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Chapter 8: Problem 72

Determine the convection heat transfer coefficient for the flow of \((a)\) air and \((b)\) water at a velocity of \(2 \mathrm{~m} / \mathrm{s}\) in an \(8-\mathrm{cm}\) diameter and 7-m-long tube when the tube is subjected to uniform heat flux from all surfaces. Use fluid properties at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
(a) The convection heat transfer coefficient for the flow of air inside the tube is approximately 44.73 W/(m²·K). (b) The convection heat transfer coefficient for the flow of water inside the tube is approximately 43346.84 W/(m²·K).

Step by step solution

01

Obtain fluid properties at 25°C

For air at 25°C: - Density (ρ) = 1.184 kg/m³ - Specific heat (Cp) = 1005 J/(kg·K) - Thermal conductivity (k) = 0.02624 W/(m·K) - Dynamic viscosity (μ) = 1.849x10⁻⁵ kg/(m·s) For water at 25°C: - Density (ρ) = 997 kg/m³ - Specific heat (Cp) = 4182 J/(kg·K) - Thermal conductivity (k) = 0.6075 W/(m·K) - Dynamic viscosity (μ) = 8.9x10⁻⁴ kg/(m·s)
02

Calculate the Reynolds number (Re)

Re = (ρ * V * D) / μ For air: Re_air = (1.184 * 2 * 0.08) / 1.849x10⁻⁵ = 10237.43 For water: Re_water = (997 * 2 * 0.08) / 8.9x10⁻⁴ = 179328.09
03

Determine the type of flow (laminar or turbulent)

For both fluids: - If Re < 2300, the flow is laminar - If Re > 2300, the flow is turbulent For air: Re_air = 10237.43, the flow is turbulent For water: Re_water = 179328.09, the flow is turbulent
04

Use appropriate correlation to calculate Nusselt number (Nu)

Since the flow is turbulent for both fluids, we will use Dittus-Boelter equation, for uniform heat flux: Nu = 0.023 * Re^0.8 * Pr^(1/3) For air: Pr_air = (1.849×10⁻⁵ * 1005) / 0.02624 = 0.707 Nu_air = 0.023 * (10237.43)^0.8 * (0.707)^(1/3) = 137.13 For water: Pr_water = (8.9×10⁻⁴ * 4182) / 0.6075 = 6.108 Nu_water = 0.023 * (179328.09)^0.8 * (6.108)^(1/3) = 5715.27
05

Calculate the convection heat transfer coefficient (h)

h = (k * Nu) / D For air: h_air = (0.02624 * 137.13) / 0.08 = 44.73 W/(m²·K) For water: h_water = (0.6075 * 5715.27) / 0.08 = 43346.84 W/(m²·K) The convection heat transfer coefficients for the flow of (a) air and (b) water inside the tube are approximately: (a) h_air = 44.73 W/(m²·K) (b) h_water = 43346.84 W/(m²·K)

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