Mechanical

A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity

Numerical analysis is one of the most researched fields today. Getting an exact solution for physical problems is too difficult and again for most of the physical problems exact solution does not exist at all, so numerical techniques are preferred to obtain a fairly exact solution with ease. In this project, you will write your own codes to simulate temperature distribution over a 1D flat plate and compare its result with the exact solution to check the accuracy of your Numerical solution.

Read more..

A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity project Looking to build projects on Mechanical?:

Mechanical Kit will be shipped to you and you can learn and build using tutorials. You can start for free today!

1. 3D Printer

2. Automobile Prototyping

3. CNC Machine using Arduino

4. Project Management with Primavera


Heat transfer is classified into various mechanisms, such as conduction, convection, radiation. The simplest mode of heat transfer is by conduction. Conductive heat transfer is the phenomena in which heat is transferred from one body to another due to temperature difference when they came in contact. In this project, you are going to solve a few conductive heat transfer problems using Finite Difference Method (FDM). You need to find the Analytical solutions to, governing differential equations for one-dimensional steady-state conduction, without heat generation and constant thermal conductivity. And after that, you need to find the Numerical solutions for those equations using FDM.

Problem Description:

One Dimensional Flat Plate Problem: A Iron wire of uniform conductivity is exposed to the environment. One side of the wire is in contact with a heat source of 1000°C. The length of the wire is 2 meter and the atmospheric temperature is 30°C. Determine the temperature distribution over a rod during steady state.

Project Description:

  1. FDM: This is one of the discretization techniques used in numerical analysis to solve differential equation by approximating the derivatives. Here we discretize both space and time into N no of data points, where we store the data and keep updating as we move forward in time.
  2. Taylors Series Expansion: To implement the finite difference method, Taylor series representation of a function should be known. In mathematics, Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function’s derivatives at a single point. That is, if a function is continuous and we know its derivative at a point, then we can easily determine its value on the next neighboring point in the domain by using Taylor series.
  3. Forward in Time Central in Space (FTCS) discretion: Among all the discretization techniques FTCS scheme is more preferred in FDM for producing an accurate and stable result. In this technique, while computing we will march forward in time and central in space.

How to build Mechanical projects Did you know

Skyfi Labs helps students learn practical skills by building real-world projects.

You can enrol with friends and receive kits at your doorstep

You can learn from experts, build working projects, showcase skills to the world and grab the best jobs.
Get started today!


Project Implementation:

  1. Find Analytical solutions to, governing equations for one-dimensional steady-state conduction, without heat generation and constant thermal conductivity. In this step, you also need to write C programming codes to calculate the temperature distribution over the given plate using the solution you got by solving above differential equations. At the end save all the result data in a text file.
  2. Then, you have to find the Numerical solution to those equations using FDM. To do so, write codes to discretize the domain and initialize the boundary condition. Chose Forward in time and Centre in space discretization (FTCS) to get a better result. Interact the solution for a number of times until you get an accuracy of 10e-5. Don’t forget to save the result data in a text file.
  3. Plot the result data using Gnuplot or Minitab. For plotting, contours use Miniplot for ease and convenience.
  4. Compare your result for an analytical solution and numerical solution by plotting them simultaneously. If both of your solutions are coinciding or near to coincide then your numerical solution is correct.

Project Brief: By doing this project you can observe that, the temperature distribution over the material is linear when the thermal conductivity of the material is assumed to be constant.

Software requirements:

  1. Dev-C++: You will be needing Dev-C++ software to write logic and interact the solution for a number of times.
  2. Gnuplot: Also, you will be needing plotting software such as Gnuplot to plot the result data and compare the solution.

Programming language: C programming language


Latest projects on Mechanical

Want to develop practical skills on Mechanical? Checkout our latest projects and start learning for free


Kit required to develop A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity:
Technologies you will learn by working on A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity:
A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity
Skyfi Labs Last Updated: 2022-04-18





Join 250,000+ students from 36+ countries & develop practical skills by building projects

Get kits shipped in 24 hours. Build using online tutorials.

More Project Ideas on Mechanical

Mechanical Foot Step Power Generator
Gearless Transmission Using Elbow Mechanism
Freedom WheelChair
Pneumatic Braking System
Automatic Braking Systems for Automobiles
Energy Glider
Water Jet Cutting Tool
Design and fabrication RC speedboat
Abrasive Jet Machine
Radio-Controlled Flying Wing
Autonomous fixed wing (drone)
Smartphone Controlled Paper Plane
Smartphone Controlled Paper Plane
Solar Endurance Flight
Smart Power Shoe
How to Develop an RC Ornithopter
AERIAL MAPPING DRONE
INDOOR POSITION HOLD MULTICOPTER DRONE
V TOL (DRONE)
OBSTACLE AVOIDANCE DRONE
Gesture Controlled Drone
Hybrid Drone
HIGH POWERED DRONE
RC-VTOL
Voice Controlled Drone
AUTONOMOUS MULTICOPTER DRONE
Ocean Drone
Saucer Solar Drone
Car Copter
Electric Balloon Car
RC Helicopter
Homework Writing Machine with Arduino and Servo Motor
Mini Refrigerator
Hard water converter
Sterling Engine Helicopter
Eco Cooler
EL-bow mechanism – Gearless Transmission System
Tricopter
Everything you need to know about mercury vortex engines
Bucky paper Technology
Cryogenic grinding
Magnetic Bearing
Zero Turn Drives
Hyper loop
Laser Ignition System
Transformer Humanoid Automobile
Zero gravity 3D printer
2 Stroke Electric engines
Shape Memory Effect–Intelligent Alloys
3D Bio-printing Technology
Rail Gun
How to select the bldc motor for multicopter
5th Wheel Car Parking System
Gauss Accelerator
Electromagnetic Hover Car
Plasma Propulsion
Plasma Rail Gun
Light Gas Gun
Space Gun
Pneumatic Vulcanizing Machine
CNC Machine using Arduino
AUTOMATIC BIKE STAND
AUTOMATIC HAMMERING MACHINE
ROLLER BENDING MACHINE
STAIRCASE CLAIMING TROLLEY
Mini Peltier Based Cooler
A Numerical Solution to One-Dimensional Euler equation, Shock tube Problem
A Numerical Solution to 2D Flat Plate Problem with Constant Conductivity Heat Transfer
Design of Water Quality Monitoring System using MSP430
3D printing using DLP Projectors
Black Box for RC Aircrafts
Electromagnetic Engines for Transportation
Glass Hybrid Fibres Epoxy Composite Material using Hand Layup Method
Vortex Bladeless Turbines
Manufacturing of MEMS
Automatic Pneumatic Paper Cutting Machine
Design and Fabrication of Automated Portable Hammering Machine
A Numerical Solution to Quasi-One-Dimensional Nozzle
A Numerical Solution to One Dimensional Conductive Heat Transfer with Constant Conductivity
A Numerical solution to One Dimensional Conductive Heat Transfer with Variable Conductivity
A Numerical Solution to Two-Dimensional Variable Conductivity Heat Transfer
Domestic Thermal Insulation with Sugarcane Composite
Understanding The Finite Difference Method by Solving Unsteady Linear Convection Equation
Understanding FVM(Lax Friedrich scheme) by solving Burger equation
Fabrication of Fiber reinforced composite material from Bamboo, Flex and Glass Fiber
A Numerical Study on Different Types of Fins
Microstructure and Thermal (TGA & DTA) Analysis of a Polymer Based Composite Material
Project on Pressure Drop Analysis in a Capillary Tube
Numerical Solution and Visualization of Two Blast Wave Interaction
Pedal Operated Water Pump
Analysis of Turbulence in a Two Dimensional Cavity Flow
Gas Detection System
Designing of Hydrogen Fuel car
Electromagnetic Shock Absorbers
Soap Free Building Sealant
Innovative Ground Storage
Dynamic Study of Soil Parameters
Centrifugal Pump
Self Priming Centrifugal Pump
Turbo Pump
Axial Flow Pump
Diaphram Pump
Plasma Ignition
Ram Accelerator
StarTram
Aluminium Powered Car
Perpendicular Wind Turbines
Electromagnetic propulsion System
Miniature Shiftless Transmission
3D Printed Etching Press
Portable Loom
Hypnotic Plotter
Reconnaissance Drone
3D Printed DNA extractor
Health Monitoring Drone
Forward swept wing RC aircraft
Laser Propulsion
Repair of carbon composites
Quadrotor using Arduino
Drone Swarm
Cylinder-shaped Coaxial Drone
Drone-hunting Drone
Racing Drone
Compressed Air Powered Drone
Window washing drone
Performance analysis of paraffin wax,bees wax and magnesium for hybrid rocket motor
Fabrication and testing of light weight composites for UAV
Unmanned Aerial Photography using Flying Robot
Underwater Turbines
Power Generation by Seebeck Effect
Application of drones in construction
Smart Photography Drone
Heat power economy
Project on Missile Detection and Automatic Destroy System
Production of biodiesel from silkworm pupae for aircraft use
Improvement of aircraft accident investigation through expert systems
Flow analysis over a cylinder using ICM CFD
Self Inflating Tyres
CFD Analysis of a car
RC Hovercraft using Arduino
Autonomous Racing Drone
Ducted Fan Drone
Airborne Virus detector (Corona,SARS,Flu)
Airborne wind energy generation using Aerostat

Subscribe to receive more project ideas

Stay up-to-date and build projects on latest technologies