Convective heat transfer plays a role in many branches of science and engineering, as well as in aspects of daily life. Due to its importance, it deserves to be given a closer look. This book shows some real complexities of convective heat transfer in more rigorous ways, with most aspects described by partial differential equations. Defined by Fourier's law, heat flux is transported by convection. Thus, the transport of heat flux can be described using the convective transport equation of the heat flux, which may provide more information. The significance of this description is that the velocity gradient's contribution to the transport of heat flux is stated implicitly and may be connected to the mechanical dissipation. A description of the transport of the momentum flux is provided in this book, focusing on both the mechanical energy prepared by production from the main flow and the mechanical energy dissipated by vorticity. Based on the convective transport equations of heat flux and momentum flux, a correlation between the contribution to the transport of heat flux and mechanical energy production and dissipation is established. Additional topics discussed herein include the transport characteristics of heat flux, the impact of velocity and its gradients on the transport of heat flux in a channel flow, a tube flow, a channel flow with vortex generators and a twisted elliptical tube flow. As secondary flow and vorticity are commonly used for the enhancement of convective heat transfer, the roles of secondary flow and vorticity in the convective transport of heat flux are discussed. The intensity of convective heat transfer is only defined by the surface which heat is transferred through; it is not defined in the fluid region. Combustion science, oceanography, meteorology, and geoscience pay much attention to local convective heat transfer intensity. This book verifies the rationality of local convective heat transfer intensity.