Solution Manual Heat And Mass Transfer Cengel 5th Edition Chapter 9 Jun 2026
L = D = 0.05 m
The Rayleigh number determines whether the natural convection boundary layer is laminar or turbulent. It is the product of the Grashof and Prandtl ( ) numbers:
In this chapter, the solution manual covers the physics of buoyancy-driven flows and the empirical correlations used to calculate heat transfer rates for various geometries. Unlike forced convection, which uses the Reynolds number ( ), natural convection relies on the ( ) to determine the flow regime. Core Concepts & Governing Equations
Analyzing flow over vertical plates, horizontal plates, cylinders, and spheres. L = D = 0
Pay close attention to the introductory assumptions listed at the beginning of each solution in the manual (e.g., steady-state operation, constant properties, radiation effects neglected). Understanding why an assumption is made builds engineering intuition.
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.
Unlike forced convection, where velocity profiles are dictated by external mechanical devices, natural convection relies on density gradients within a fluid. When a fluid touches a hot surface, its temperature increases, its density decreases, and it rises. Cooler, denser fluid moves in to take its place. Key Physical Indicators Core Concepts & Governing Equations Analyzing flow over
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), which governs the transition from laminar to turbulent free convection, functioning similarly to the Reynolds number in forced convection. Apply empirical Nusselt number ( using the text's Appendix tables (Table A-9 for
h = (k * Nu) / L = (0.0287 * 25.8) / 0.1 = 7.42 W/m^2·K
Let me know if you’re stuck on a specific problem (e.g., 9-42, 9-78, or 9-101). Happy to walk through the logic.
A 2m high vertical plate at 80°C is exposed to air at 20°C. Determine the boundary layer thickness at the top of the plate.
The Grashof number governs natural convection much like the Reynolds number governs forced convection. It represents the ratio of the buoyancy force to the viscous force acting on the fluid:
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 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 ( 3. The Rayleigh Number (
