Question

A hot steel spherical ball is suddenly dipped into a low temperature oil bath. Which of the following dimensionless parameters are required to determine the instantaneous center temperature of the ball using a Heisler chart?

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

Hint:

When using Heisler charts for transient heat conduction problems, ensure you calculate the Biot number and Fourier number correctly, as these are essential for determining the temperature distribution in the object.

Answer 1

The Correct Option is A

In heat transfer problems involving the cooling or heating of objects in fluids, Heisler charts are commonly used to determine the temperature distribution within the object as a function of time.
The Heisler chart is particularly useful for transient heat conduction problems and requires two dimensionless parameters:
1. Biot number (Bi), which is a measure of the thermal resistance within the object to the thermal resistance between the object and the surrounding fluid. It is given by: \[ Bi = \frac{hL}{k}, \] where \( h \) is the heat transfer coefficient, \( L \) is the characteristic length (in this case, the radius of the sphere), and \( k \) is the thermal conductivity of the material.
2. Fourier number (Fo), which is a measure of the relative importance of transient heat conduction within the object. It is given by: \[ Fo = \frac{\alpha t}{L^2}, \] where \( \alpha \) is the thermal diffusivity and \( t \) is the time.
Thus, the correct dimensionless parameters required for using the Heisler chart to determine the instantaneous center temperature are Biot number and Fourier number, corresponding to Option (A).
Final Answer: (A)