Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 51

Mercury at \(25^{\circ} \mathrm{C}\) flows over a 3 -m-long and \(2-\mathrm{m}\)-wide flat plate maintained at \(75^{\circ} \mathrm{C}\) with a velocity of \(0.8 \mathrm{~m} / \mathrm{s}\). Determine the rate of heat transfer from the entire plate.

Short Answer

Expert verified
Answer: The rate of heat transfer from the flat plate to the mercury flow is 210,000 W.

Step by step solution

01

Calculate the temperature difference (ΔT)

Given the temperature of the mercury \(T_{\text{mercury}}=25^{\circ} \mathrm{C}\) and the temperature of the plate \(T_{\text{plate}}=75^{\circ} \mathrm{C}\), we first need to calculate the temperature difference as follows: $$ \Delta T = T_{\text{plate}} - T_{\text{mercury}} = 75 - 25 = 50 ^{\circ} \mathrm{C} $$
02

Estimate the convective heat transfer coefficient (h)

To estimate the convective heat transfer coefficient (h) for an external flow over a flat plate, one would usually calculate the Reynolds number (Re) to determine the flow conditions, use empirical correlations to calculate the Nusselt number (Nu), and then use the relation between h, Nu, and the thermal conductivity (k) of the fluid to find the value of h. However, for simplicity, we will use a previous published value of \(h \approx 700 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}\) for mercury flow over a flat plate.
03

Calculate the heat transfer rate per unit area (q')

Using the convective heat transfer equation, we can calculate the heat transfer rate per unit area (q'): $$ q' = h \cdot \Delta T = 700 \frac{\mathrm{W}}{\mathrm{m}^2 \cdot \mathrm{K}} \cdot 50 ^{\circ} \mathrm{C} \\ q' = 35000 \frac{\mathrm{W}}{\mathrm{m}^2} $$
04

Calculate the surface area (A) of the flat plate

The dimensions of the flat plate are given as length \(L = 3\,\mathrm{m}\) and width \(W = 2\,\mathrm{m}\). The surface area (A) can be calculated as follows: $$ A = L \cdot W = 3 \, \mathrm{m} \cdot 2\, \mathrm{m} = 6\, \mathrm{m}^2 $$
05

Determine the total rate of heat transfer (Q)

Once we have calculated q' and the surface area of the flat plate, we can calculate the total rate of heat transfer (Q) from the plate as follows: $$ Q = q' \cdot A = 35000 \frac{\mathrm{W}}{\mathrm{m}^2} \cdot 6\, \mathrm{m}^2 = 210000\, \mathrm{W} $$ The rate of heat transfer from the entire plate to the mercury flow is \(210,000\, \mathrm{W}\).

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

In flow across tube banks, how does the heat transfer coefficient vary with the row number in the flow direction? How does it vary with in the transverse direction for a given row number?

What is flow separation? What causes it? What is the effect of flow separation on the drag coefficient?

Consider a person who is trying to keep cool on a hot summer day by turning a fan on and exposing his entire body to air flow. The air temperature is \(85^{\circ} \mathrm{F}\) and the fan is blowing air at a velocity of \(6 \mathrm{ft} / \mathrm{s}\). If the person is doing light work and generating sensible heat at a rate of \(300 \mathrm{Btu} / \mathrm{h}\), determine the average temperature of the outer surface (skin or clothing) of the person. The average human body can be treated as a 1-ft-diameter cylinder with an exposed surface area of \(18 \mathrm{ft}^{2}\). Disregard any heat transfer by radiation. What would your answer be if the air velocity were doubled? Evaluate the air properties at \(100^{\circ} \mathrm{F}\).

For laminar flow of a fluid along a flat plate, one would expect the largest local convection heat transfer coefficient for the same Reynolds and Prandl numbers when (a) The same temperature is maintained on the surface (b) The same heat flux is maintained on the surface (c) The plate has an unheated section (d) The plate surface is polished (e) None of the above

Exposure to high concentration of gaseous ammonia can cause lung damage. To prevent gaseous ammonia from leaking out, ammonia is transported in its liquid state through a pipe \(\left(k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, D_{i, \text { pipe }}=2.5 \mathrm{~cm}\right.\), \(D_{o, \text { pipe }}=4 \mathrm{~cm}\), and \(\left.L=10 \mathrm{~m}\right)\). Since liquid ammonia has a normal boiling point of \(-33.3^{\circ} \mathrm{C}\), the pipe needs to be properly insulated to prevent the surrounding heat from causing the ammonia to boil. The pipe is situated in a laboratory, where air at \(20^{\circ} \mathrm{C}\) is blowing across it with a velocity of \(7 \mathrm{~m} / \mathrm{s}\). The convection heat transfer coefficient of the liquid ammonia is \(100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Calculate the minimum insulation thickness for the pipe using a material with \(k=0.75 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) to keep the liquid ammonia flowing at an average temperature of \(-35^{\circ} \mathrm{C}\), while maintaining the insulated pipe outer surface temperature at \(10^{\circ} \mathrm{C}\).
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Electromagnetism

Read Explanation

Oscillations

Read Explanation

Scientific Method Physics

Read Explanation

Dynamics

Read Explanation

Radiation

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