Solution Manual Heat And Mass Transfer Cengel 5th Edition Chapter 7 ✮
For flow past a sphere, the Whitaker correlation is widely preferred. Note that this correlation handles fluid property variations by evaluating all properties at T∞cap T sub infinity end-sub , except for μsmu sub s , which is evaluated at the surface temperature Tscap T sub s
Using the critical Reynolds number ( for a flat plate) to determine the flow regime.
| Geometry | Flow Regime | Correlation Name / Formula | |----------|-------------|----------------------------| | Flat plate, laminar | ( Re_x < 5\times10^5 ) | ( Nu_x = 0.332 Re_x^1/2 Pr^1/3 ) | | Flat plate, turbulent | ( Re_x > 5\times10^5 ) | ( Nu_x = 0.0296 Re_x^4/5 Pr^1/3 ) | | Flat plate, mixed | Entire length | Average ( Nu = (0.037 Re_L^4/5 - 870) Pr^1/3 ) | | Cylinder in cross flow | ( Re_D ) 0.4–4e5 | Churchill-Bernstein: ( Nu_D = 0.3 + \frac0.62 Re_D^1/2 Pr^1/3[1+(0.4/Pr)^2/3]^1/4 [1+(Re_D/282000)^5/8]^4/5 ) | | Sphere | ( Re_D ) 3.5–7.6e4 | Whitaker: ( Nu_D = 2 + (0.4 Re_D^1/2 + 0.06 Re_D^2/3) Pr^0.4 (\mu_\infty/\mu_s)^1/4 ) | For flow past a sphere, the Whitaker correlation
). Finally, apply Newton's Law of Cooling to find the total heat transfer rate:
Is the fluid moving over a plate, a cylinder, or a bank of tubes? Finally, apply Newton's Law of Cooling to find
: Choose the appropriate empirical correlation (e.g., Churchill-Bernstein for cylinders) based on the geometry and Find Convection Coefficient ( : Rearrange to solve for Calculate Heat Transfer Rate ( : Apply Newton’s Law of Cooling: Example Problem Overviews Flat Plate Flow (Problem 7-1)
Nusph=2+[0.4ReD1/2+0.06ReD2/3]Pr0.4(μ∞μs)1/4cap N u sub s p h end-sub equals 2 plus open bracket 0.4 space cap R e sub cap D raised to the 1 / 2 power plus 0.06 space cap R e sub cap D raised to the 2 / 3 power close bracket cap P r to the 0.4 power open paren the fraction with numerator mu sub infinity end-sub and denominator mu sub s end-fraction close paren raised to the 1 / 4 power 4. Step-by-Step Problem Solving Methodology For flow past a sphere
Finally, apply Newton's Law of Cooling to find the total thermal energy transfer:
