In the design of a certain computer application, a heat flow simulation is required. In the simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface. The temperature at both ends of the conductor is kept consistently at zero. The initial temperature at any point of the conductor is uniform at 25°C. The 1-dimensional heat equation is given as follows: for all 0< x 10 and t20 (a) Describe the initial and boundary conditions of the 1-dimension heat equation in the simulation. Hence, deduce the temperature function (x, t) of the conductor, subjected to the conditions in (a).

In the design of a certain computer application, a heat flow simulation is required. In the simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface. The temperature at both ends of the conductor is kept consistently at zero. The initial temperature at any point of the conductor is uniform at 25°C. The 1-dimensional heat equation is given as follows: for all 0< x 10 and t20 (a) Describe the initial and boundary conditions of the 1-dimension heat equation in the simulation. Hence, deduce the temperature function (x, t) of the conductor, subjected to the conditions in (a).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: The side of a home can be modeled as a plane wall. The wall is 12 centimeters thick. If the outdoor…

Q: PROBLEM: Solve the following 2-dimensional heat conduction problem by Gauss-Seidel iteration. 3T2 at…

Q: Passage of an electric current through a long conducting rod of radius r; and thermal conductivity…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Q3 A thin rod of 3 cm length having a thermal diffusivity coefficient (a) of 0.835 cm²/s is…

Q: A very long, rectangular cross-section block is made from metal with the following properties:…

A: Given Data: Thermal Conductivity k = 130 W/mK Density ρ=2771 kg/m3 Specific heat cp=703 J/kgK…

Q: 1. COMBINED CONDUCTION CONVECTION ON CYLINDRICAL WALL A hot-water pipe (k = 60 W/m K) in a house,…

Q: Which series helps us to derive the discretized form of the governing equation

A: The finite element method, like the finite difference method or the separation of variables…

Q: Q2/ A thermopane window consists of two pieces of glass 7 mm thick that enelose an air space 7 mm…

A: T∞i=20°C, hi=10 Wm2KL=L1=L2=L3=.007 mA=.8×.5=.4 m2Kg=1.4 WmK and Kair=.0245 Wm Kh0=80 Wm2K,T∞0=-10°C…

Q: The temperature gradient is inversely proportional to the cross sectional area for one dimensional…

A: Solution: Mathematical relation for one dimension heat transfer equation is given by,…

Q: The TPD method measures temperature elevations in a tissue region during a heating pulse and its…

A: The Thermal Pulse Decay (TPD) method, which relies on the Pennes bioheat equation for estimating…

Q: = How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has…

Q: A hollow infinite cylinder has internal radius 0.5 and exterior radius 2.0. The external surface is…

A: Internal radius of hollow infinite cylinder= 0.5Exterior radius of hollow infinite cylinder=…

Q: 8. The wall of a cold storage room is composed of brick, concrete and cork insulation with thickness…

Q: A Zamboni is a multi-step mechanical ice rink resurfacer. The first step is shaving the ice surface…

Q: 22. Develop an algorithm, along with the program (preferably in python), to find the temperature…

A: import numpy as np # Constants and parameters L = 0.01 # Thickness of the wall (m) h = 1100 #…

Q: 2. Discrete :(+) using ADI method and explain the advantage of ADI on Implicit method. 3. A solid…

A: Here solving the 3rd part of the question the typical boundary condition at the base (x=0) is…

Q: The following graph shows the thermal behavior of 2 kg of a material called Uniandesato undergoing a…

Q: An iron rod 10 m long is heated at end A to a constant temperature of 100°C, while the other end (B)…

A: Through conduction, heat moves from point A to point B.The rate of heat travel, or heat flow per…

Q: Chilled pharmaceutical is transported through a steel pipe ( k= 15.0 W/m.k) with an inner diameter…

A: Given that, Thermal conductivity of steel, k=15 W/m.K,Inner diameter of pipe, di=36mm,Thickness of…

Q: Two-dimensional, steady-state conduction occurs in a hollow cylindrical solid of hermal conductivity…

A: Solution:

Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

In the design of a certain computer application, a heat flow simulation is required. In the
simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface.
The temperature at both ends of the conductor is kept consistently at zero. The initial
temperature at any point of the conductor is uniform at 25°C.
The 1-dimensional heat equation is given as follows:
for all 0<x<10 and :20
Describe the initial and boundary conditions of the 1-dimension heat equation in
the simulation.
(a)
Hence, deduce the temperature function (x, t) of the conductor, subjected to the
conditions in (a).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

One of the strengths of numerical methods is their ability to handle complex boundary conditions. In the sketch, the boundary condition changes from specified heat flux ′′ qs (into the domain) to convection, at the location of the node (m, n). Write the steady-state, two- dimensional finite difference equation at this node.
1. Suppose you have a 4-foot metal rod, made out of steel which has a thermal conductive factor of a = 4 Assume the temperature on the ends of the rod is always 0 degrees. a) Filling in the numerical parameters mentioned above in the problem, write down the general solution to this heat equation, which should include some unknown coefficients (c,'s), in addition to t's and x's.
any help would be much appreciated thanks
Transient Heat Conduction Cooking a Thanksgiving turkey is an art form and, if your skills in the kitchen are like mine, it is sometimes more of a mystical, elusive art form. Thankfully, science also has much to contribute in the kitchen as well as the laboratory. Let us consider the change in temperature of a common, 20-lb holiday fowl as it is cooked in a convection oven. To simplify the analysis, let's assume the bird can be modeled as a uniform sphere of radius 7.0 in. with a specific heat of 3.53 kJ/kg-K. Moreover, the turkey will be assumed to have a uniform temperature, T, throughout that will change with time as it is cooked according to the following relationship: 。 + (To - T∞)ept T(t) = T∞ + where To is the initial temperature of the turkey, T∞, is the oven temperature, V is the volume of the turkey, As is the surface area of the turkey, and h is the convection coefficient for the scenario which is 11.3 W/m²-K. If the oven is set to 325 °F and the initial temperature of the…
An engineer seeks to study the effect of temperature on the curing of concrete by controlling the curing temperature in the following way. A sample slab of thickness L is subjected to a heat flux, qw, on one side, and it is cooled to temperature T1 on the other. Derive a dimensionless expression for the steady temperature in the slab. Plot the expression and offer a criterion for neglecting the internal heat generation in the slab.
2. The slab shown is embedded in insulating materials on five sides, while the front face experiences convection off its face. Heat is generated inside the material by an exothermic reaction equal to 1.0 kW/m'. The thermal conductivity of the slab is 0.2 W/mk. a. Simplify the heat conduction equation and integrate the resulting ID steady form of to find the temperature distribution of the slab, T(x). b. Present the temperature of the front and back faces of the slab. n-20- 10 cm IT- 25°C) 100 cm 100 cm