Solutions in the manual typically follow these standard steps:
The Rayleigh number is the product of the Grashof and Prandtl numbers. It is the primary parameter used in empirical correlations to calculate the Nusselt number.
The Grashof number represents the ratio of the buoyancy force to the viscous force acting on the fluid. It is defined as: Solutions in the manual typically follow these standard
The Grashof number represents the ratio of the buoyancy force to the viscous force acting on the fluid. It determines whether the natural convection flow is laminar or turbulent.
Understand the physical mechanism of natural convection and the role of the volumetric expansion coefficient ( Assess Grashof Number: Evaluate the Grashof number ( It is defined as: The Grashof number represents
Using the tables in Appendix A of Çengel's textbook (Table A-15 for air, Table A-9 for water), find the following properties at Tfcap T sub f Thermal conductivity ( Kinematic viscosity ( Prandtl number ( Volume expansion coefficient (
Chapter 9 of the 5th edition focuses on the physics of natural (or "free") convection, where fluid motion is driven solely by buoyancy forces. Familiarizing yourself with the main topics will help you identify the correct solutions and understand the underlying concepts: Familiarizing yourself with the main topics will help
Since $Ra_L < 10^9$, the flow is laminar . We use the correlation for a vertical isothermal plate (Churchill and Chu):
Ra=Gr⋅Pr=gβ(Ts−T∞)Lc3ναRa equals Gr center dot Pr equals the fraction with numerator g beta open paren cap T sub s minus cap T sub infinity end-sub close paren cap L sub c cubed and denominator nu alpha end-fraction
) — remember to convert to Kelvin if dealing with air/gas. Step 4: Determine the Characteristic Length ( Lccap L sub c The definition of Lccap L sub c changes strictly depending on geometry: (height of the plate) Horizontal Cylinder: (diameter of the cylinder) Sphere: (diameter of the sphere) Horizontal Plate: (surface area divided by the perimeter) Step 5: Calculate the Rayleigh Number (
). For a vertical plate, the transition from laminar to turbulent flow typically occurs at a critical Rayleigh number of 4. Nusselt Number Correlation Selection
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