Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 111

For the same initial conditions, one can expect the laminar thermal and momentum boundary layers on a flat plate to have the same thickness when the Prandtl number of the flowing fluid is (a) Close to zero (b) Small (c) Approximately one (d) Large (e) Very large

Short Answer

Expert verified
Answer: (c) Approximately one

Step by step solution

01

Understanding Prandtl Number

The Prandtl number (Pr) is a dimensionless number that represents the ratio between the momentum diffusivity (kinematic viscosity) and thermal diffusivity. It is given by the formula: Pr = ν/α Where, Pr: Prandtl number ν: kinematic viscosity (momentum diffusivity) α: thermal diffusivity The Prandtl number gives an indication of the relative thickness of the momentum and thermal boundary layers. A high Prandtl number indicates that the thermal boundary layer is thinner than the momentum boundary layer, while a low Prandtl number indicates that the momentum boundary layer is thinner than the thermal boundary layer. Now, let's examine each option:
02

Option (a) Close to zero

If the Prandtl number is close to zero, it means that the thermal diffusivity (α) is much larger than the kinematic viscosity (ν). In this case, the thermal boundary layer would be much thicker than the momentum boundary layer. So, this option is not correct.
03

Option (b) Small

If the Prandtl number is small, it indicates that the thermal diffusivity is still larger than the kinematic viscosity, but the difference between them is not as significant as in the case of Pr being close to zero. Nevertheless, the momentum boundary layer would still be thinner than the thermal boundary layer, so this option is also not correct.
04

Option (c) Approximately one

When the Prandtl number is close to one (1), it means that the kinematic viscosity (ν) and the thermal diffusivity (α) are of the same order of magnitude. In this case, both the momentum and thermal boundary layers have similar thicknesses. Therefore, this is the correct option.
05

Option (d) Large

A large Prandtl number indicates that the kinematic viscosity is much greater than the thermal diffusivity. In this case, the momentum boundary layer would be thicker than the thermal boundary layer, so this option is not correct.
06

Option (e) Very large

A very large Prandtl number also indicates that kinematic viscosity is much larger than thermal diffusivity, making the momentum boundary layer thicker than the thermal boundary layer. This option is also not correct. To sum up, the correct answer is: (c) Approximately one

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider a fluid flowing over a flat plate at a constant free stream velocity. The critical Reynolds number is \(5 \times 10^{5}\) and the distance from the leading edge at which the transition from laminar to turbulent flow occurs is \(x_{\mathrm{cr}}=7 \mathrm{ft}\). Determine the characteristic length \(\left(L_{c}\right)\) at which the Reynolds number is \(1 \times 10^{5}\).

During air cooling of a flat plate \((k=1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\), the convection heat transfer coefficient is given as a function of air velocity to be \(h=27 V^{0.85}\), where \(h\) and \(V\) are in \(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(\mathrm{m} / \mathrm{s}\), respectively. At a given moment, the surface temperature of the plate is \(75^{\circ} \mathrm{C}\) and the air \((k=0.266 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) temperature is \(5^{\circ} \mathrm{C}\). Using EES (or other) software, determine the effect of the air velocity \((V)\) on the air temperature gradient at the plate surface. By varying the air velocity from 0 to \(1.2 \mathrm{~m} / \mathrm{s}\) with increments of \(0.1 \mathrm{~m} / \mathrm{s}\), plot the air temperature gradient at the plate surface as a function of air velocity.

What is Newtonian fluid? Is water a Newtonian fluid?

Saturated liquid water at \(5^{\circ} \mathrm{C}\) is flowing over a flat plate at a velocity of \(1 \mathrm{~m} / \mathrm{s}\). Using EES (or other) software, determine the effect of the location along the plate \((x)\) on the velocity and thermal boundary layer thicknesses. By varying \(x\) for \(0

What is the physical significance of the Reynolds number? How is it defined for external flow over a plate of length \(L\) ?
See all solutions

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Read Explanation

Radiation

Read Explanation

Quantum Physics

Read Explanation

Magnetism

Read Explanation

Physical Quantities And Units

Read Explanation

Electric Charge Field and Potential

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free