Heat Transfer Coefficients — External Forced Convection

Figure 4-35: Schematic representation of geometry and parameters for the averaged heat transfer coefficient correlation applied to forced convection on an horizontal plate.

This correlation is a combination of equations 7.33 and 7.41 in Ref. 21:

(4-185)

where Pr = μCp ⁄ k and ReL = ρUL ⁄ μ. The plate length, L, and the exterior velocity, U, are correlation inputs. The material data are evaluated at (T + Text) ⁄ 2.

The laminar-turbulent transition at ReL = 5.105 is handled by the use of a smoothed Heaviside function with a transition of size 5.104, which corresponds to 10% of the threshold value.

Plate, Local Transfer Coefficient

Figure 4-36: Schematic representation of geometry and parameters for the local heat transfer coefficient correlation applied to forced convection on an horizontal plate.

This correlation corresponds to equations 5.79b and 5.131’ in Ref. 41:

(4-186)

where Pr = μCp ⁄ k and Rex = ρUx ⁄ μ. The correlation inputs are x, the position along the plate, and U, the exterior velocity. The material data are evaluated at (T + Text) ⁄ 2. To avoid division by zero when the position along the plate is located at the origin point (x = 0), the implementation replaces k ⁄ x by k ⁄ max(x, √ε) where ε is the floating-point relative accuracy.

The laminar-turbulent transition at Rex = 5.105 is handled by the use of a smoothed Heaviside function with a transition of size 5.104, which corresponds to 10% of the threshold value.

Cylinder in Cross-Flow

Figure 4-37: Schematic representation of geometry and parameters for the averaged heat transfer coefficient correlation applied to forced convection on a cylinder in cross-flow.

This correlation is given by equation 7.54 in Ref. 21:

(4-187)

where Pr = μCp ⁄ k and ReD = ρUD ⁄ μ. The cylinder diameter, D, and the exterior velocity, U, are correlation inputs. The material data are evaluated at (T + Text) ⁄ 2.

Sphere

Figure 4-38: Schematic representation of geometry and parameters for the averaged heat transfer coefficient correlation applied to forced convection on a sphere.

This correlation corresponds to equation 7.56 in Ref. 21:

(4-188)

where Pr = μCp ⁄ k and ReD = ρUD ⁄ μ. The sphere diameter, D, and the exterior velocity, U, are correlation inputs. All material data are evaluated at Text except μs, which is evaluated at the wall temperature, T.