SME
Heat Transfer · Problem type
Newton’s law of cooling
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?”
Diagram
q″ = h(Tₛ − T∞) = 25 × 40 = 1,000 W/m²; q = q″A = 1,000 × 1.5 = 1,500 W
The temperature falls across the thin film; the heat crosses it out of the wall.
This is an example. Type your own values to start a new problem.
q (W)
=
h (W/(m²·K))
×
A (m²)
×
(
Tₛ (°C)
−
T∞ (°C)
)
Formulas
q
=
h
×
A
×
(Tₛ
−
T∞)
+1,500 = 25 × 1.5 × (60 − 20)
Assumptions
•
h is the average film coefficient over the whole surface.
•
q > 0 is heat leaving the surface; it is negative when the fluid is warmer.
•
Steady: Tₛ and T∞ hold still while q flows.
Step-by-step
WE KNOW
h = 25 W/(m²·K), A = 1.5 m², Tₛ = 60 °C, T∞ = 20 °C
FIND
heat rate (q)
Step 1 · Find heat rate (q)
Use q = h × A × (Tₛ − T∞)
The heat grows with the film coefficient, the area and the temperature step across the film.
q
=
25
×
1.5
×
(60
−
20)
q
=
25
×
1.5
×
40
q
=
37.5
×
40
q
=
+1,500
W
Check
Put the numbers back in. Both sides should match.
+1,500 = 25 × 1.5 × (60 − 20) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Convection
Main lesson
Laminar flow over a flat plate
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.”
Free convection on a vertical plate
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.”