Question

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate of q can be written

• A. $\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial T}{\partial r}\right)+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$
• B. $\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial T}{\partial r}\right)+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$
• C. $\frac{{\partial }^{2}T}{\partial r^2}+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$
• D. $\frac{{\partial }^2}{\partial r^2}\left(rT\right)+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$

Answer 1

The correct option is B $\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial T}{\partial r}\right)+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate of q can be written as
$\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial T}{\partial r}\right)+\frac{q}{k}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$