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APPLICATION OF NUMERICAL METHODS TO SOLVE HEAT TRANSFER CONDUCTION EQUATIONS

HEAT TRANSFER CONDUCTION EQUATIONS

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APPLICATION OF NUMERICAL METHODS TO SOLVE HEAT TRANSFER CONDUCTION EQUATIONS

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  1. APPLICATION OF NUMERICAL METHODS TO SOLVE HEAT TRANSFER CONDUCTION EQUATIONS

  2. What is Heat Transfer? Why Heat Transfer? Itisthemovementofthermalenergyfrom one thing to another thing of different temperature. UPTO EX- TREME BLAST BOOM!! MORE HEATE -D HEAT -ED

  3. HOWHEATCAN BE TRANSFERRED? HEAT TRANSFER MODES:

  4. SIMPLEDERIVATION BY ENERGYCONSERVATION

  5. FURTHER SIMPLIFICATIONS

  6. Heat generation rate-Thickness - 120mm • Conductivity - 200W/mk • Surface Temperatures –130and150 ( degree celsius) • Determine temperature at quarter and midplanes. Proving Finite Diference Methodbysolvingareallife Problem

  7. T1 T2T3 T1 =151.75 T2 =149 T3 =141.75 (All temperatures are in degree centigrade ) ANALYTICAL SOLUTION-- NUMERICAL SOLUTION-- T1 =150 T2 =148 T3 =140

  8. Analytical solutions are limited to problems that aresimple • or can be simplified with reasonableapproximations. • Tendency to oversimplify the problem to make the mathematical model sufficiently simple to warrant an analytical solution. • Solving such equations usually requires mathematical sophistication beyond that acquired at the undergraduate level, such as orthogonality, eigenvalues, Fourier and Laplace transforms, Bessel and Legendre functions, and infinite series. • A mathematical model intended for a numerical solution is likely to represent the actual problembetter. • Computers and numerical methods are ideally suited for such calculations, and a wide range of related problems can be solved by minor modifications in the code or inputvariables. WhyNumerical Methods?

  9. 2 Dimensional Steady StateConduction with heat generation - leads to LAPLACEEQUATION without heat generation - LEADS TO POISSON EQUATION Can be solved byLIEBMAN’S ITERATION PROCESS FOLLOWED BY GAUSS SEIDALMETHOD. MajorApplications

  10. 1 Dimensional Transient heat conduction equation : Can be solved by Schmidt explicit method Crank-Nicolson implicit method Continued..

  11. Used in AnalysisSoftwares Ex.-ANSYS Continued..

  12. Thank you.

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