Question:
Which one of the following ratios does Grashof number represent?
Which one of the following ratios does Grashof number represent?
Show Hint
Grashof number plays the role in natural convection that Reynolds number plays in forced convection, comparing buoyancy force against viscous force.
Updated On: Aug 10, 2026
- buoyancy force to inertia force
- buoyancy force to viscous force
- viscous force to capillary force
- viscous force to inertia force
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Recall the physical origin of the Grashof number.
The Grashof number, Gr, is a dimensionless group that arises in free (natural) convection heat transfer problems, where fluid motion is driven purely by density differences caused by temperature gradients, without any externally imposed velocity. It plays the same role in natural convection that the Reynolds number plays in forced convection.
Step 2: Write the defining expression and identify each force.
For a characteristic length L, the Grashof number is defined as Gr = g beta Delta T L^3 / nu^2, where g is gravitational acceleration, beta is the volumetric thermal expansion coefficient, Delta T is the temperature difference driving the flow, and nu is the kinematic viscosity. This can be interpreted physically as Gr ~ (buoyancy force)/(viscous force).
Step 3: Contrast with the other options.
Option (A), buoyancy to inertia force, is closer to an intermediate ratio used only inside the derivation. Option (C), viscous to capillary force, is closer to the Capillary number. Option (D), viscous to inertia force, is essentially the inverse-style comparison used inside the Reynolds number.
Step 4: Conclude.
By its standard physical definition used throughout heat transfer texts, the Grashof number represents the ratio of buoyancy force to viscous force acting on the fluid. \[ \boxed{Gr = \dfrac{\text{buoyancy force}}{\text{viscous force}} \ \text{(option B)}} \]
The Grashof number, Gr, is a dimensionless group that arises in free (natural) convection heat transfer problems, where fluid motion is driven purely by density differences caused by temperature gradients, without any externally imposed velocity. It plays the same role in natural convection that the Reynolds number plays in forced convection.
Step 2: Write the defining expression and identify each force.
For a characteristic length L, the Grashof number is defined as Gr = g beta Delta T L^3 / nu^2, where g is gravitational acceleration, beta is the volumetric thermal expansion coefficient, Delta T is the temperature difference driving the flow, and nu is the kinematic viscosity. This can be interpreted physically as Gr ~ (buoyancy force)/(viscous force).
Step 3: Contrast with the other options.
Option (A), buoyancy to inertia force, is closer to an intermediate ratio used only inside the derivation. Option (C), viscous to capillary force, is closer to the Capillary number. Option (D), viscous to inertia force, is essentially the inverse-style comparison used inside the Reynolds number.
Step 4: Conclude.
By its standard physical definition used throughout heat transfer texts, the Grashof number represents the ratio of buoyancy force to viscous force acting on the fluid. \[ \boxed{Gr = \dfrac{\text{buoyancy force}}{\text{viscous force}} \ \text{(option B)}} \]
Was this answer helpful?
0
0
Top GATE CH Heat Transfer Questions
- If the Prandtl number Pr = 0.01, which of the following statements is/are correct?
- The opposite faces of a metal slab of thickness 5 cm and thermal conductivity 400 W m\(^{-1}\) °C\(^{-1}\) are maintained at 500 °C and 200 °C. The area of each face is 0.02 m\(^2\). Assume that the heat transfer is steady and occurs only in the direction perpendicular to the faces. The magnitude of the heat transfer rate, in kW, rounded off to the nearest integer, is ____.
- The temperatures of two large parallel plates of equal emissivity are 900 K and 300 K. A reflection radiation shield of low emissivity and negligible conductive resistance is placed parallelly between them. The steady-state temperature of the shield, in K, is
- Hot oil at \( 110^\circ \)C heats water from \( 30^\circ \)C to \( 70^\circ \)C in a counter-current double-pipe heat exchanger. The flow rates of water and oil are \( 50 \) kgmin\(^{-1}\) and \( 100 \) kgmin\(^{-1}\), respectively, and their specific heat capacities are \( 4.2 \) kJ kg\(^{-1}\)°C\(^{-1}\) and \( 2.0 \) kJ kg\(^{-1}\)°C\(^{-1}\), respectively. Assume the heat exchanger is at steady state. If the overall heat transfer coefficient is \( 200 \) W m\(^{-2}\)°C\(^{-1}\), the heat transfer area \( A \) in m\(^{2}\) is:
- A solid slab of thickness \( H1 \) is initially at a uniform temperature \( T0 \). At time \( t = 0 \), the temperature of the top surface at \( y = H1 \) is increased to \( T1 \), while the bottom surface at \( y = 0 \) is maintained at \( T0 \) for \( t \geq 0 \). Assume heat transfer occurs only in the \( y \)-direction, and all thermal properties of the slab are constant. The time required for the temperature at \( y = \frac{H1}{2} \) to reach 99% of its final steady value is \( T1 \). If the thickness of the slab is doubled to \( H2 = 2H1 \), and the time required for the temperature at \( y = \frac{H2}{2} \) to reach 99% of its final steady value is \( T2 \), then \( \frac{T2}{T1} \) is .
View More Questions
Top GATE CH Questions
- Consider a Leniar Homogeneous system AX = 0, where A is N × N matrix and X is N × 1 vector. When we solve this 0 is null matrix of N × 1. Let R be the rank matrix for a for a Non-trivial solution.
- Which are true for Petroleum / Petrochemicals?
- F(x) = ex - 5x and the value of X0 = 1 then what will be the value of X1?
- The first non-zero term in the taylor series expansion of (1 - x) - e- x, about x = 0
- \(\frac{P}{Q}\) is not equal 1, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)
View More Questions