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Numerical Methods for Thermal and Fluid Sciences* is written for students ready to move beyond formulas and see how numerical methods are applied in thermal and fluid engineering. The book begins with a simple but powerful idea: heat transfer, fluid flow, species transport, and momentum transport share a common foundation in conservation laws. From this starting point, it develops the numerical tools needed to solve real engineering problems, including interpolation, numerical integration, linear and nonlinear algebraic equations, finite difference methods, ordinary differential equations, partial differential equations, and finite volume concepts.
Unlike general numerical methods textbooks, this book keeps thermal and fluid sciences at the center of the discussion. The examples are drawn from problems students already recognize: heat conduction in solids, transient diffusion, fin equations, convection-diffusion transport, boundary layer heat transfer, internal flows, and benchmark CFD problems. The emphasis is not only on deriving numerical schemes but also on understanding what the computed results mean physically.
A strong theme throughout the book is verification. Students are encouraged to question their numerical answers, refine grids, examine time-step effects, interpret residuals, and compare results with exact solutions, benchmark values, or expected physical trends. This approach helps build the judgment needed to use computational tools responsibly. With worked examples, end-of-chapter problems, benchmark verification cases, and sample Python and MATLAB codes, this book provides a practical and physically grounded introduction to numerical methods. It is especially suitable for first-year master’s students, senior undergraduates, and engineers who want to connect numerical analysis with real problems in heat transfer and fluid flow.
Dr. Arvind Pattamatta is a Professor in the Department of Mechanical Engineering at IIT Madras. His research interests encompass microscale energy transport, phase change heat transfer, multiphase flows, electronics and battery thermal management, as well as computational fluid dynamics. He obtained his Ph.D. from the State University of New York at Buffalo in 2009, after completing his M.Tech. at the Indian Institute of Science, Bangalore.
He has held prestigious fellowships, including the Alexander von Humboldt Fellowship (2013–14, 2024), the JSPS Fellowship (Kyushu University, 2017), and the DAAD Visiting Professorship (2011, 2016). At IIT Madras, he has taught core undergraduate courses such as Thermodynamics and Heat Transfer, as well as advanced graduate courses on Convective Heat Transfer and Micro/Nanoscale Energy Transport, with NPTEL courses reaching a wider audience. Prof. Pattamatta has published over 175 peer-reviewed journal and conference articles, authored two books, guided more than 20 graduate students, and organized several international workshops and conferences. He also coordinates the ISRO-IITM Centre of Excellence for Research in Fluid and Thermal Sciences, fostering collaborations with leading researchers worldwide.
Dr. Laxman Kumar Mala is an Assistant Professor in the Department of Mechanical Engineering at the College of Engineering, Bhubaneswar, Odisha. His research spans convective heat transfer, multiphase flows, surface wettability engineering, and advanced thermal management systems. He obtained his Ph.D. from the IIT Bombay–Monash Research Academy and completed his M.Tech. from IIT Bhubaneswar.
During his doctoral research, he specialized in interfacial phenomena and droplet dynamics, focusing on both the fundamental and applied aspects of fluid surface interactions. Before joining academia, Dr. Mala served as an Institute Postdoctoral Fellow at IIT Madras, where he worked on cutting-edge thermal management technologies, including pulsating heat pipes and thermosyphons. He has published extensively in reputed international journals and holds patents related to novel heat-transfer devices. With a strong commitment to teaching, research, and innovation, Dr. Mala continues to explore emerging frontiers in thermal engineering and develop advanced methods for enhancing heat transfer.
1. Transport Equations in Thermal and Fluid Sciences
2. Foundations: Taylor Series, Interpolation, and Numerical Integration
3. Linear Algebraic Equations
4. Nonlinear Algebraic Equations
5. Basics of Finite Difference Methods
6. Numerical Solution of Ordinary Differential Equations
7. Numerical Solution of Partial Differential Equations
8. Overview of Discretization Methods for Transport Equations
9. Standard Benchmark Problems for Numerical Verification in Thermal and Fluid Sciences
10. Sample Python and MATLAB Codes
