Answered step by step
Verified Expert Solution
Question
1 Approved Answer
PLEASE DO ALL PARTS: Problem 3: A one-dimension slab of thickness 2L is initially at a uniform temperature T. Suddenly, electric current is passed through
PLEASE DO ALL PARTS:
Problem 3: A one-dimension slab of thickness 2L is initially at a uniform temperature T. Suddenly, electric current is passed through the slab causing uniform volumetric heating q (W / m3) . At the same time, both outer surfaces (x = L) are subjected to a convection process at T with a heat transfer coefficient h. Use the explicit time-stepping scheme ion ihis probe. 1% 12. . 3. L+L (a) Starting from an energy balance on node 1, derive the finite-difference equation expressing conservation of energy for node 1 located on the outer surface at x =-L. Rearrange your equation to identify any important dimensionless coefficients (b) Starting from an energy balance on an arbitrary interior node j, derive the finite-difference equation expressing conservation of energy for an arbitrary interior node. (c) Starting from an energy balance on the centerline node (node N at x - 0), derive the finite-difference equation expressing conservation of energy for node N. (d) Implement your equations using the explicit time-stepping scheme. A template for the Matlab code is attached and posted online. You may also use other programs. Your program should: a. calculate and plot the temperature distribution (from x --L to 0) in system at 120 s, t 24,000, and t = 4. calculate and plot the surface temperature (Node 0) and centerline temperature (node N) as a function of time for 48,000 s. b. (e) Derive and plot the analytical solution to the steady state temperature profile and compare to the numerical results at long timeStep by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started