) dictates the fluid behavior. In natural convection, the takes its place. It represents the ratio of the buoyancy force to the viscous force acting on the fluid.
When you locate the correct , you will find solutions for approximately 50–70 problems, ranging from conceptual discussions to complex numerical analyses. Here is a breakdown of the typical problem categories and how the manual approaches them.
using the text's Appendix tables (Table A-9 for water, Table A-15 for air, etc.). Note: If the fluid is an ideal gas, calculate in Kelvin. Step 2: Identify Geometry & Characteristic Length ( Lccap L sub c Different geometries use different definitions for Lccap L sub c (Height of the plate/cylinder) Horizontal Cylinder: (Diameter) Sphere: (Diameter) Horizontal Rectangular Plate: (Surface Area divided by Perimeter) Step 3: Calculate the Rayleigh Number ( Plug your evaluated properties and Lccap L sub c into the Rayleigh number formula. ) dictates the fluid behavior
Gr=gβ(Ts−T∞)Lc3ν2Gr 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 squared end-fraction = acceleration due to gravity ( m/s2m/s squared = volumetric expansion coefficient ( ) — Note: For ideal gases, Tfcap T sub f is the film temperature in Kelvin. Tscap T sub s = surface temperature ( ∘Craised to the composed with power C T∞cap T sub infinity end-sub = ambient fluid temperature ( ∘Craised to the composed with power C Lccap L sub c = characteristic length of the geometry ( = kinematic viscosity of the fluid ( The Rayleigh Number (
Turbulent (
Chapter 9 focuses on natural convection.Fluid moves without a fan or pump.Buoyancy forces drive the fluid motion.Warm fluid rises because it is less dense.Cold fluid sinks because it is more dense.
Determine if the flow is laminar or turbulent based on the geometry’s critical threshold. Step 4: Select the Appropriate Nusselt Number Correlation Empirical equations take the generic form When you locate the correct , you will
The momentum and energy equations for natural convection.
Solution Manual for Heat and Mass Transfer: Fundamentals and Applications (5th Edition) — Chapter 9 Guide Note: If the fluid is an ideal gas, calculate in Kelvin