1 / 1

Numerical Simulation of Heat Transfer: Explicit and Implicit Methods Comparison

This document details a computational method for simulating heat transfer using both explicit and implicit algorithms. It sets parameters such as time and space steps, iterations, and boundary conditions. The method incorporates a point-by-point solver approach, with a focus on achieving accurate temperature distribution over time. The results compare the derived temperatures from both approaches, noting their effectiveness at reaching equilibrium at a center temperature of 50°C. Insights into the differences in performance based on time step configurations are highlighted, providing a comprehensive view of numerical methodologies in heat simulation.

lynnea
Download Presentation

Numerical Simulation of Heat Transfer: Explicit and Implicit Methods Comparison

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Transient Homework Hints Set a time step and number of time steps in control program %control clear all delta=1/11; %space step-KEEP FIXED t_total=0.4 %total time KEEP fixed delt=0.001; %time step--can vary n_time_steps=t_total/delt; data coefficient tran_coef solve_exp %or solve_imp plot(tim,Thist) hold on Make sure all BVALS are zero %tran_coeff for i=1:n at(i)=delta^2/delt; end %solve_imp %implict solver %A simple point by point solver %initial values for i=1:n T(i)=100; Told(i)=100; end for tim_step=1:n_time_steps for it=1:250 %iterations set to a large number for i=n:-1:1 SUM=0; for j=1:Nsup(i) % loop on nb points SUM=SUM+a(i,j)*T(S(i,j)); end SUM=SUM+b(i)+at(i)*Told(i); T(i)=SUM/(ai(i)+at(i)); end end %Befor next time step do an old for new for i=1:n Told(i)=T(i); end Thist(tim_step)=T(61); tim(tim_step)=tim_step*delt; end %solve_exp %implict solver %A simple point by point solver %initial values for i=1:n T(i)=100; Told(i)=100; end for tim_step=1:n_time_steps for i=n:-1:1 SUM=0; for j=1:Nsup(i) % loop on nb points SUM=SUM+a(i,j)*Told(S(i,j)); end SUM=SUM+b(i)+at(i)*Told(i)-ai(i)*Told(i); T(i)=SUM/(at(i)); end %Befor next time step do an old for new for i=1:n Told(i)=T(i); end Thist(tim_step)=T(61); tim(tim_step)=tim_step*delt; end Solve-IMP Solve-EXP Result check With a time step of 0.001 the explicit and implicit codes are almost identical Tcenter =50 is reached between 0.059 and 0.06 in explicit and between 0.06 and 0.061 in imp. When delt=0.01 the imp code raches Tceter=50 between 0.06 and 0.07

More Related