CORRELATIONS FOR CONVECTIVE HEAT TRANSFER Oct 30 …

1 CORRELATIONS FOR CONVECTIVE heat TRANSFER . I. CORRELATIONS FOR FORECD convection . 1. forced convection from flat plate Flow regime Range of application Correlation Tw const , Re x 5 105 , Laminar, local Nu x Re1/2. x Pr 1/3. Pr 50. Re1/2. x Pr 1/3. Tw const , Re x 5 10 , 5 Nu x 1/ 4. Laminar, local 2/3 . Re x Pr 100 1 . Pr . qw const , Re x 5 105 , Laminar, local Nu x Re1/2. x Pr 1/3. Pr 50. Re1/2. x Pr 1/3. Nu x 1/4. Laminar, local qw const , Re x 5 105 2/3 . 1 . Pr . Laminar, average Re L 5 105 , Tw const Nu L 2 Nu x=L Re1/2. L Pr 1/3. Tw const , Re x 5 105 , Laminar, local Nu x Re1/3. x Pr 1/3. Pr 1 (liquid metals). 1/3. Tw const , starting at x x0 , x0 3/ 4 . Laminar, local Nu x Re Pr 1 . 1/2 1/3. Rex 5 105 , Pr 50. x x . Turbulent, local Tw const , 5 105 Re x 107 St x Pr 2/3 x St x Pr 2/3 log Re x . Turbulent, local Tw const , 107 Re x 109. Turbulent, local qw const , 5 105 Re x 107 Nu x Nu x,Tw =const Laminar-turbulent, Tw const , Re x 107 , St Pr 2/3 L 871 Re L , -1.

2 Average Recrit 5 105 Nu L Pr1/3 Re L 871 . 1/4.. Tw const , Re x 10 , liquids, Re 9200 . 7. Laminar-turbulent, Nu L Pr w . L. average at T and w at Tw Same as for low-speed flow with High-speed flow Tw const , q hA Tw T properties evaluated at T T Tw T Taw T . *. [Note: All properties are evaluated at T f T Tw 2 ]. 2. Boundary layer thickness CORRELATIONS over flat plate Flow regime Range of application Correlation . Laminar Re x 5 105 Re-1/2. x x . Turbulent Re x 107 , 0 at x 0 Re-1/5. x x 5 105 < Re x 107 , . Turbulent Re-1/5 10256 Re-1x Recrit 5 10 , lam at Recrita 5 x x 3. Friction coefficient CORRELATIONS over flat plate Flow regime Range of application Correlation Laminar, local Re x 5 105 C fx Re1/2. x Turbulent, local 5 105 < Re x 107 C fx Re-1/5. x C fx log Re x . Turbulent, local 107 < Re x 109. A. Turbulent, average 109 < Re x Re crit C fx . log ReL . Re L.

3 Where A can be obtained from the following table Recrit 3 105 5 105 106 3 106. A 1055 1742 3340 8940. 4. Nusselt number CORRELATIONS in forced convection heat TRANSFER over flat plate with unheated starting length Nu x x 0. Nu x 0 , where Nu x x 0 C Rem x Pr1/3. x a b 0. 1 0 . x . Values of a , b , C and m can be obtained from the following table Laminar, local Turbulent, local Tw const qw const Tw const qw const a 3/4 3/4 9/10 9/10. b 1/3 1/3 1/9 1/9. C m 1/2 1/2 4/5 4/5. 5. Nusselt number CORRELATIONS in forced convection heat TRANSFER over sphere and cylinder Average Nusselt number for forced convection over an isothermal sphere: 1/4. 1/2 2/3 Nu D 2 D Pr .. , s . which is valid for ReD 80000 and Pr 380 . The fluid properties in this case are evaluated at the free-stream temperature T , except for s which is evaluated at the surface temperature Ts . Average Nusselt number for cross flow over an isothermal cylinder: 1/3 4/5.

4 Re1/2 ReD . 5/8. Nu D D Pr 1 . 1/4 282000 . , 2/3 . 1 . Pr . which is valid for ReD Pr . The fluid properties are evaluated at the film temperature T f T Ts 2 . Average Nusselt number for cross flow over isothermal tube banks: 1/4. m n Pr . Nu D C ReD Pr , Prs . which is valid for 0 Re D <2 106 and Pr 500 . The fluid properties in this case are evaluated at the free-stream temperature T , except for Prs which is evaluated at temperature Tm Ti Te 2 , where Ti and Te are temperature of the fluid at the inlet and outlet of the tube bank, respectively. Typical arrangement of tubes in a tube bank is depicted in the schematic below. Schematic representation of the arrangement of the tubes in in-line and staggered tube banks (A1, AT, and AD are flow areas at indicated locations, and L is the length of the tubes). Values of C , m and n can be obtained from the following table (valid when number of tubes is greater than 16).

5 Arrangement Range of ReD Correlation 1/4. Pr . 0 100 Nu D Re D Pr . Prs . 1/4. Pr . 100 1000 Nu D Re D Pr . Prs . In-line 1/4. Pr . 1000 2 105 Nu D Re D Pr . Prs . 1/4. Pr . 2 105 2 106 Nu D ReD Pr . Prs . 1/4. Pr . 0 500 Nu D ReD Pr . Prs . 1/4. Pr . 500 1000 Nu D ReD Pr . Prs . Staggered 1/4. S Pr . 1000 2 105 Nu D T Re D Pr . SL Prs . 1/4. S Pr . 2 105 2 106 Nu D T ReD Pr . SL Prs . 6. Nusselt number CORRELATIONS in forced convection heat TRANSFER inside circular pipes: case of hydrodynamically and thermally fully developed flow Laminar flow with isothermal wall: Nu D Laminar flow with isoflux wall: Nu D For every other geometry, separate analysis to be made but Nu D const . Turbulent flow: (i) Dittus-Boelter correlation for smooth wall ReD 10000 : Nu D Re4/5 n L Pr (. n for heated wall; n for cold wall), f / 8 Re D 1000 Pr ReD 3000 : Nu D .. (ii) Gnielinski correlation ( f for 1 f / 8.)

6 1/2. Pr 2/3 1. 2. smooth surface can be obtained as f log Re D , while for rough surface look into Moody chart). Above results may be used for other geometries by replacing diameter by hydraulic diameter. 7. Nusselt number CORRELATIONS in forced convection heat TRANSFER inside circular pipes: Developing region Laminar flow (isothermal wall): (i) Combined entry length: 1/3 Re Pr . for Re D Pr/ L / D / s 2, 1/3. Nu D D . L/D s . and Nu D for Re D Pr/ L / D / s 2. 1/3. D / L Re D Pr (ii) Thermal entry length: Nu D . 1 D / L Re D Pr . 2/3. Turbulent flow (isothermal wall): L. (i) Long tubes with 60 : Nu D Nu D, fd D. L Nu D C. (ii) Short tubes with 60 : 1 where C 1 and m 2 / 3. D Nu D, fd L / D m 8. Nusselt numbers for fully developed laminar flow in concentric tube annuals Nusselt number for fully developed laminar flow in a circular tube annulus (of inner diameter Di and outer diameter Do ) with one surface insulated and the other at constant temperature Di/Do Nu Di Nu Do 0 - 1 II.

7 CORRELATIONS FOR NATURAL convection . 1. Nusselt number CORRELATIONS in natural convection heat TRANSFER over isothermally heated flat plate Vertical flat plate: 1/4. Gr x For Pr , Pr : 5 x x x1/4. 4 Grx 1/4.. (i) Laminar flow RaL 109 : Nu L . Ra1/4. L. 1 / Pr 9/16 . 4/9.. 2.. 1/6.. RaL. (ii) Turbulent flow 109 RaL 1012 : Nu L . 4/9 . 1 / Pr 9/16 .. Vertical flat plate: (i) Facing up: Nu L Ra1/4 4. L for 10 RaL 10. 7. Nu L Ra1/3 7. L for 10 RaL 10. 11. (ii) Facing down: Nu L Ra1/4 5. L for 10 RaL 10. 10. 2. Nusselt number CORRELATIONS in natural convection heat TRANSFER over isothermally heated sphere and cylinder Ra1/4. Sphere: Nu D 2 D. 4/9. 1 / Pr 9/16 .. 2.. Ra1/6 . Long cylinder: Nu D D for RaD 1012. 8/27 . 1 / Pr 9/16 .. Over the years it has been found that average Nusselt number can be represented in the following functional form for a variety of circumstances.

8 M Nu C Gr f Pr f C Ra m f , where the subscript f indicates that the properties in the dimensionless groups are evaluated at the film temperature T f T Tw 2 . Values of C and m can be obtained from the following table Geometry Gr f Pr f C m 10 1 104 Use Fig. 1 Use Fig. 1. Vertical planes and 104 109 1/4. cylinders 109 1013 2/5. 109 1013 1/3. 0 10 5 0. 10 5 104 Use Fig. 2 Use Fig. 2. 104 109 1/4. 109 1012 1/3. Horizontal cylinders 10 10 10 2 10 2 102 102 104 104 107 1/4. 107 1012 1/3. Fig. 1: Fig. 2: 3. Nusselt number CORRELATIONS in natural convection heat TRANSFER inside enclosures Average Nusselt number for a horizontal cavity (two of the opposing walls are maintained at different temperatures T1 and T 2 , while other walls are thermally insulated from surroundings) when heated from below: Nu L Ra1/3. L Pr for 3 105 RaL 7 109 , where all properties are evaluated at the average temperature Tav T1 T2 2.