In the preceding section of Steady State, 1-D
heat conduction analysis, we considered
conduction problems for which the
temperature distribution in a medium was
determined solely by conditions at the
boundaries of the medium
Derivation and solution of the heat equation in 1-DIJESM JOURNAL
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
The Mean Value Theorem is the most important theorem in calculus. It is the first theorem which allows us to infer information about a function from information about its derivative. From the MVT we can derive tests for the monotonicity (increase or decrease) and concavity of a function.
Solution Manual for Heat Convection second edition by Latif M. Jijiphysicsbook
Solution Manual for Heat Convection
https://unihelp.xyz/solution-manual-for-heat-convection-by-latif-jiji/
****
Solution Manual for Heat Conduction
https://unihelp.xyz/solution-manual-heat-conduction-latif-jiji/
Solution Manual for Heat Convection second edition by Latif M. Jiji
Heat Conduction with thermal heat generation.pptxBektu Dida
Heat Conduction analysis is done in one dimensional steady state heat conduction considering internal heat generation per unit volume on plane and radial walls. Examples are directly taken from textbooks.
Derivation and solution of the heat equation in 1-DIJESM JOURNAL
Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
The Mean Value Theorem is the most important theorem in calculus. It is the first theorem which allows us to infer information about a function from information about its derivative. From the MVT we can derive tests for the monotonicity (increase or decrease) and concavity of a function.
Solution Manual for Heat Convection second edition by Latif M. Jijiphysicsbook
Solution Manual for Heat Convection
https://unihelp.xyz/solution-manual-for-heat-convection-by-latif-jiji/
****
Solution Manual for Heat Conduction
https://unihelp.xyz/solution-manual-heat-conduction-latif-jiji/
Solution Manual for Heat Convection second edition by Latif M. Jiji
Heat Conduction with thermal heat generation.pptxBektu Dida
Heat Conduction analysis is done in one dimensional steady state heat conduction considering internal heat generation per unit volume on plane and radial walls. Examples are directly taken from textbooks.
One dim, steady-state, heat conduction_with_heat_generationtmuliya
This file contains slides on One-dimensional, steady-state heat conduction with heat generation.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
It is hoped that these Slides will be useful to teachers, students, researchers and professionals working in this field.
This chapter contains:-.
Analytical Methods of two dimensional steady state heat conduction
Finite difference Method application on two dimensional steady state heat conduction.
Finite difference method on irregular shape of a system
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
Similar to Conduction with Thermal Energy Generation.pdf (20)
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
ML for identifying fraud using open blockchain data.pptx
Conduction with Thermal Energy Generation.pdf
1. 20ME301T – Heat Transfer
Dr. Rajesh Patel
Mechanical Engineering Department
School of Technology
Pandit Deendayal Petroleum University
Conduction with Thermal Energy
Generation
2. Conduction with Thermal Energy
Generation
In the preceding section of Steady State, 1-D
heat conduction analysis, we considered
conduction problems for which the
temperature distribution in a medium was
determined solely by conditions at the
boundaries of the medium.
The objective of this study is to consider
situations for which thermal energy is
being generated due to conversion from
some other energy form.
3. Conduction with Thermal Energy
Generation
A common thermal energy generation process involves:
Exothermic Chemical Reaction
Conversion from electrical to thermal energy in a
current-carrying medium (Ohmic, or resistance, or
Joule heating).
The rate at which energy is generated by
passing a current I through a medium of
electrical resistance Re is
4. Conduction with Thermal Energy
Generation
If this power generation (W) occurs uniformly
throughout the medium of volume V, the
volumetric generation rate (W/m3) is then
5. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Consider the plane wall with uniform energy generation per unit volume
( is constant) and the surfaces are maintained at Ts,1 and Ts,2.
6. Heat Conduction with Thermal Energy
Generation in a Plane Wall
For steady state, 1-D heat conduction with heat
generation in a isotropic material (constant thermal
conductivity k), above equation will be reduced to
(1)
The general solution of Eqn. (1) is given by
(2)
7. Heat Conduction with Thermal Energy
Generation in a Plane Wall
(2)
Boundary Conditions:
B.C - I At x = -L T(-L) = Ts,1 (3)
B. C –II At x = L T(L) = Ts,2 (4)
Substituting B.C’s in Eqn. (2) , The constants may be evaluated as
(5)
Substituting constants
C1 and C2 in Eqn. (2)
8. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Eqn. (6) represents the temperature distribution
(6)
9. Heat Conduction with Thermal Energy
Generation in a Plane Wall
(6)
Case-I: Symmetric boundary conditions
The temperature distribution is then symmetrical about
the mid-plane as shown in Figure. Ts,1 = Ts,2 = Ts
For the symmetric boundary conditions, Eqn. (6)
will be reduced to;
(7)
10. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(7)
The maximum temperature exists at the mid-
plane (x=0)
(8)
Combining Eqn. (7) and (8), temperature distribution can be written as;
(9)
11. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
Note that at the plane of symmetry in Figure, the
temperature gradient is zero, (dT/dx)x=0 = 0.
Accordingly, there is no heat transfer across this
plane, and it may be represented by the
adiabatic surface
(9)
12. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(9)
Above results (equations) can be applied to
plane walls that are perfectly insulated on one
side (x=0) and maintained at a fixed temperature
Ts on the other side (x = L).
13. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
Estimation of surface temperature Ts
Applying the energy balance at the surface at x = L
(Heat Conduction at surface at x = L) = (Heat
convection from surface x = L)
(1)
(2)
14. Heat Conduction with Thermal Energy
Generation in a Plane Wall
Case-I: Symmetric boundary conditions
(1)
(2)
Getting value of (dT/dx)x=L from Eqn. (1)
and substituting in Eqn. (2)
(3)
15. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
For steady-state conditions the rate at which heat
is generated within the cylinder must equal the
rate at which heat is convected from the surface
of the cylinder to a moving fluid.
For steady state,radial heat conduction with heat generation in a isotropic
material (constant thermal conductivity k), above equation will be reduced to
(1)
(2)
16. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(2)
Integrating above equation twice, the general
solution for the temperature distribution can be
written as;
(3)
Boundary Conditions:
B.C - I At r = 0 (dT/dr) r=0) = 0 (4)
B. C –II At r = r T = Ts (5)
Substituting B.C’s into Eqn. (3), C1 and C2 can be estimated as;
17. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(2)
(3)
Substituting C1 and
C2 into Eqn. (3)
(4)
Represents temperature distribution
For steady state radial heat
conduction with heat generation on
cylindrical component
18. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
Centerline temperature can be evaluated as
(4)
(5)
From Eqn (4) and (5), the temperature distribution in non-dimensional form
can be written as
19. Radial Heat Conduction with Thermal
Energy Generation in a Cylinder
(4)
Estimation of surface temperature Ts
From Overall Energy balance
(Heat Generation rate in system) = (Heat Convection from Surface)