Allied & ICAR Exam Bank • ALLIED_0083 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Partial Differential Equations – Laplace, heat and wave equations

Question Statement:

Two-dimensional steady-state temperature distribution in a solid plate with no heat generation satisfies:

Options:

  • (A) Laplace equation $\nabla^2 T = 0$
  • (B) Wave equation
  • (C) Poisson equation $\nabla^2 T = q/k$
  • (D) Helmholtz equation

Answer Key:

A

Step-by-Step Solution & Explanation

In steady state with no internal heat generation, the Fourier conduction law yields Laplace's equation $\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$.
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