When a sheet metal is suddenly removed from an oven and exposed to the environment, it cools due to loss due to convection. The rate at which the plate temperature T varies with time is given by: A, F[ h(T– T„)] pVC, dT dt where As is the surface area of the plate, p = 300 kg / m³ is its mass density, V is its volume, CV= 900 J/ kg / K is your specific heat in the volume condition constant. In addition, h = 30 W / m² / K is the coefficient heat transfer and To is the temperature environment. Given the information above, obtain: a) The algebraic equation that represents the ODE described by the model using a power series. b) The Txt graph using 10 terms of the series, and compare the result with the solution analytical method obtained by the Laplace transform. Data: V = 0,003 m³; As = 0,25 m²; T(0) = 673 K; T = 298 K

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
icon
Related questions
Question

Please use power series solution. Also the temperature should decrease

When a sheet metal is suddenly removed from an oven and
exposed to the environment, it cools due to loss due to
convection. The rate at which the plate temperature T varies
with time is given by:
A,
-[ h(T– T„)]
pVC,
dT
%3D
dt
where As is the surface area of the plate, p = 300 kg / m³ is
its mass density, V is its volume, CV= 900 J/ kg / K is your
specific heat in the volume condition constant. In addition,
h = 30 W / m² / K is the coefficient heat transfer and To is
the temperature environment. Given the information above,
obtain:
a) The algebraic equation that represents the ODE described
by the model using a power series.
b) The T xt graph using 10 terms of the series, and compare
the result with the solution analytical method obtained by
the Laplace transform.
Data: V = 0,003 m³; As = 0,25 m²; T(0) = 673 K; To = 298
K
Transcribed Image Text:When a sheet metal is suddenly removed from an oven and exposed to the environment, it cools due to loss due to convection. The rate at which the plate temperature T varies with time is given by: A, -[ h(T– T„)] pVC, dT %3D dt where As is the surface area of the plate, p = 300 kg / m³ is its mass density, V is its volume, CV= 900 J/ kg / K is your specific heat in the volume condition constant. In addition, h = 30 W / m² / K is the coefficient heat transfer and To is the temperature environment. Given the information above, obtain: a) The algebraic equation that represents the ODE described by the model using a power series. b) The T xt graph using 10 terms of the series, and compare the result with the solution analytical method obtained by the Laplace transform. Data: V = 0,003 m³; As = 0,25 m²; T(0) = 673 K; To = 298 K
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Basic Thermodynamic Processes
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.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY