# Constitutive Laws (CL)

The mathematical analysis of the diffusion of heat, mass, or momentum is incorporated into constitutive laws that relate this diffusion to easily measurable quantities (like temperature, velocity (pressure), and concentration).

• Use a resistor analogy to solve for heat flows [15.5, 17.1]
• Calculate the thermal resistance and magnitude of conductive heat flow/flux through a planar wall
• Calculate the thermal resistance and magnitude of conductive heat flow/flux through multiple planar walls
• Calculate the thermal resistance and magnitude of conductive heat flow/flux through a cylindrical shell
• Calculate the thermal resistance and magnitude of conductive heat flow/flux through a spherical shell
• Calculate the resistance and magnitude of heat flow in systems in which multiple modes of heat transfer are present
• Extend the resistor analogy to non-one-dimensional problems using shape factors [Ch 17.4]
• Determine the heat flow through these solids from their temperature profiles
• Use film theory and other correlations to obtain h [19.5]
• Explain and calculate viscous stresses [7.1, 7.2, 7.4]
• Calculate viscous stresses/forces from velocity distributions
• Identify Newtonian and non-Newtonian behavior from stress versus strain curves
• Solve diffusive mass flows problems
• Explain the difference between the total flux and the diffusive flux [24.1]
• Calculate the magnitude of diffusive mass flow/flux through a planar film in equimolar counter-diffusion [25.4]
• Calculate the magnitude of diffusive mass flow/flux through a planar stagnant film [26.1]
• Calculate the magnitude of diffusive mass flow/flux for systems with non-zero bulk flow
• Calculate the magnitude of diffusive mass flow/flux through a cylindrical and spherical shells
• Use film theory and other correlations to obtain kc [28.6]
• Use the two-resistance model to perform fluid-fluid mass transfer calculations [29.1-29.3]
• Calculate mass/molar flows/fluxes from concentration profiles

A microscopic or continuum description of transport requires that we examine "diffusion" of our conserved quantities at the molecular level.

• Estimate transport properties from molecular calculations
• Explain the molecular origins of fluid viscosity and shear stresses.
• Estimate fluid viscosities [7.3]
• Explain the molecular origins of thermal and mass diffusion/conduction [15.2, 24.2]
• Estimate thermal and mass diffusivities/conductivities [15.2, 24.2]