please help me solve this problem show step by step 1. A two-dimensional rectangular plate is subjected to prescribed boundary conditions. Using theresults of the exact solution for the heat equation presented in Section 4.2, calculate the temperatureat the midpoint (1, 0.5) by considering the first five nonzero terms of the infinite series that mustbe evaluated. Assess the error resulting from using only the first three terms of the infinite series.Plot the temperature distributions T(x, 0.5) and T(1.0, y).Answer: T(1,0.5)=94.5°Cy (m)T₂ = 150°C1T₁ = 50°C-%T₁ = 50°C►x (m)2-T₁ = = 50°C

Step 1:Series Solution for the Temperature: The temperature at any point on the plate can be…

Answered: 1. A two-dimensional rectangular plate…

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 4.21P

See similar textbooks

Similar questions

5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?
T1=68 T2=43 Q3:
Q1 Passage of an electric current through a long conducting rod of radius r; and thermal conductivity k, results in uniform volumetric heating at a rate of ġ. The conduct- ing rod is wrapped in an electrically nonconducting cladding material of outer radius r, and thermal conduc- tivity k, and convection cooling is provided by an adjoining fluid. Conducting rod, ġ, k, 11 To Čladding, ke For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express ap- propriate boundary conditions for the solution of these equations.
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
Please show all work for this mechnical measure problem. Not Ai generated the answers have been wrong I need to understand.
2
A 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170
Suppose that a finite-difference solution has been obtained for the temperature T, near but not at an adiabatic boundary. in most instances, it would be necessary or desirable to evaluate the temperature at the boundary point itself. for this case of an adiabatic boundary, develop an expression for the temperature at the boundary T1, in the terms of temperatures at neighbouring points T2, T3, etc, by assuming that the temperature distribution in the neighbourhood of the boundary is a straight line a second-degree polynomial a cubic polynomial (you only need to indicate how you would derive this one) indicate the order of T.E in each of the above approximations used to evaluate T1
A solid cylinder of radius R and length L is made from material with thermal conductivity 2. Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time). (a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature distribution in the cylinder, given that the surface temperature is Ts. (b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along the axis of the mouse, as in part a.)
2. A slab of thickness Lis initially at zero temperature. For times t> 0, the boundary surface at x 0 is subjected to a time-dependent prescribed temperature f(t) defined by: a + bt for 0Ti and the boundary at x = L is kept insulated. Using Duhamel's theorem, develop an expression for the temperature distribution in the slab for times (i) t t1.
The subject is Mechanics of Deformable Bodies
After a thorough derivation by Doraemon to establish an equation for cylindrical fuel rod of a nuclear reactor. Here he was able to come up an equation of heat generated internally as shown below. 96 = 9. where qG is the local rate of heat generation per unit volume at radius r, ro is the outside radius, and qo is the rate of heat generation per unit volume at the centre line. Calculate the temperature drop from the centre line to the surface for a 2.5 cm outer diameter rod having k = 25 W/m K, if the rate of heat removal from the surface is 1650 kW/m2 A 619 °C 719 °C C) 819 °C 919 °C E 1019 °C F None of these

SEE MORE QUESTIONS

Recommended textbooks for you

Principles of Heat Transfer (Activate Learning wi…

Mechanical Engineering

ISBN:

9781305387102

Author:

Kreith, Frank; Manglik, Raj M.

Publisher:

Cengage Learning