Temperature Inside Solid Cylinder At Given Radius Calculator

Temperature Solid Cylinder Formula:

\[ t = \frac{q_G}{4k} (R_{cy}^2 - r^2) + T_w \]

Internal Heat Generation (qG):

W/m³

Thermal Conductivity (k):

W/m·K

Radius of Cylinder (Rcy):

Radius (r):

Surface Temperature of Wall (Tw):

Temperature Solid Cylinder (t):

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1. What is the Temperature Inside Solid Cylinder Formula?

The temperature inside a solid cylinder formula calculates the temperature distribution in a solid cylinder with internal heat generation. It provides the temperature at any given radial position within the cylinder based on the cylinder's properties and boundary conditions.

2. How Does the Calculator Work?

The calculator uses the temperature solid cylinder formula:

\[ t = \frac{q_G}{4k} (R_{cy}^2 - r^2) + T_w \]

Where:

\( t \) — Temperature at radius r (K)
\( q_G \) — Internal heat generation (W/m³)
\( k \) — Thermal conductivity (W/m·K)
\( R_{cy} \) — Radius of cylinder (m)
\( r \) — Radial position where temperature is calculated (m)
\( T_w \) — Surface temperature of wall (K)

Explanation: The formula calculates the temperature distribution in a solid cylinder with uniform internal heat generation and constant surface temperature.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal analysis of cylindrical components, heat transfer engineering, and designing systems with internal heat generation such as nuclear reactors, electrical components, and chemical reactors.

4. Using the Calculator

Tips: Enter internal heat generation in W/m³, thermal conductivity in W/m·K, cylinder radius in meters, radial position in meters, and surface temperature in Kelvin. All values must be valid and r must be between 0 and Rcy.

5. Frequently Asked Questions (FAQ)

Q1: What is internal heat generation?
A: Internal heat generation refers to the conversion of electrical, chemical, or nuclear energy into thermal energy within the material itself, leading to temperature rise.

Q2: Why does the temperature vary with radius?
A: The temperature varies radially because heat generated internally must be conducted to the surface, creating a temperature gradient from the center to the surface.

Q3: What is the maximum temperature in the cylinder?
A: The maximum temperature occurs at the center (r = 0) of the cylinder where heat conduction resistance is highest.

Q4: What are the assumptions of this formula?
A: The formula assumes steady-state conditions, uniform internal heat generation, constant thermal conductivity, and constant surface temperature.

Q5: Can this formula be used for hollow cylinders?
A: No, this formula is specifically for solid cylinders. Different equations apply for hollow cylinders with internal and/or external convection.