Flow across cylinders: Churchill and Bernstein correlation or Hilpert's equation depending on the specific conditions. 4. Determine the Convection Heat Transfer Coefficient (
Understanding Heat and Mass Transfer: Cengel 5th Edition Chapter 7 Solutions
Q=hAs(Ts−T∞)cap Q equals h cap A sub s open paren cap T sub s minus cap T sub infinity end-sub close paren
): Determining if the flow is laminar, turbulent, or combined. The Nusselt Number ( The Nusselt Number ( This public link is
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Selecting air/fluid properties at the film temperature. Analysis: Calculating , and finally (heat transfer rate). 4. Typical Problems Found in Chapter 7 Solutions
is the thermal conductivity of the fluid. The solution manual heavily relies on finding the correct empirical correlation to solve for , which subsequently yields 3. Step-by-Step Problem Solving Methodology Can’t copy the link right now
): For a flat plate, the transition from laminar to turbulent flow typically occurs at Prandtl Number (
). Pay close attention to whether the plate has an unheated starting length, which requires modified Nusselt correlations. Flow Across Cylinders and Spheres (Cross Flow)
Analyzing laminar, turbulent, and combined flows over smooth or rough flat surfaces. laminar | ( Re_x <
By the time you reach Chapter 7, you understand the laws of conduction (Fourier’s Law) and the basic concept of the convection coefficient ($h$). Chapter 7 asks the crucial question:
The chapter emphasizes the use of the Reynolds number (
| 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 ) |