Momentum, heat, and mass transfer are three fundamental transport phenomena that occur in various engineering fields, including chemical, mechanical, aerospace, and environmental engineering. The study of these transport phenomena is crucial in designing and optimizing various engineering systems, such as heat exchangers, reactors, and separation units.
where c_p is the specific heat capacity, T is the temperature, k is the thermal conductivity, and Q is the heat source term.
ρc_p(∂T/∂t + v⋅∇T) = ∇⋅(k∇T) + Q
Momentum transfer refers to the transfer of momentum from one fluid element to another due to the velocity gradient. The momentum transfer can occur through two mechanisms: viscous forces and Reynolds stresses. Viscous forces arise due to the interaction between fluid molecules, while Reynolds stresses arise due to the turbulent fluctuations in the fluid.
Mass transfer refers to the transfer of mass from one phase to another due to the concentration gradient. There are two types of mass transfer: diffusion and convection. Diffusion occurs due to the random motion of molecules, while convection occurs due to the fluid motion.
Heat transfer refers to the transfer of thermal energy from one body to another due to the temperature gradient. There are three modes of heat transfer: conduction, convection, and radiation. Conduction occurs due to the vibration of molecules, convection occurs due to the fluid motion, and radiation occurs due to the electromagnetic waves.
where T is the stress tensor, ρ is the fluid density, v is the fluid velocity vector, and ∇ is the gradient operator.
