Discussion
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)
\[ \begin{aligned} u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} &= g\beta(T - T_{\infty}) \\ &\quad + \nu\frac{\partial^{2}u}{\partial y^{2}} , \end{aligned} \]
the term \(g\beta(T - T_{\infty})\) represents
Answer: D
The term \(g\beta(T - T_{\infty})\) is the buoyancy force per unit mass.
Each term of the boundary-layer momentum equation is a force per unit mass (an acceleration). Where the fluid is warmer than the far field, its density is lower by about \(\rho\beta(T - T_{\infty})\), and gravity acting on that density deficit gives an upward force \(\rho g\beta(T - T_{\infty})\) per unit volume, which is \(g\beta(T - T_{\infty})\) per unit mass. This term drives natural convection.
The viscous force per unit mass is the last term, \(\nu\,\partial^{2}u/\partial y^{2}\). The ratios of forces in the first two options are dimensionless groups (the Reynolds and Grashof numbers), not individual terms of this equation.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development