Heat Transfer

Use this for “A 10 m pipe has insulation from radius 50 mm to 80 mm, k = 0.05 W/(m·K). Its inner surface is 100 K hotter than its outer. Find the heat lost.”

Use this for “A 10 mm steel ball (ρ = 7800 kg/m³, c = 450 J/(kg·K), k = 40 W/(m·K)) at 300 °C cools in 25 °C air with h = 50 W/(m²·K). What is its temperature after 120 s?”

Use this for “An aluminum pin fin (k = 200 W/(m·K)) is 0.005 m across and 0.05 m long, in air with h = 20 W/(m²·K). Its base is 60 K above the air. How much heat does it shed?”

Use this for “A 1.5 m² panel at 60 °C sits in 20 °C air with h = 25 W/(m²·K). How much heat does it lose?”

Use this for “Air at 5 m/s flows along a 1 m plate; ν = 1.6 × 10⁻⁵ m²/s, Pr = 0.71, k = 0.026 W/(m·K). Find the average h.”

Use this for “A 0.5 m tall plate is 40 K warmer than still air; film 320 K, ν = 1.75 × 10⁻⁵, α = 2.5 × 10⁻⁵ m²/s, k = 0.028. Find h.”

Use this for “The Sun’s surface is close to a 5800 K blackbody. At what wavelength does it radiate most, and what is its emissive power?”

Use this for “Two large parallel plates face each other: one at 500 K with ε = 0.8, the other at 300 K with ε = 0.6. Find the net radiation flux between them.”

Use this for “A 1 m² convex body sits inside a 4 m² enclosure, so F₁₂ = 1. Find F₂₁ and F₂₂.”

Use this for “A surface with ε = 0.8 is at 400 K in surroundings at 300 K. Find its radiation coefficient hᵣ and the net radiation flux.”

Use this for “Oil at 0.5 kg/s (cₚ = 2 kJ/(kg·K)) cools from 120 °C to 70 °C. Water (cₚ = 4.18) warms from 20 °C to 50 °C. Find the water flow.”

Use this for “A counterflow exchanger has UA = 841 W/K. The oil’s Cₘᵢₙ is 1000 W/K and Cᵣ = 0.6. Oil enters at 120 °C, water at 20 °C. Find the heat rate.”

Use this for “Oil cools from 120 °C to 70 °C and water warms from 20 °C to 50 °C in a parallel-flow exchanger. The duty is 50 kW and U = 300 W/(m²·K). Find the area.”

Use this for “An 80 mm thick slab (L = 40 mm, α = 1.2 × 10⁻⁵ m²/s) at 200 °C is dropped in 20 °C fluid with Bi = 1 (C₁ = 1.1191, ζ₁ = 0.8603). Find the centre temperature after 300 s.”

Use this for “Air flows over a wet 0.5 m² surface with h = 25 W/(m²·K) (ρ = 1.18 kg/m³, cₚ = 1007 J/(kg·K), Le = 0.85). The vapor density is 0.0230 kg/m³ at the surface and 0.0070 in the air. Find hₘ and the evaporation rate.”