Correct Answer - Option 1 : Steady state heat conduction with heat generation
Concept:
Generalized 3D conduction equation is given by Fourier equation which is:
\(\frac{{{\partial ^2}T}}{{\partial {x^2}}} + \frac{{{\partial ^2}T}}{{\partial {y^2}}} + \frac{{{\partial ^2}T}}{{\partial {z^2}}} + \frac{{\dot q}}{k} = \frac{1}{\alpha }\left( {\frac{{\partial T}}{{\partial \tau }}} \right)\)
For Poisson's equation, the form of the equation should be ∇2T + a = 0;
For steady-state, \(\frac{{\partial T}}{{\partial \tau }} = 0\)
With heat generation, the equation takes the form
\({\nabla ^2}T + \frac{q}{k} = 0 \Rightarrow Poisson's \; equation\)
Without heat generation, the equation takes the form
\({\nabla ^2}T = 0 \Rightarrow Laplace \; equation\)