Heat and mass transfer are central to many engineering processes, including distillation, drying, absorption, crystallization, reactors, and heat exchangers. In these systems, energy moves because of temperature differences, while chemical species move because of concentration or partial pressure differences. Engineers control these transfers to improve yield, safety, efficiency, and product purity.
A process vessel often has heat flow, diffusion, convection, and reaction happening at the same time.
Key Facts
- Heat conduction through a flat wall: q = kA(Delta T)/L
- Convective heat transfer: q = hA(T_s - T_fluid)
- Fick's law of diffusion: J_A = -D_AB dC_A/dx
- Mass transfer across a film: N_A = k_cA(C_A,s - C_A,b)
- Overall heat transfer rate: q = UA Delta T_lm
- The heat and mass transfer analogy compares Nu = hL/k with Sh = k_cL/D_AB
Vocabulary
- Driving force
- A driving force is the difference in temperature, concentration, pressure, or chemical potential that causes heat or mass to move.
- Transfer coefficient
- A transfer coefficient measures how easily heat or mass crosses a boundary layer between a surface and a moving fluid.
- Diffusion
- Diffusion is the net movement of molecules from higher concentration to lower concentration due to random molecular motion.
- Convection
- Convection is transfer caused by the bulk motion of a fluid carrying heat, mass, or both.
- Boundary layer
- A boundary layer is the thin region near a surface where velocity, temperature, or concentration changes rapidly.
Common Mistakes to Avoid
- Using the wrong sign for flux is incorrect because heat and diffusion flux point from high potential to low potential, while gradients may be written in the opposite direction.
- Mixing area units is incorrect because transfer rates depend directly on area, so using cm2 in one term and m2 in another changes the answer by large factors.
- Treating transfer coefficients as constants in every situation is wrong because h and k_c depend on flow speed, fluid properties, geometry, and turbulence.
- Confusing total rate with flux is wrong because flux is per unit area, such as W/m2 or mol/(m2 s), while total rate includes the transfer area.
Practice Questions
- 1 A heat exchanger wall has k = 16 W/(m K), area A = 2.0 m2, thickness L = 0.010 m, and a temperature difference of 40 K. Calculate the conductive heat transfer rate q.
- 2 A gas species diffuses across a stagnant film with D_AB = 2.0 x 10^-5 m2/s and concentration changes from 0.80 mol/m3 to 0.20 mol/m3 across 0.0030 m. Estimate the molar diffusive flux magnitude using J_A = D_AB(Delta C)/L.
- 3 In a reactor with a hot wall and a membrane that removes product, explain how increasing fluid velocity can affect both heat transfer and mass transfer, and why the two effects are often similar.