATURAL CONVECTION MODELS

  2. SPECIFIC NATURAL CONVECTION MODELS • EXTENDED SURFACES • THE NUSSELT NUMBER FOR FINNED SYSTEMS IS BASED ON THE SPACING BETWEEN FINS, S, AND THE FIN HEIGHT, L: • FOR CONSTANT SURFACE TEMPERATURE

  3. EXTENDED SURFACES • FOR CONSTANT HEAT FLUX:

  4. VERTICAL FINS • PARAMETERS FOR THESE EQUATIONS: • VERTICAL ISOTHERMAL FINS (EQN 9-31) • TRANSFER FROM BOTH SIDES: C1 = 576, C2 = 2.87 • ONE SIDE ADIABATIC: C1 = 144, C2 = 2.87 • VERTICAL CONSTANT HEAT FLUX FIND (EQN 9-36) • TRANSFER FROM BOTH SIDES: C1 = 48, C2 = =2.51 ONE SIDE ADIABATIC: C1 = 24, C1 = 2.51

  5. TYPICAL INSTALLATIONS • ALTERNATE CONFIGURATIONS FOR COOLING FINS http://www.thermalsoftware.com/vert_vs_horz_sink.pdf

  6. OPTIMUM VERTICAL FIN SPACING • BALANCE BETWEEN FLOW CROSS-SECTION AND SURFACE AREA http://www.thermalsoftware.com/vert_vs_horz_sink.pdf

  7. OPTIMUM VERTICAL FIN SPACING • A FUNCTION OF MATERIALS Avram Bar-Cohen,*, Raj Bahadur, Madhusudan Iyengar, Least-energy optimization of air-cooled heat sinks for sustainability-theory, geometry and material selection, Energy 31 (2006) 579–619

  8. OPTIMUM VERTICAL FIN SPACING • ALSO A FUNCTION OF FIN THICKNESS Avram Bar-Cohen,*, Raj Bahadur, Madhusudan Iyengar, Least-energy optimization of air-cooled heat sinks for sustainability-theory, geometry and material selection, Energy 31 (2006) 579–619

  9. OPTIMUM VERTICAL FIN SPACING • ISOTHERMAL FINS: • OPTIMUM NUSSELT: Nu = 1.307 = hSopt/K • TRANSFER FROM BOTH SIDES (EQN 9-32): Sopt = 2.714(S3L/Ras) 1/4 • CONSTANT HEAT FLUX • TRANSFER FROM BOTH SIDES (EQN 9-37): Sopt = 2.12(S4L/Ra*s)1/5 • PROPERTIES FOR THESE CORRELATIONS ARE ALL BASED ON AN AVERAGE VALUE FOR THE FILM TEMPERATURE

  10. NATURAL CONVECTION INSIDE ENCLOSURES • THERE ARE MANY RESEARCH PROJECTS FOR THIS SYSTEM, SO THEREFORE MANY CORRELATIONS • HEAT FLUX ACROSS AN ENCLOSURE IS TYPICALLY EXPRESSED AS Q = hA(T1 - T2) • h DEPENDS STRONGLY ON THE ASPECT RATIO, H/L • THE Ra NUMBER FOR THIS SYSTEM IS DEFINED IN TERMS OF THE SPACING BETWEEN HEATED PLATES, L:

  11. NATURAL CONVECTION INSIDE ENCLOSURES • FOR LOW RALEIGH NUMBERS, Ra < 1000, DUE TO CLOSE PLATE SPACING: • THERE IS MINIMAL BOUYANCY DRIVEN FLOW • .THIS BECOMES A CONDUCTION SYSTEM

  12. HORIZONTAL RECTANGULAR ENCLOSURES • INSULATED ON THE ENDS • THERE IS NO TRANSFER WHEN THE TOP TEMPERATURE IS GREATER THAN THE BOTTOM • THERE IS SIGNIFICANT TRANSFER WHEN THE BOTTOM TEMPERATURE IS GREATER THAN THE TOP AND Ra > 1700 • FOR THIS CONDITION, THERE ARE LOCAL CIRCULATION CELLS FOR 1700 < Ra < 5x104 • FOR HIGHER Ra NUMBERS, THE FLOW IS TURBULENT • CORRELATIONS: • TEXT (9-47) IS GENERAL • (9-44 THRU 9-46) ARE BASED ON SPECIFIC COMPONENTS

  13. VERTICAL RECTANGULAR ENCLOSURES • CORRELATIONS ARE BASED ON ASPECT RATIOS • NOTE THE GENERAL CORRELATIONS IN THE TEXT (9-52 THRU 9-53) CAN BE APPLIED TO HORIZONTAL ENCLOSURES AS WELL AS VERTICAL ENCLOSURES.

  14. CONCENTRIC CYLINDERS • FOR VERTICAL SYSTEMS, THE VERTICAL RECTANGULAR CORRELATIONS MAY BE USED • FOR HORIZONTAL SYSTEMS • EQUATIONS USE A MODIFIED CONDUCTION MODEL: • kEff IS CALCULATED FROM: • L = Do - Di AND Lc = (Do - Di)/2 • PROPERTIES ARE BASED ON AVERAGE TEMPERATURE

  15. CONCENTRIC SPHERES • EMPLOY THE CONCEPT OF kEff • kEff IS CALCULATED FROM: • L = Do - Di AND Lc = (Do - Di)/2 • PROPERTIES ARE BASED ON AVERAGE TEMPERATURE

  16. COMBINED NATURAL & FORCED CONVECTION • FACTOR APPLIED WHEN MODELING A SYSTEM WITH BOTH FORMS OF CONVECTION IS Gr/Re2 • WHEN Gr/Re2 << 1, THEN NATURAL CONVECTION CAN BE IGNORED • WHEN Gr/Re2 >> 1, THEN FORCED CONVECTION CAN BE IGNORED

  17. COMBINED NATURAL & FORCED CONVECTION • FOR CONDITIONS WHERE 0.1 < Gr/Re2 < 10, THEN BOTH MECHANISMS ARE SIGNIFICANT • THE NUSSELT FOR THIS COMBINED CONDITION IS TYPICALLY MODELED WITH • n = 3 FOR A WIDE RANGE OF SYSTEMS • n = 7/2 OR 4 APPEARS TO WORK BETTER FOR TRANSVERSE FLOWS OVER HORIZONTAL PLATES OR HORIZONTAL CYLINDERS

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