Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 12

Consider the cooking process of a roast beef in an oven. Would you consider this to be a steady or transient heat transfer problem? Also, would you consider this to be one-, two-, or three-dimensional? Explain.

Short Answer

Expert verified
Answer: The heat transfer during the cooking process of roast beef in an oven is transient and occurs in three dimensions.

Step by step solution

01

Understanding Steady and Transient Heat Transfer

First, we need to understand the difference between steady and transient heat transfer. In steady heat transfer, the temperature at any point in the system remains constant over time. In transient heat transfer, the temperature at any point can change with time.
02

Understanding Dimensions of Heat Transfer

Next, we need to understand the dimensions of heat transfer. One-dimensional heat transfer assumes that heat only moves in one direction. Two-dimensional heat transfer occurs in two directions, and three-dimensional heat transfer occurs in all three directions.
03

Determining Steady or Transient Heat Transfer

Now, we need to determine if the cooking process of roast beef in an oven is a steady or transient heat transfer problem. We know that the temperature of the roast beef changes with time during the cooking process. Therefore, we can conclude that it’s a transient heat transfer problem since the temperature at any point in the roast beef does not remain constant over time.
04

Determining Dimensionality of Heat Transfer

Lastly, we need to determine the dimensionality of the heat transfer. During the cooking process, the heat is transferred from the oven to the roast beef in all directions. The heat not only moves from the outer surface to the inner parts of the roast beef but also throughout the roast beef in multiple directions. Considering that the roast beef has a non-uniform geometry, the heat transfer will likely occur in all three directions (length, width, and height), making it a three-dimensional heat transfer problem. In conclusion, the cooking process of a roast beef in an oven can be considered a transient and three-dimensional heat transfer problem.

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

Heat is generated in a 10 -cm-diameter spherical radioactive material whose thermal conductivity is \(25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) uniformly at a rate of \(15 \mathrm{~W} / \mathrm{cm}^{3}\). If the surface temperature of the material is measured to be \(120^{\circ} \mathrm{C}\), the center temperature of the material during steady operation is (a) \(160^{\circ} \mathrm{C}\) (b) \(205^{\circ} \mathrm{C}\) (c) \(280^{\circ} \mathrm{C}\) (d) \(370^{\circ} \mathrm{C}\) (e) \(495^{\circ} \mathrm{C}\)

The thermal conductivity of stainless steel has been characterized experimentally to vary with temperature as \(k(T)=9.14+0.021 T\) for \(273

Consider a large 5-cm-thick brass plate \((k=\) \(111 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) ) in which heat is generated uniformly at a rate of \(2 \times 10^{5} \mathrm{~W} / \mathrm{m}^{3}\). One side of the plate is insulated while the other side is exposed to an environment at \(25^{\circ} \mathrm{C}\) with a heat transfer coefficient of \(44 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Explain where in the plate the highest and the lowest temperatures will occur, and determine their values.

Consider a \(1.5\)-m-high and \(0.6-\mathrm{m}\)-wide plate whose thickness is \(0.15 \mathrm{~m}\). One side of the plate is maintained at a constant temperature of \(500 \mathrm{~K}\) while the other side is maintained at \(350 \mathrm{~K}\). The thermal conductivity of the plate can be assumed to vary linearly in that temperature range as \(k(T)=\) \(k_{0}(1+\beta T)\) where \(k_{0}=18 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(\beta=8.7 \times 10^{-4} \mathrm{~K}^{-1}\). Disregarding the edge effects and assuming steady onedimensional heat transfer, determine the rate of heat conduction through the plate. Answer: \(22.2 \mathrm{~kW}\)

Consider the uniform heating of a plate in an environment at a constant temperature. Is it possible for part of the heat generated in the left half of the plate to leave the plate through the right surface? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Turning Points in Physics

Read Explanation

Nuclear Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Radiation

Read Explanation

Circular Motion and Gravitation

Read Explanation

Solid State Physics

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