Question

What is an impermeable surface in mass transfer? How is it expressed mathematically (on a mass basis)? To what does it correspond in heat transfer?

Short answer

Answer: An impermeable surface in mass transfer is a surface that does not allow the transfer of mass through it, acting as a barrier. Mathematically, it is expressed as having a flux (J) of zero. In heat transfer, the corresponding concept is an adiabatic or insulating surface, which does not allow heat transfer through it, also expressed as having a heat flux (q) of zero.

Step-by-step solution

Definition of an impermeable surface in mass transfer

An impermeable surface in mass transfer is a surface or a boundary that does not allow the transfer of mass (particularly in the form of solute particles or molecules) through it. In other words, it acts as a barrier that prevents the mass from crossing it.

Mathematical expression for an impermeable surface on a mass basis

In mass transfer, Fick's first law is often used to define the flux (mass crossing a unit area per unit time) of a diffusing component through a surface. The flux (J) is given by: J = -D * (dC/dx) where D is the diffusivity, C is the concentration, and x is the distance. For an impermeable surface, the flux (J) would be zero since no mass transfer can occur through it. Hence, the mathematical expression for an impermeable surface on a mass basis can be expressed as: J = 0

Correspondence of impermeable surfaces in heat transfer

In heat transfer, the corresponding concept to an impermeable surface is an adiabatic surface or an insulating surface. An adiabatic surface is a surface or a boundary that does not allow heat transfer (in the form of conduction, convection, or radiation) through it. In other words, it acts as a barrier that prevents the flow of heat or thermal energy. In heat transfer, Fourier’s law is often used to define the heat flux (heat transferred per unit area per unit time) through a surface. The heat flux (q) is given by: q = -k * (dT/dx) where k is the thermal conductivity, T is the temperature, and x is the distance. For an adiabatic surface, the heat flux (q) would be zero since no heat transfer can occur through it. Hence, the mathematical expression for an adiabatic surface in heat transfer can be expressed as: q = 0