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GATE 2022 ME (ME1) – Question 25

Heat Transfer · Convection: boundary layer, dimensionless parameters and correlations · 1 mark · Multiple choice

In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_\infty$ ($g$ is the gravitational acceleration, $\beta$ is the volumetric thermal expansion coefficient, $\nu$ is the kinematic viscosity, $u$ and $v$ are the velocities in $x$ and $y$ directions, respectively, and T is the temperature)
$u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} = g\beta(T - T_\infty) + \nu\frac{\partial^2u}{\partial y^2}$,
the term $g\beta(T - T_\infty)$ represents

  1. Ratio of inertial force to viscous force.
  2. Ratio of buoyancy force to viscous force.
  3. Viscous force per unit mass.
  4. Buoyancy force per unit mass.

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Show answer and explanation

Correct answer: (D) Buoyancy force per unit mass.

Explanation

Every term of the equation has the dimension of acceleration (force per unit mass). The left side is the inertia per unit mass, the last term is the viscous force per unit mass, and $g\beta(T - T_\infty)$ is the buoyancy force per unit mass.