Foundations of Transport Phenomena with Vector and Tensor Analysis

Transport phenomena form the backbone of modern chemical, mechanical, and materials engineering, yet mastering the underlying mathematics can often feel like a hurdle. Understanding how mass, momentum, and energy move requires a solid grasp of spatial changes and physical directions. This text-only course breaks down complex mathematical frameworks into intuitive, readable concepts, giving you the confidence to set up and solve transport equations. You will start by learning fundamental physical quantities before advancing to the coordinate systems and vector calculus used to describe fluid flow and heat transfer. What you'll learn: Understand the physical meaning of scalar, vector, and tensor fields in engineering contexts; Master vector operations including dot products, cross products, and gradient calculations; Apply divergence and curl theorems to formulate conservation laws; Learn to work confidently with cylindrical and spherical coordinate systems; Translate physical transport problems into precise mathematical equations; Examine how modern computational tools utilize tensor grids to simulate fluid dynamics. This course begins with essential definitions of transport properties and basic mathematical notation, then guides you through vector calculus and coordinate transformations, and concludes with practical applications in fluid flow and heat transfer. This course is designed for undergraduate engineering students and self-directed learners who want to build a strong mathematical foundation in transport processes without any prior advanced calculus prerequisites. Begin reading today to unlock the mathematical language of engineering transport.