Question: Show that in the limit ??x ?? 0, the difference equation for one-dimensional steady conduction with heat generation, Equation (3.1), is equivalent to the differential

Show that in the limit ??x ?? 0, the difference equation for one-dimensional steady conduction with heat generation, Equation (3.1), is equivalent to the differential equation, Equation (2.27).

GIVENOne dimensional steady conduction with heat generationSHOW(a) In the limit of small ??x, the difference equation is equivalent to the differential equation

(3.1) dx Tx) dx (2.27)

Step by Step Solution

★★★★★

3.62 Rating (178 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

From Equation 31 By definition so we can re... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

66-E-M-E-H-M-T (1564).docx

120 KBs Word File

Students Have Also Explored These Related Mechanical Engineering Questions!

Show that in the limit ??x ?? 0, ??y ?? 0, ??t ??0, the difference Eq. (3.22) is equivalent to the two-dimensional version of the differential Eq. (2.6). GIVENDifference equation, Equation...

Show that in the limit ??x ?? 0 and ??t ?? 0, the difference Equation (3.12) is equivalent to the differential Equation (2.5). GIVENThe difference equation for one-dimensional transient...

Show that in the bivariate situation, E is a linear or distributive operator. That is, for constants a1 and a2, show that Ela1111 (X, Y) + a2112(X, Y)] = a1E[111 (X, Y)] + a2Elu2(X, Y)]

MAT 402 - EBM 607 Mini Project In this project we will go over all steps of scientific computing. We will first derive the differential equation of a physical phenomenon, namely, unsteady heat...

Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Chemical Engineering Department MODELING AND SIMULATION OF FCC RISERS A RESEARCH SUBMITTED TO THE...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

please use an excel document and also show what equations are used! General information: For this assignment, you will use the finite difference method and Excel to solve a two- dimensional,...

\f3nd Lecture What's cause production performance go south? VARIABILITY ASSESSMENT & ITS IMPACT 1 Books for this class 2 From previous lecture We learn about a method to evaluate the production...

With reference to Exercise 3.97, In exercise Two textbooks are selected at random from a shelf that contains three statistics texts, two mathematics texts, and three physics texts. If X is the number...

Using slide #22 of the service line marketing for success PowerPoint presentation as a model (see Week 3 Multimedia), choose an early detection screening (e.g., mammogram, hearing or vision, or...

Where can one find details of an actively managed mutual fund? Morningstar The fund s prospectus The fund s filings on SEC.gov Investment Company Institute ( ICI ) All of the above

The following is an excerpt from a conversation between Evan Eberhard, the warehouse manager for Greenbriar Wholesale Co., and its accountant, Marty Hayes. Greenbriar operates a large regional...

How much money does a typical family of four spend at a McDonalds restaurant per visit? The amount is a normally distributed random variable with a mean of $16.40 and a standard deviation of $2.75....

The following is a graph of a density function. a. Determine the density function. b. Find the probability that X is greater than 10. c. Find the probability that X lies between 6 and12. 10 0 20

Thorup Company had gross wages of $200,000 during the week ended December 10. The amount of wages subject to social security tax was $180,000, while the amount of wages subject to federal and state...

Most Miami Beach restaurants offer early-bird specials. These are lower-priced meals that are available only from 4 to 6 p.m. However, not all customers who arrive between 4 and 6 p.m. order the...

According to Eurostat, in 2020, the European Union had a current account surplus of 349 million, corresponding to 2.6 percent of GDP. What are the main policies that the European Union might take to...

A shell-and-tube heat exchanger is to heat an acidic liquid that flows in un-finned tubes of inside and outside diameters D i = 10 mm and D o = 11 mm, respectively. A hot gas flows on the shell side....

A steel tube (k = 50 W/m K) of inner and outer diameters D i = 20 mm and D o = 26 mm. respectively, is used to transfer heat from hot gases flowing over the tube (h h = 200 W/m 2 K) to cold water...

A heat recovery device involves transferring energy from the hot flue gases passing through an annular region to pressurized water flowing through the inner tube of the annulus. The inner tube has...

Write a 2-page research paper about incoterms (International Commercial Terms) Guidelines 2-page research paper (no including cover page), 12 font size, double-spaced, include references/citations...

1. Which of the following comes closest to the profitability index (PI) of a project that requires an initial investment of $100 and produces a single cash flow of $160 at the end of year 10 if the...

Phil's Army Surplus calculator business was going great guns -- especially the newest models with exclusive camouflage color schemes. Phil sold the calculators from his own dedicated web site:...