2) iterations. At the end of the second iteration, calculate the percentage errors of all de temperatures and identify the max. % error. Also, compute the heat fluxes for all terior and insulated boundary nodes. The heated plate dimensions are 12 x 12 cm and ermal conductivity K = 0.47 cal/(s.cm.°C). A square grid is used for discretization. y central finite difference expressions for the temperature derivatives in the x- and y- ions. Express the computed temperatures and heat fluxes on a square plate domain ically (temperatures will be represented by their values written next to the nodes in omain and heat flux vectors will be represented by arrows in which the length of the will show the magnitude of the resultant heat flux and the arrow will show the ation of the heat flux vector). Each student is supposed to solve his own problem ding to the problem set distribution shown below. 87.5°C 75°C 37.5°C (1, 2) (1, 1) 100°C 0°℃ (2, 2) (2, 1) 100°C (3, 2) Insulated (3, 1) 0°C 12 cm

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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show the solution on paper with all details and draw nudes direction

 
Use Liebmann method (Gauss-Seidel) to solve for the unknown steady-state temperatures
of the heated plate interior and insulated nodes of a heated square plate as shown in the
figure below with the given boundary conditions. Use a relaxation factor of 1.3 and perform
two (2) iterations. At the end of the second iteration, calculate the percentage errors of all
the node temperatures and identify the max. % error. Also, compute the heat fluxes for all
the interior and insulated boundary nodes. The heated plate dimensions are 12 x 12 cm and
the thermal conductivity k' = 0.47 cal/(s.cm.°C). A square grid is used for discretization.
Apply central finite difference expressions for the temperature derivatives in the x- and y-
directions. Express the computed temperatures and heat fluxes on a square plate domain
graphically (temperatures will be represented by their values written next to the nodes in
the domain and heat flux vectors will be represented by arrows in which the length of the
arrow will show the magnitude of the resultant heat flux and the arrow will show the
orientation of the heat flux vector). Each student is supposed to solve his own problem
according to the problem set distribution shown below.
87.5°C
75°C
37.5°C
(1, 2)
(1, 1)
100°C
0°C
(2, 2)
Problem Set
(2, 1)
12 cm
100°C
(3, 2)
Insulated
(3, 1)
0°C
12 cm
Transcribed Image Text:Use Liebmann method (Gauss-Seidel) to solve for the unknown steady-state temperatures of the heated plate interior and insulated nodes of a heated square plate as shown in the figure below with the given boundary conditions. Use a relaxation factor of 1.3 and perform two (2) iterations. At the end of the second iteration, calculate the percentage errors of all the node temperatures and identify the max. % error. Also, compute the heat fluxes for all the interior and insulated boundary nodes. The heated plate dimensions are 12 x 12 cm and the thermal conductivity k' = 0.47 cal/(s.cm.°C). A square grid is used for discretization. Apply central finite difference expressions for the temperature derivatives in the x- and y- directions. Express the computed temperatures and heat fluxes on a square plate domain graphically (temperatures will be represented by their values written next to the nodes in the domain and heat flux vectors will be represented by arrows in which the length of the arrow will show the magnitude of the resultant heat flux and the arrow will show the orientation of the heat flux vector). Each student is supposed to solve his own problem according to the problem set distribution shown below. 87.5°C 75°C 37.5°C (1, 2) (1, 1) 100°C 0°C (2, 2) Problem Set (2, 1) 12 cm 100°C (3, 2) Insulated (3, 1) 0°C 12 cm
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