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

Correct Answer: Biot number and Fourier number

Explanation:
When a hot steel spherical ball is suddenly cooled in a low-temperature oil bath, the transient heat conduction within the sphere can be determined using a Heisler chart.

By analyzing the provided chart, we can identify the following parameters:

1. The vertical axis represents the dimensionless center temperature ratio:

$$\frac{T_o\left(t\right)-T_{\infty }}{T_i-T_{\infty }}$$

where $T_o\left(t\right)$ is the center temperature at time $t$, $T_i$ is the initial temperature, and $T_{\infty }$ is the oil bath temperature.

2. The horizontal axis represents the Fourier number ($f_0$), which is a dimensionless time parameter:

$$f_0=\frac{\alpha t}{L_c^2}$$

where $\alpha$ is the thermal diffusivity, $t$ is the time, and $L_c$ is the characteristic length.

3. The curves within the plot are labeled as "Various Biot number lines", where the Biot number ($\mathrm{Bi}$) is defined as:

$$\mathrm{Bi}=\frac{h{L}_c}{k}$$

where $h$ is the convection heat transfer coefficient and $k$ is the thermal conductivity of the solid.

Therefore, to determine the instantaneous center temperature using a Heisler chart, we require the Biot number and the Fourier number.