Answered: Problem 1 Show that if the following…

Problem 1 Show that if the following problem has a solution it is unique -k = f in (0,L)× (0,T), (1) ди u(0,t) = g,(t),"(L,t) = g,(t),0

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.17P

See similar textbooks

Related questions

Q: 4) Consider the following mass spring damper system: k m2 u(t) Assuming that y, > y1, equation of…

Q: k1 k2 k3 k4 k5 k6

A: Given that , k1=20N/mk2=30N/mk3=25N/mk4=35N/mk5=50N/mk6=60N/m

Q: Given the folowing conditions: Q = 0.05 m3/s %3D P1 = 12.5 kPa P2 = 11.5 kPa P3 = 10.3 kPa %3D Find…

Q: Consider the following linear equations -7x + 8y + 4z - 7x + (25 – k)y + 3z = 11 - 7x + 8y + (7 –…

A: The given set of equations are:

Q: An orifice of diameter 200 mm is fitted at the bottom of a boiler drum of length 6 m and diameter 2…

Q: estion (4): Let f(x) = 2x2 + 1. Use the limit definition of the derivative to find f'(x).

Q: F1 = 48i + 73j - 14k F2 = 73i - 11j + 131k for vectors F1 + F2 =?

Q: =D4 Course da In a certain inhomogeneous linear ODE ym) +...+a,(t)y f(t). the functions y =t and…

A: As, y=t and y=t+t2.. are the solutions...

Q: A point P has position vector r, op a t?i + b t³j + c tº k. Assume: a=1.7 m/s², b = 1.1 m/s³, c =…

A: Given:Position vector, rop=at2i^+bt3j^+ct6k^

Q: Detcrmine the displacement at point 8 using the principle of virtual work. zET is constant

Q: + Ato * ES Cet 1e Share Q/ $ = x6 – 15x*y? + 15x?y4 – y6 Find the stream function.

Q: x(t) K M > At) fy a. Mä+ fx + kx + f(t) = 0 b. Mä + f* + kx = f(1) c. fä+ Mx + kx = 0 d. fä+ Mx + kx…

A: we know that, v=dxdt (eq-1) where , v= velocity,…

Q: We are considering a homogeneous linear system Ax b, where b = 0 and with A being an nxn, then the…

A: From Homogeneous linear system Ax = b Where b = 0 One solution is non zero then it is non trivial…

Q: A mechanical system is shown in the figure below. This system consists of a damper (b), spring (k)…

A: Given : To find : Change in response

Q: Obtain the differential equation of the system with its representation in Laplace transform f(t) ky…

Q: Use Lecture 3 to show that function u defined by u(x,t)= e" sin x is the unique solution of 1 du = 0…

Q: 24. Show that the function u(x, y) = x² – y? + xy is harmonic, solute the function v(x, y), so that…

Q: 6. The equation shown here is the static and dynamic coupling k +k, k,l, k,l, m ml, I, k,l, те

Q: Q10/ Four masses A, B, C and D as shown below are to be completely balanced. A B C D 30 50 40 Mass…

Q: C(s) R(s) ± G1 G2 G3 H1 H2

A: It is required to reduce given block diagram

Q: Which of the following is a scalar quantity A) electric current B) electric field C) Acceleration D)…

A: A) electric current = scalar quantity B) electric field = vector quantity C) Acceleration = vector…

Q: 2. Obtain the solution x(t) of the differential equation (using Laplace transform): * + x = sin(3t),…

Q: 置一 with spring constants e= wn is the positive direction. fhess matrix K - e the external force…

Q: Obtain the dual of the LPP given here. Maximise Z= 8X1 +10X2 + 5X3 Xi – X3 (2+AA) Subject to X1,…

Q: A spring with spring constant k = 708 N/m is attached to the ceiling. A mass m = 5.2 kg is attached…

Q: s2 + 2s o) F(s) Find inverse s4 laplace transform

A: Find the inverse laplace of the given function.

Q: The solution sets as intervals of the following inequality ǀ 3y - 7 ǀ

A: The inequality is given as, 3y-7<4

Q: Dv 1 -+-V(v•v)-vx(Vxv) Dt at 2 where Dt +v.V is known as the "substantial derivative" operator = -

A: It is to be proved as, DvDt=∂v∂t+12∇v·v-v×∇×vWhere,DDt=∂∂t+v·∇

Q: Problem 1) Determine the spring constant, k if the unstretched length of the spring is 3.2 meters…

A: Given Data: Unstretched length, L=3.2 m

Q: 9. The Normal Force is always parallel to the surface. True O False 10. When solving projectile…

Q: Given the differential equation dy = x² + y² 2 dx = with y (0) 1, compute y (0.02) using Euler's…

A: Apply modified Euler's method with serp size 0.01

Q: A conical tank having a height of 5ft and base of 12 in radius contains 0.7ft of water. How much…

A: Given:h=5 ftr=12 in =1 ft The answer does not match any options although the applied concept is…

Q: 3. A tank contains 100 gal of brine in which 50 lb of salt is dissolved. Brine containing 2 lb/gal…

Q: f (t) = t 2.

A: Given, ft=t2

Q: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

Q: Solve the given linear system by any method. 211 - I, + 3I3 + 4I, = 9 – 2I3 + 7I4 = 11 311 - 312 +…

Q: The value of the constant a of (r² + 5æy)dr + (ax² + 3y²)dy if the differential equation is exact,…

A: EXACT DIFFERENTIAL EQUATION: The differential equation Mdx+Ndy=0, is said to to be exact…

Q: a) Find c such that the vibration will be critically damped and find y(t). b) Find y(t) if c = 0.5…

A: The given values are - k=654Nm, m=4kgξ=Damping ratio = cccNatural frequency wn is given by…

Q: Determine the equivalent spring constant of the system where the spring will be located in the…

Q: An engine has three single-acting cylinders whose cranks are spaced at 120° to each other. The turn-…

A: The torque-crank angle diagram for individual cylinders can be sketched as follows,

Q: 4) Consider the following mass spring damper system: m2 u(t) Assuming that y, > y1, equation of…

Q: (15.3 cm) when it is loaded. If the body is drawn down (10 cm) from the position of time (t) if:…

A: Given DataW=1.84Nm=0.188kgx=153cm

Q: PROBLEM 2.4 A car travels at 24.0 m/s north for 40.0 min and then shift east and travels at 30.0 m/s…

A: Car's displacement is 6.79 x 104 m.

Q: The motion of a body is given by X; = X, +aX,! X, = X, +aX,t with a constant x; = X; with (x1, x2,…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 3. A skier with mass m slides up a hill, inclined with angle 0, for distance s and there is an air…

Q: Example C.W: by using the definition of the derivative, find dy/dx of the function 1- f2) fx) - х*+x…

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

100%

Problem 1
Show that if the following problem has a solution it is unique
-k
= f in (0,L)× (0,T),
(1)
u(0,t) = g,(t),"(L,t) = g,(t),0<t < T,
u(x,0) = u,(x),0<<x<L.
In (1), k is a positive constant and the functions f, go, gi and uo are given.

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 2 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

Whether this function satisfies Laplace equations are harmonic U=x²-y²-2xy-2x
1) A cylindrical rod of constant shear modulus, G is of length L and located between z=0 and z=L. It has a polar moment of inertia given by J=(Jo)/(1-Z/L) and t=-sin(πZ/2L)where Jo is a constant.The boundary conditions are dΦ(o)/dz =0 AND Φ(L)=0 Find Φ(z) and graph (1/GJo)Φ(Z), and (1/GJo)(dΦ(Z)/dz) ?
ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴍɪɴɪᴍᴜᴍ ᴅɪᴀᴍᴇᴛᴇʀ ᴏꜰ ᴀ ᴛᴀᴘᴇʀ ᴘɪɴ ꜰᴏʀ ᴜꜱᴇ ᴛᴏ ꜰɪx ᴀ ʟᴇᴠᴇʀ ᴛᴏ ᴀ ꜱʜᴀꜰᴛ, ɪꜰ ɪᴛ ɪꜱ ᴛᴏ ᴛʀᴀɴꜱᴍɪᴛ ᴀ ᴍᴀxɪᴍᴜᴍ ᴛᴏʀQᴜᴇ ᴏꜰ 750 ɪɴ-ʟʙ. ᴛʜᴇ ꜱʜᴀꜰᴛ ᴅɪᴀᴍᴇᴛᴇʀ ɪꜱ 1.5 ɪɴᴄʜᴇꜱ ᴀɴᴅ ʜᴀꜱ ᴀ ꜱᴛʀᴇꜱꜱ ᴏꜰ 20,000 ᴘꜱɪ. ᴀ. 0.252 ɪɴ ʙ. 0.452 ɪɴ ᴄ. 0.642 ɪɴ ᴅ. 0.826 ɪɴ
Find the particular solution of the following differential equation: 100 V' = 200 - 10 V where V is the dependent and t is independent. Given that when t= 0 , V = 0. Find V at 2 seconds.
Consider the following linear equations,
Integrate the function X^2+2*x on the interval 0 to 3 with a step size of .5 using the trapezoid rule.
Show step by step x = 100 SN = 7
Describe Lagrangian Approach hence show that Lagrangian's equation is given as d/dt dL/dqj - dL/dqj = 0
Using the variation of parameters, find the particular solution of (D ^ 2 + 1) * y = sec(x)
Water at T = 20°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r).
In Figure , the radial distribution function P(r) for the 2s state of hydrogen has two maxima. Find the values of r (in terms of a0) where these maxima occur.
The dependence of thermal conductivity of a material on temperature is given by an empirical equation k = a ebT where a and b are constants, and k is in W/m-K and T is in K. Spot the true statement from the following set. a, a and b have the same dimension as k. b. a has the dimension of k and b is dimensionless. c. a and b are dimensionless. d. a has the dimension of k and b has the dimension of T.