Repeat Example 31.1, but for
To calculate: The solution to the Poisson’s equation
Answer to Problem 1P
Solution: Solution to the Poisson’s equation for provided boundary equation is
Explanation of Solution
Given Information:
Poisson’s equation:
Here, function
Boundary conditions are as
The value of the uniform heat source is
Formula used:
If a differential is in the form
Calculation:
Consider the problem statement, the expression for the boundary condition is:
The Boundary condition is provided as follows:
The general solution to the differential equation is:
Differentiate it with respect to
Compares the equations with each other.
Apply the boundary condition
Apply the boundary condition
Substitute
Use the following MATLAB command to execute the code and plot the temperature as a function of position along the rod.
Now, execute the program by pressing run button. Following plot is obtained that shows the plot of temperature verses distance.
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Chapter 31 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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- For Heat transfer through cylinder tube wall, the temperature is to be a linear function of r (radius) of the tube. Select one: O True O False The conductivity of H20 in solid form (ice) is higher than that of H20 in liquid form (water). Select one: O True O False F, (Correction factor for temperature in some heat exchangers) should be 1.0 or greater than 1.0 in some cases. Select one: O True Falsearrow_forwardThe pressurized water that enters a cross-flow heat exchanger with a flow of 1 kg / s at 35 ° C and leaves at 125 ° C, where fluids do not mix, is heated by exhaust gases entering the heat exchanger at 300 ° C and exiting at 100 ° C. . The total heat transfer coefficient defined according to the surface on the gas side is 100 W / m ° K. Thermal properties of exhaust gases are considered as atmospheric air. a) Find the required surface area on the gas side. (15P) Due to the contamination that occurs over time, the inlet temperature and flow rate of the water in the heat exchanger remain the same, while the outlet temperature drops to 105 ° C *.a) Calculate the new condition with the acceptance of fixed thermal properties, b) Heat transfer, c) Exhaust gases exit temperature.arrow_forwardAnswer this using 7 steps below: GIVEN: REQUIRED: ASSUMPTION: ILLUSTRATION: FOMULA: SOLUTION: ANSWER:arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning