Question

Assuming both non-circular cylinders are experiencing the same external fluid flow (identical density, viscosity, fluid velocity), which orientation would experience a higher convective heat transfer coefficient? What is the ratio of Nusselt numbers for the flat cross-section over the angled cross-section? Please show work, and explain conceptually if possible. Thank you!

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Answer 1

Empirical correlations for the average Nusselt number for forced convection non-cinculer cylinder's im Gassflow ( Zukauskas and Jakob over X sle Fluid Re-range Nusselt number 450 tilted Square Gas 5000-100000 0.588 Nu=0°246 Re Pr 0.675 Nu=0.102 Re Gas Square 5000-1000 00 12 Pr Smaller Elted square say, Re-5000 The answer for orientation in which flow experience higher convective heat transton Coethicient depends on the value of Reynolds number. For Reynolds number enperience higher convective heat trarster coefficient Compared square cross-sectional cylinder. While for Reynolds numbes say, Res 100000, Square crossectional cylinder in cross flow experience righer Convective heat transter Coefficient compared to tilted square crossectional Cylinder .

was on intense in the The for higher convective heat transfer Coeffuent is due to the mixing Separated flow region wiki region ie, the 0.588 13 Ratio of Nurselt number for flat cross-section over the angled crossection Nus 0.246 Re Nus, tilted 0.102 Re Pr 0.675 Pr/ -0.087 Re Nus 2.41176 1 Nuo tilted

Put the value of Reynolds number (5,000 and 100,000) in the empirical correlations for respective cases by assuming same Prandtl number, we will get the clear picture of importance of Reynolds number in non-circular circular cross-section in cross flow. Flow over cylinders involve flow spearation which is difficult to handle analytically so flow are stuidie experimentally or numerically.