Finite Difference Methods in Heat TransferCRC Press, 12 de jul. de 2017 - 600 páginas Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions. |
Conteúdo
Basic Relations | 7 |
Discrete Approximation of Derivatives | 20 |
Methods of Solving Sets of Algebraic Equations | 43 |
OneDimensional SteadyState Systems 75 KK 22 | 75 |
OneDimensional Parabolic Systems 99 | 100 |
Elliptic Systems | 189 |
Hyperbolic Systems | 227 |
Nonlinear Diffusion | 249 |
Hybrid NumericalAnalytic Solutions | 359 |
Convection Inside a Parallel Plate Duct with Step Change | 369 |
References | 377 |
Appendices | 395 |
Program to Solve Example 101 | 401 |
w w | 407 |
| 409 | |
Phase Change Problems | 275 |
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Termos e frases comuns
algebraic equations algorithm boundary conditions boundary node boundary surface calculations central difference formula central differencing computational domain Consider the following constant control volume convection convection boundary condition convection term coordinates Crank-Nicolson method derivative determined difference approximation diffusion equation dimensionless discretize energy equation enthalpy exact solution explicit method Figure finite finite-difference approximation finite-difference equations finite-difference form finite-difference representation first-order flow fluid Gauss-Seidel given by Eq grid points heat conduction equation heat conduction problem heat transfer coefficient hyperbolic heat conduction implicit initial condition integral transform internal nodes iteration level n+1 mesh nonlinear numerical solution Nusselt one-dimensional parabolic partial differential equations physical domain Poisson's equation prescribed heat flux second-order accurate simple explicit scheme solidification solved stability criterion step stream function symmetry T₁ thermal conductivity Thomas algorithm TM+1 transient heat conduction truncation error two-dimensional unknown node temperatures upwind values variables vector vorticity αΔι Δχ ат дх ду эт ᎧᎢ