Temperature At Given Thickness X Inside Plane Wall Surrounded By Fluid Calculator

Temperature Formula:

\[ T = \frac{q_G}{8k} \times (b^2 - 4x^2) + \frac{q_G \times b}{2h_c} + T_{\infty} \]

Internal Heat Generation (qG):

W/m³

Thermal Conductivity (k):

W/(m·K)

Wall Thickness (b):

Thickness (x):

Convection Heat Transfer Coefficient (hc):

W/(m²·K)

Fluid Temperature (T∞):

Temperature (T):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Temperature at Given Thickness X Inside Plane Wall Surrounded by Fluid?

This calculation determines the temperature distribution within a plane wall that has internal heat generation and is surrounded by fluid on both sides. It accounts for conduction through the wall and convection to the surrounding fluid.

2. How Does the Calculator Work?

The calculator uses the temperature formula:

\[ T = \frac{q_G}{8k} \times (b^2 - 4x^2) + \frac{q_G \times b}{2h_c} + T_{\infty} \]

Where:

\( T \) — Temperature (K)
\( q_G \) — Internal Heat Generation (W/m³)
\( k \) — Thermal Conductivity (W/(m·K))
\( b \) — Wall Thickness (m)
\( x \) — Thickness (m)
\( h_c \) — Convection Heat Transfer Coefficient (W/(m²·K))
\( T_{\infty} \) — Fluid Temperature (K)

Explanation: The equation calculates temperature at a specific point within the wall, considering internal heat generation, thermal conduction, and convective heat transfer to the surrounding fluid.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal analysis in engineering applications, including building insulation, electronic cooling, and industrial process design.

4. Using the Calculator

Tips: Enter all values in appropriate units. Internal heat generation, thermal conductivity, wall thickness, and convection coefficient must be positive values. Thickness must be non-negative and less than or equal to half the wall thickness.

5. Frequently Asked Questions (FAQ)

Q1: What is internal heat generation?
A: Internal heat generation refers to heat produced within the material itself, such as from electrical resistance, chemical reactions, or nuclear processes.

Q2: How does convection affect temperature distribution?
A: Convection to the surrounding fluid creates temperature gradients and affects the overall heat transfer rate from the wall surface.

Q3: What are typical values for thermal conductivity?
A: Thermal conductivity varies widely: metals (15-400 W/(m·K)), building materials (0.03-2 W/(m·K)), and fluids (0.1-0.7 W/(m·K)).

Q4: When is this formula applicable?
A: This formula applies to steady-state conditions with uniform internal heat generation and constant thermal properties.

Q5: What are limitations of this calculation?
A: The calculation assumes constant properties, uniform convection coefficients, and neglects radiation heat transfer effects.