Mass Diffusion P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Physically distinct & Mathematically analogous to Heat Conduction……
Mass Transfer • Mass transfer: The transfer of mass (Chemical species) into or out of a substance. • The transfer of a chemical compound from one phase to another • Examples: • Evaporation: liquid → gas • Diffusion: high concentration → low concentration
Various Mass Transfer Phenomenon Evaporation: Drying Baking Frying Boiling Diffusion: Salt through cheese. Smoke through meat. Curing solution through meat Not mass transfer: Moving a fluid from one place to another
Osmosis • Osmosis is the net movement of water across a partially permeable membrane from a region of high solvent potential to an area of low solvent potential, up a solute concentration gradient. • Osmosis is responsible for the ability of plant roots to suck up water from the soil. • There are many fine roots, which have a large surface area, water enters the roots by osmosis, and • Generates the pressure required for the water to travel up the plant. • Osmosis can also be seen very effectively when potato slices are added to a high concentration of salt solution. • The water from inside the potato moves to the salt solution, causing the potato to shrink and to lose its 'turgor pressure'. • The more concentrated the salt solution, the bigger the difference in size and weight of the potato slice. • For example, freshwater and saltwater aquarium fish placed in water of a different salinity than that they are adapted to will die quickly, and in the case of saltwater fish, rather dramatically.
DIFFUSION OF 02 AND C02 ACROSS THE ALVEOLAR-CAPILLARY MEMBRANE • All gas movement in the lung occurs as a result of passive diffusion, • Gas moves from one region to another only when the partial pressure of gas is greater in one region than another. • The transfer of gas from the alveolus to the blood occurs by simple diffusion. • The rate of transfer depends on what?
Engineering Application of Mass Diffusion • The turbine blades used in aircraft engines must be periodically inspected. • After some time in service, minute cracks appear on the blades and they must be removed to see if they can be repaired. • A common blade repair process is the isothermal solidification process in which an alloy powder with a relatively high concentration of Boron and mixed with a binder is applied on the cracks. • Subsequently, the entire blade is heated in an oven at a pre-selected temperature. • Then the Boron in the powder depresses the melting point and forms a thin liquid layer inside the crack. • Over time, boron diffuses out of layer and into the sides of the crack. • As the boron content in the crack decreases, the melting point increases and when the boron level has decreased sufficiently, the layer solidifies and the crack is repaired. • A diffusion analysis is useful in the determination of the process parameter values required for optimal performance of the repair process.
Mass Diffusion • Diffusional transport is a fundamental physical mechanism available for atomic rearrangement in the solid state. • The rate of transport is particularly important at high temperatures. • Atoms vibrate rapidly about their lattice positions and sometimes they are able to move into a neighboring location. • The aggregate movement of many such atoms constitutes mass diffusion. • Application of Diffusional mass transfer in metals and alloys, ceramics and polymeric materials is the primary interest to Mechanical Engineer.
Rate of molecularflow Difference in concentration Resistance: depends on ability of molecules to pass through, k and membrane dimensions, Dx and A Fick's law of diffusion where C is the concentration, Ex is the rate of mass diffusion, and D is the diffusion coefficient.
The diffusion flux is defined as : D is the diffusion coefficient or diffusivity, m2/s Multidimensional Diffusion equation in isotropic medium Multidimensional Diffusion equation in anisotropic medium
Heat Convection • Convection uses the motion of fluids to transfer heat. • In a typical convective heat transfer, a hot surface heats the surrounding fluid, which is then carried away by fluid movement such as wind. • The warm fluid is replaced by cooler fluid, which can draw more heat away from the surface. • Since the heated fluid is constantly replaced by cooler fluid, the rate of heat transfer is enhanced.
Natural Convection • Natural convection (or free convection) refers to a case where the fluid movement is created by the warm fluid itself. • The density of fluid decrease as it is heated; thus, hot fluids are lighter than cool fluids. • Warm fluid surrounding a hot object rises, and is replaced by cooler fluid. • The result is a circulation of air above the warm surface
Forced Convection • Forced convection uses external means of producing fluid movement. • Forced convection is what makes a windy, winter day feel much colder than a calm day with same temperature. • The heat loss from your body is increased due to the constant replenishment of cold air by the wind. • Natural wind and fans are the two most common sources of forced convection.
Newton's Law of Cooling • The rate at which a hot body cools to the temperature of its surroundings is given by an empirical formula first discovered by Sir ISAAC NEWTON • Newton's law of cooling states, "For a body cooling in a draft, the rate of heat loss is proportional to the difference in temperatures between the body and its surroundings." • Since the temperature change is proportional to the heat transfer. • where m is the mass of the body and Cp is its heat capacity, we can write
Newton’s Law of Cooling States : Where h is the local convective heat transfer coefficient
Both heat flux and local convective heat transfer coefficient vary along the surface. The total rate of heat transfer is: For a finite body in a large cooling medium
Where havg is Average convective heat transfer coefficient for the entire surface As. What decides the value of Average Heat Transfer Coefficient? How to Evaluate havg ?
Speed of Stirring • Stirring the water and sugar is another type of mass transfer called convection. • Convection is the movement of mass due to forced fluid movement. • Fluid, such as water, is forced to move when it is stirred. • Convective mass transfer is a faster mass transfer than diffusion. • Convective mass transfer is commonly applied to many cooking recipes. • Whenever stirring is involved, you are applying convective mass transfer theories. • Using a blender, beating an egg and kneading bread dough are all examples of mass transfer due to convection. • Using a mixer creates more convective mass transfer than using a spoon because there is more forced fluid motion. • The faster the fluid moves the more mass transfer and therefore the less time it will take to mix the ingredients together. • Cookie batter could be mixed using just a spoon, but it would take a much longer time than it would using a mixer.
Convection Mass Transfer JA The local convective flux of A:
In summary, the local flux (and/or total transfer rate) depends on the conditions during convection, i.e., fluid properties (T, C, k, ρ, ν, cp, etc.), surface geometry (As) and flow conditions (V).
Heat Radiation • Radiative heat transfer does not require a medium to pass through; thus, it is the only form of heat transfer present in vacuum. • It uses electromagnetic radiation (photons), which travels at the speed of light and is emitted by any matter with temperature above 0 degrees Kelvin (-273 °C). • Radiative heat transfer occurs when the emitted radiation strikes another body and is absorbed. • We all experience radiative heat transfer everyday; solar radiation, absorbed by our skin, is why we feel warmer in the sun than in the shade. • The electromagnetic spectrum classifies radiation according to wavelengths of the radiation. • Main types of radiation are (from short to long wavelengths): gamma rays, x-rays, ultraviolet (UV), visible light, infrared (IR), microwaves, and radio waves. • Radiation with shorter wavelengths are more energetic and contains more heat.
X-rays, having wavelengths ~10-9 m, are very energetic and can be harmful to humans, while visible light with wavelengths ~10-7 m contain less energy and therefore have little effect on life. • A second characteristic which will become important later is that radiation with longer wavelengths generally can penetrate through thicker solids. • Visible light, as we all know, is blocked by a wall. • However, radio waves, having wavelengths on the order of meters, can readily pass through concrete walls. • Any body with temperature above 0 Kelvin emits radiation. • The type of radiation emitted is determined largely by the temperature of the body. • Most "hot" objects, from a cooking standpoint, emit infrared radiation. • Hotter objects, such as the sun at ~5800 K, emits more energetic radiation including visible and UV. • The visible portion is evident from the bright glare of the sun; the UV radiation causes tans and burns.
Depending on the degree of their permeability for heat rays, substances are said to be diathermal or athermal – • diathermal if they let radiation pass more or less unhindered, • athermal, if they partly absorb it and heat up themselves. • For example, air and rock salt are diathermal; • glass for long waves (>4mm), metals and lampblack are athermal. • We sense the action of the Sun's rays as heat, because our skin absorbs the radiation, while the air remains cold, because is lets the rays pass. • The same explanation applies to the difference between the temperatures of thermometers and air.
MicroWave Oven • A typical microwave oven uses between 500 and 1000 W of microwave energy at 2.45 GHz to heat the food. • This heating is caused mainly by the vibration of the water molecules. • Thus plastic, glass, or even paper containers will heat only through conduction from the hot food. • There is little transfer of energy directly to these materials. • This also means that the food does not need to be a conductor of electricity and that electromagnetic induction is not involved. • The oven chamber cavity is a good reflector of microwaves, nearly all the energy generated by the oven is available to heat the food and heating speed is thus only dependent on the available power and how much food is being cooked. • The penetration depth of the microwave energy is a few cm so that the outside is cooked faster than the inside. • However, unlike a conventional oven, the microwave energy does penetrate these few cm rather than being totally applied to the exterior of the food.
Radiation Theory • No single theory - both wave theory and quantum mechanics is required to explain all radiative phenomena. • For our purposes we use the wave phenomenon. • Highest temperature in engineering application is about 6000 K. • Emissive power (E): The total amount of energy flux emitted by a surface at a given temperature is the emissive power. • It depends on the temperature of the surface, and the surface characteristics. • At a defined temperature there is a maximum limit to the emissive power of a surface.
Black Body • The maximum emissive power at a given temperature is the black body emissive power (Eb). • The black body emissive power is given by the Stefan-Boltzman Law: • Black body: Theoretical concept, but useful in practice • Gives estimate of maximum absorption and emission for surface • Blackbody emissive power (W/m2) depends on temperature (T) of surface
From Where Does Eb=T4 Come? • Plot Eb = monochromatic emissive power = spectral blackbody emissive power = power at each wavelength against wavelength • This relationship changes with temperature • Curve gets higher, more power • Peaks at lower wavelength, higher frequency (more lower wavelengths at higher temperatures)
General Body • The amount of radiation emitted by an object is given by: • ε is a material property called emissivity. • The emissivity has a value between zero and 1, and is a • measure of how efficiently a surface emits radiation. • It is the ratio of the radiation emitted by a surface to the radiation emitted by a perfect emitter at the same temperature.
where I is the incident radiation. Interaction between a surface and incident radiation I • The emitted radiation strikes a second surface, where it is reflected, absorbed, or transmitted. • The portion that contributes to the heating of the surface is the absorbed radiation. • The percentage of the incident radiation that is absorbed is called the absorptivity, α. • The amount of heat absorbed by the surface is given by: