Question

In transient heat conduction, the two significant dimensionless numbers are

• A. Biot number and Fourier number
• B. Fourier number and Reynolds number
• C. Reynolds number and Prandtl number
• D. Prandtl number and Biot number

Hint:

In transient heat conduction, the Biot number (\( \text{Bi} \)) assesses internal vs. external resistance, and the Fourier number (\( \text{Fo} \)) represents dimensionless time.

Answer 1

The Correct Option is A

Step 1: Understand transient heat conduction.
Transient heat conduction refers to the time-dependent heat transfer within a solid, where the temperature changes with time. Dimensionless numbers simplify the analysis by grouping physical parameters. Step 2: Identify relevant dimensionless numbers.
Biot number (Bi): \( \text{Bi} = \frac{hL}{k} \), where \( h \) is the convective heat transfer coefficient, \( L \) is the characteristic length, and \( k \) is the thermal conductivity. It compares the internal conduction resistance to the external convection resistance, significant in transient conduction to determine if temperature gradients within the solid are negligible (lumped capacitance, \( \text{Bi}<0.1 \)).
Fourier number (Fo): \( \text{Fo} = \frac{\alpha t}{L^2} \), where \( \alpha = \frac{k}{\rho c_p} \) is the thermal diffusivity, \( t \) is time, and \( L \) is the characteristic length. It represents the dimensionless time, comparing the rate of heat conduction to the rate of thermal energy storage, crucial in transient problems.
Reynolds number (Re): Relevant in fluid flow, not directly in transient heat conduction within a solid.
Prandtl number (Pr): Relevant in convection, comparing momentum diffusivity to thermal diffusivity, not directly in transient conduction within a solid.
Step 3: Evaluate the options.
(1) Biot number and Fourier number: Both are directly relevant to transient heat conduction. Correct.
(2) Fourier number and Reynolds number: Reynolds number is for fluid flow, not transient conduction. Incorrect.
(3) Reynolds number and Prandtl number: Both are for fluid flow and convection, not transient conduction. Incorrect.
(4) Prandtl number and Biot number: Prandtl number is for convection, not transient conduction. Incorrect.
Step 4: Select the correct answer.
The two significant dimensionless numbers in transient heat conduction are the Biot number and Fourier number, matching option (1).