Heat Flow Rate Through Spherical Composite Wall of 2 Layers in Series Calculator

Heat Flow Rate Formula:

\[ Q' = \frac{T_i - T_o}{\frac{1}{4\pi k_1} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) + \frac{1}{4\pi k_2} \left( \frac{1}{r_2} - \frac{1}{r_3} \right)} \]

Inner Surface Temperature (Ti):

Outer Surface Temperature (To):

Thermal Conductivity of 1st Body (k1):

W/m·K

Radius of 1st Concentric Sphere (r1):

Radius of 2nd Concentric Sphere (r2):

Thermal Conductivity of 2nd Body (k2):

W/m·K

Radius of 3rd Concentric Sphere (r3):

Heat Flow Rate (Q'):

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1. What is Heat Flow Rate Through Spherical Composite Wall?

The heat flow rate through a spherical composite wall of 2 layers in series represents the amount of thermal energy transferred per unit time through concentric spherical layers with different thermal conductivities. This calculation is essential in thermal engineering and heat transfer analysis.

2. How Does the Calculator Work?

The calculator uses the heat flow rate formula:

\[ Q' = \frac{T_i - T_o}{\frac{1}{4\pi k_1} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) + \frac{1}{4\pi k_2} \left( \frac{1}{r_2} - \frac{1}{r_3} \right)} \]

Where:

\( Q' \) — Heat flow rate (W)
\( T_i \) — Inner surface temperature (K)
\( T_o \) — Outer surface temperature (K)
\( k_1 \) — Thermal conductivity of 1st body (W/m·K)
\( r_1 \) — Radius of 1st concentric sphere (m)
\( r_2 \) — Radius of 2nd concentric sphere (m)
\( k_2 \) — Thermal conductivity of 2nd body (W/m·K)
\( r_3 \) — Radius of 3rd concentric sphere (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula accounts for thermal resistance of each spherical layer and calculates the overall heat transfer through the composite wall structure.

3. Importance of Heat Flow Rate Calculation

Details: Accurate heat flow rate calculation is crucial for designing thermal insulation systems, analyzing heat transfer in spherical vessels, and optimizing energy efficiency in various engineering applications.

4. Using the Calculator

Tips: Enter all temperature values in Kelvin, thermal conductivities in W/m·K, and radii in meters. Ensure all values are positive and radii follow the sequence r1 < r2 < r3.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of spherical geometry in heat transfer?
A: Spherical geometry provides uniform heat distribution and is commonly used in pressure vessels, storage tanks, and various industrial applications where symmetrical heat transfer is desired.

Q2: How does thermal conductivity affect heat flow rate?
A: Higher thermal conductivity materials allow more heat to flow through them, while lower conductivity materials provide better insulation and reduce heat transfer.

Q3: What are typical applications of this calculation?
A: This calculation is used in designing insulated spherical tanks, analyzing heat transfer in planetary bodies, and optimizing thermal performance of spherical containers.

Q4: Are there limitations to this equation?
A: The equation assumes steady-state conditions, constant thermal properties, perfect spherical geometry, and neglects convective and radiative heat transfer effects.

Q5: How does layer thickness affect heat flow rate?
A: Thicker layers generally reduce heat flow rate by increasing thermal resistance, but the effect depends on the thermal conductivity of each material.