Correct Answer - Option 4 : Biot number
Concept:
Generally, the temperature of a body varies with time as well as position. In heat conduction under steady conditions, the temperature of a body at any point does not change with time.
In heat conduction under unsteady state conditions, the temperature of a body at any point varies with time as well as position in one- dimensional and multidimensional systems. This type of heat conduction is also known as transient heat conduction.
One such phenomenon is Lumped heat analysis, in which temperature varies with time but not space.
It is given by
\(\begin{array}{l} T = \frac{{T - {T_\infty }}}{{{T_o} - {T_\infty }}} = exp\left( { - \frac{{hA}}{{\rho cV}}t} \right)\\ \frac{{hA}}{{\rho cV}}t = \frac{h}{{\rho c{L_c}}}t = \left( {\frac{{h{L_c}}}{k}} \right)\left( {\frac{k}{{\rho c}}} \right).\frac{1}{{L_c^2}}t = \left( {\frac{{h{L_c}}}{k}} \right)\left( {\frac{\alpha }{{L_c^2}}t} \right) = Bi \times Fo \end{array}\)
Thermal Diffusivity: \(\alpha = \frac{k}{{\rho C}}\)
Fourier number: \(Fo = \frac{\alpha }{{L_c^2}}t\)
So \(T = \exp \left( { - Bi \times Fo} \right)\)
∴ Biot number and Fourier number are the dimensionless numbers associated with transient heat conduction.
