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convection

convection. Free (Natural) & Forced Convection. Dear Diary,

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convection

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  1. convection • Free (Natural) • & • Forced Convection

  2. Dear Diary, • Last year I replaced all the windows in my house with those expensive double pane energy efficient kind, but this week, I got a call from the contractor who installed them. He was complaining that the work had been completed a whole year ago and I hadn't paid for them. • Now just because I'm blonde doesn't mean that I am automatically stupid.  So, I told him just what his fast talking sales guy had told ME last year....namely, that in ONE YEAR these windows would pay for • themselves!  Hellooooo? It's been a year! (I told him.) There was only silence at the other end of the line, so I finally just hung up... He didn't • call back.  Guess I won that stupid argument.

  3. FREE CONVECTION • When a solid body is heated by a hotter fluid surrounding it (potato in an oven) heat is first transferred to the body by convection then subsequently conducted through it. • Convection • Heat transfer due to fluid movement on a macro scale • Density change, velocity, thermal conductivity, Cp, important variables

  4. Natural or Free Convection • Laminar boundary layer on a flat plate where temperature gradients are present in the flow • For small Ts-T∞ & μ, H/T problems are not acute • For high μ fluids (petroleum oils) where Tw-T∞is very large the fluid property variations (μ, ,ρ) heat transfer rate calculations are difficult.

  5. Convection • This explains why heat transfer to fluids without phase change is complex and treated as a set of special cases rather than as a general theory. • Thermal boundary layer or prandtl boundary layer • Surface of arbitrary shape • v, T∞, Ts ≠ T∞ • q = h(Ts-T∞) ---------------- (1) • v varies from point to point as do h & q T∞ Vt q As As Ts Newton’s law of cooling

  6. Convection • Total heat transfer • Let h = average convection coefficient for the entire surface. Then the total heat transfer rate is:

  7. Flat plate UooToo q h varies with distance, x As Ts x dx L

  8. Example • Experimental results for the local heat transfer coefficient, hx for flow over a flat plate with an extremely rough surface were found to fit the relation: • hx(x) = ax-0.1 • Where a (w/m1.9 K) is a coefficient and x(m) the distance from the leading edge of the plate • Develop an expression for the ratio of the average heat transfer coefficient for a plate of length, x to the total heat transfer coefficient at x • Show in a quantitative manner the variation of hx and hxas a function of x

  9. ConvectionBoundary Layers (Thermal & velocity) • Fluid flow over non porous surface u∞ The fluid at the surface retards the motion of the layers above In the boundary layer temperature gradient decrease with distance from the leading edge qconv = qcondt = -kfluid dt/dy -------(8) T∞ Free stream Thermal Boundary layer Heat is then conducted away from the surface due to fluid motion

  10. Dimensionless Numbers • Reynolds number (ratio of inertia forces to viscous forces) • Graetz number • Prandtl number (ratio of molecular diffusivity of momentum to molecular diffusivity of heat)

  11. DimensionlessNumbers • Peclet number • Stanton number • Grashoff number(ratio of buoyancy to viscous forces) • Releigh number

  12. The volume expansion coefficient • A measure of the variation of the density of a fluid with temperature at constant pressure • From thermodynamics we know that

  13. Convection • For free convection u=0 so no need forRe, use Ra • For forced convection no need for Gr, use Re • For many gases Cpμ/k = constant for a wide range of temperatures so Pr may be disregarded • Fluid properties are referenced at the film temperature (Ts+T∞)/2

  14. Vertical Plates and cylinders - free convection • Characteristic length is the height • Kato et al conducted experiments to show that: • Churchill& Chu

  15. Vertical Plates and cylinders A more complicated relationship is:

  16. External Forced Convection • Flow fields and geometry too complicated for analytical treatment hence emphasis on correlations of experimental data • Flat plate (isothermal surface) in laminar fluid flow • Critical flow at Re = 5.0 x 105 For turbulent flow:

  17. Combined flow • If the plate is not long enough to disregard laminar flow region resulting in combined laminar and turbulent flow:

  18. Example • A 60.0 oC stream of engine oil flows at 2.0 ms-1over the upper surface of a 5.0 m long flat plate that is kept at 20.0 oC. What is the rate of heat transfer per unit width of the entire plate?

  19. Turbulent flow through tubes • Dittus & Boelter correlated works by a variety of researchers using gases (air, CO2, H2O) and liquids (H2O, acetone, kerosene, benzene) in smoth tubes. • For heating of the fluid • For cooling of the fluid • McAdams reevaluated the Dittus/Boelter correlations for both heating and cooling fluids:

  20. Turbulent flow through tubes • Winterton & Colburn found the literature of the Dittus/Boelter correlation to be confusing and introduced the j factor for heat transfer:

  21. Turbulent flow through tubes • Multiplying jH by Re*Pr0.33 gives: • Similar to the McAdams equation • Sieder & Tate looked at very viscous fluids where there is marked difference between the fluid at the wall and that in the bulk . • Knudsen & Katz found that this relationship was valid for:

  22. Bulk Temperature For gases where Pr=0.74 (usually) Fluid properties calculated at the bulk temperature No clear free stream in tubes hence the need for a representative temperature (bulk temperature) Sometimes referred to as the mixing cup temperature, the bulk temperature is the average fluid temperature of the fluid in the tube.

  23. Tubes • **For fully developed turbulent flows in a tube, Nusselt recommended: • h varies with distance from the tube entrance For low h/d ratios: • Tube roughness also affects heat transfer capabilities • COPE found out that for a variety of tubes friction loss was six times greater than for smooth tubes but the heat transfer improved by ony100-120%.

  24. Smooth Tubes • These equations, though simple to compute give rather inaccurate results • A more accurate, though complicated, expression was recommended by Petukov for fully developed turbulent flow in smooth tubes:

  25. Smooth Tubes • Properties are evaluated at the film temperature, Tf=(Tw + Tb)/2 except for μb & μw. • The friction factor is given by: • **For fully developed laminar flow in tubes, Hausen proposed: • Note that for sufficiently long tubes Nu=3.66

  26. Forced convection outside smooth tubes & spheres flow • Common practice: Shell & tube H/E (Internal & external) • Critical Re=2.0 x 105 • Reiher, Hilpert & Griffiths studied flow of gases past various cylindrical shapes ranging from thin wires to tubes of 150.0 mm diameter and temperatures reaching 1073K with gas velocity up to 30.0 ms-1 and 103<Re<105

  27. Smooth Cylinder & sphere • Flow pattern complicated and have great impact on heat transfer • Churchill & Burnstein offered a comprehensive relation : • For spheres Whitake recommends:

  28. Smooth Cylinders & Spheres • McAdams recommends the following relationship for heat transfer to spheres: • Properties are evaluated at the bulk temperature except for μSwhich is evaluated at the wall temperature, Tw • Eg. • A long 10.0 cm diameter steam pipe with external temperature of 110.0 oC passes through an open area that is not protected against the winds. What is the rate of heat loss from the pipe per unit length if the air is at 1.0 atm and 10.0 oC and the wind blows across the pipe at 8.0 ms-1?

  29. Liquid metals • Mercury & bismuth have high thermal conductivities but very small Prandtl numbers (0.01) so their thermal boundary layers develop much faster than the velocity boundary layer • Prandtl numbers for liquid metals

  30. Liquid metals • Assuming constant velocity • In order to find a correlation for all fluids Churchill & Ozoe proposed: • For smooth, turbulent free, isothermal surfaces.

  31. Liquid metals • For fully developed turbulent flow of liquid metals in smooth tubes, Lubarsky and Kaufman posited that: • More recent data were correlated by Skupinshi, Tortel and Vautrey with sodium-potassium mixtures: • Witte measured heat transfer from a sphere to liquid sodium and correlated:

  32. Summary • General procedure • Evaluate the fluid properties, usually at the film temperature • Establish the flow regime via the Reynolds number • Select the appropriate equation • Calculate Nu, h or Q

  33. Thank You

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