GATE Agricultural Engineering Agricultural Process Engineering Syllabus

What is boiling-point elevation (BPE) in evaporators and why does it matter?

BPE is the increase in the boiling point of a solution above that of pure water at the same pressure, caused by dissolved solids (a colligative effect). It reduces the effective temperature-difference driving force $\Delta T$ available for heat transfer, lowering evaporator capacity. It is accounted for using Dühring's rule.

Why are falling-film and rising-film evaporators preferred for heat-sensitive liquid foods?

They give thin liquid films with short residence times and high heat-transfer coefficients, allowing low-temperature operation (often under vacuum). This minimizes thermal damage, fouling and quality loss in heat-sensitive foods such as fruit juices and milk.

Describe the operating principle of a tray (cabinet) dryer.

A tray dryer is a batch convective dryer: product is spread on perforated or solid trays stacked in an insulated chamber; heated air is circulated (by fans, parallel or through-flow) over/through the trays. Moisture is carried away by the air. It is simple, low-cost, used for small batches of fruits, vegetables and spices, but gives non-uniform drying between trays.

Describe the construction and use of a drum (roller) dryer.

A drum dryer consists of one or two slowly rotating, internally steam-heated metal drums. A thin film of liquid/slurry food is applied to the hot drum surface, dries within part of a revolution, and is scraped off by a doctor blade as flakes/sheet. Used for milk, mashed potato, starch, baby foods; gives short contact time but high surface temperatures.

Explain the working principle of a spray dryer.

A spray dryer atomizes a liquid feed into fine droplets (by rotary atomizer, pressure nozzle, or two-fluid nozzle) into a chamber of hot air. The huge surface area gives almost instantaneous drying; dried powder falls and is separated (cyclone/bag filter) from the exhaust air. Used for milk powder, instant coffee, eggs; very short residence time protects heat-sensitive products.

Compare drum drying and spray drying on contact temperature, product form and residence time.

Drum drying: conductive, high surface temperature, product as flakes/sheet, residence a few seconds to tens of seconds, lower capital cost. Spray drying: convective, lower particle temperature (evaporative cooling), product as free-flowing powder, residence very short (seconds), higher capital cost but better quality for heat-sensitive liquids.

What is parboiling of paddy and what are its main objectives?

Parboiling is a hydrothermal treatment of paddy involving soaking, steaming and drying before milling. Objectives: gelatinize starch, increase head (whole) rice yield by reducing breakage, drive water-soluble vitamins/minerals from bran into the endosperm (nutrient retention), and harden the kernel. It is a classic hydrothermal treatment of cereals.

List the three sequential operations of paddy parboiling.

(1) Soaking — paddy is hydrated in warm water to raise moisture (~30% wb); (2) Steaming/heating — gelatinizes the starch; (3) Drying — moisture is reduced for safe storage and milling. Subsequent milling then removes husk and bran.

Differentiate the husking and polishing/whitening steps in rice milling.

Husking (dehusking/shelling) removes the outer husk (hull) to give brown rice, typically with rubber-roll or disc shellers. Polishing/whitening (milling) removes the bran layers and germ from brown rice by abrasion/friction to give white (polished) rice, optionally followed by polishing for shine.

What is the degree of milling (DOM) in rice processing?

Degree of milling is the extent to which bran and germ are removed from brown rice, usually expressed as the percentage of bran removed or the percentage weight reduction of brown rice during whitening. Higher DOM gives whiter rice but lower yield and reduced nutrients.

Distinguish dry milling and wet milling of cereals such as maize.

Dry milling tempers grain to a moderate moisture then breaks it to separate germ, bran and endosperm, yielding grits, meal and flour. Wet milling steeps grain (often with $\ce{SO2}$), then mills and separates components in water to give relatively pure starch, gluten, germ (oil) and fibre. Wet milling gives purer fractions; dry milling is simpler and cheaper.

Define moisture content on wet basis and dry basis, and give the conversion between them.

Wet basis: $M_{wb} = \dfrac{m_{w}}{m_{w}+m_{d}}$. Dry basis: $M_{db} = \dfrac{m_{w}}{m_{d}}$. Conversions: $$M_{db} = \frac{M_{wb}}{1 - M_{wb}}, \qquad M_{wb} = \frac{M_{db}}{1 + M_{db}}$$ where $m_w$ is water mass and $m_d$ is dry-matter mass.

Define equilibrium moisture content (EMC) and free moisture content in drying.

EMC ($M_{e}$) is the moisture content a material attains in equilibrium with air of a given temperature and relative humidity (no further net moisture exchange). Free moisture content is the moisture available for removal: $$M_{free} = M - M_{e}$$ where $M$ is the current moisture content (dry basis).

Sketch and label the phases of a typical drying-rate curve.

Plotting drying rate vs free moisture: (1) an initial transient (warming-up) period; (2) the constant-rate period, where rate is limited by surface evaporation and moisture is freely available; (3) the falling-rate period(s), beginning at the critical moisture content, where internal moisture diffusion controls and rate declines to zero at EMC.

What is the critical moisture content in drying?

The critical moisture content $M_{c}$ is the free moisture content at which drying changes from the constant-rate period to the falling-rate period. Above $M_c$ the surface stays saturated; below it the surface begins to dry and internal moisture movement limits the rate.

Write the constant-rate-period drying equation for heat-controlled surface evaporation.

$$R_{c} = \frac{h\,(T_{a} - T_{s})}{\lambda}$$ where $R_c$ = constant drying rate per unit area, $h$ = convective heat-transfer coefficient, $T_a$ = air temperature, $T_s$ = wet-surface (wet-bulb) temperature, and $\lambda$ = latent heat of vaporization. Equivalently mass-transfer form: $R_{c} = k_{y}(H_{s} - H_{a})$.

Give the thin-layer (exponential) drying model for the falling-rate period.

Assuming drying rate proportional to free moisture (first-order): $$\text{MR} = \frac{M - M_{e}}{M_{0} - M_{e}} = e^{-k t}$$ where MR is the moisture ratio, $M_0$ the initial moisture, $M_e$ the equilibrium moisture, $k$ the drying constant and $t$ time. (Page model: $\text{MR}=e^{-k t^{n}}$.)

Define psychrometry and the dry-bulb temperature of air.

Psychrometry is the study of the thermodynamic properties of moist air (air-water-vapour mixtures) and their use in processes that change air temperature and humidity. The dry-bulb temperature is the air temperature measured by an ordinary thermometer shielded from radiation and moisture.

Define absolute humidity (humidity ratio) of moist air and give its formula.

Absolute humidity (humidity ratio) $W$ is the mass of water vapour per unit mass of dry air: $$W = \frac{m_{v}}{m_{a}} = 0.622\,\frac{p_{v}}{P - p_{v}}$$ where $p_{v}$ is the partial pressure of water vapour, $P$ is total pressure, and $0.622$ is the ratio of molar masses ($18/29$).

Define relative humidity and contrast it with absolute humidity.

Relative humidity is the ratio of the actual vapour partial pressure to the saturation vapour pressure at the same temperature: $$\mathrm{RH} = \frac{p_{v}}{p_{vs}} \times 100\%$$ It is a dimensionless percentage that depends on temperature, whereas absolute humidity (humidity ratio) is the actual mass of vapour per kg dry air and is temperature-independent.

Distinguish dew-point temperature and wet-bulb temperature of moist air.

Dew-point temperature is the temperature to which moist air must be cooled at constant pressure and humidity ratio to reach saturation (condensation begins). Wet-bulb temperature is the steady temperature reached by a wetted thermometer in moving air, reflecting simultaneous heat and mass transfer (evaporative cooling). For unsaturated air: $T_{dry} > T_{wet} > T_{dew}$.

Define the enthalpy of moist air per kg of dry air.

$$h = c_{pa}\,T + W\,(\lambda_{0} + c_{pv}\,T)$$ where $c_{pa}\approx1.005\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$ (dry air), $c_{pv}\approx1.88\ \mathrm{kJ\,kg^{-1}\,K^{-1}}$ (vapour), $\lambda_{0}\approx2501\ \mathrm{kJ\,kg^{-1}}$ (latent heat at $0\,^{\circ}\mathrm{C}$), $W$ = humidity ratio, $T$ = dry-bulb temperature in $^{\circ}\mathrm{C}$.

Define humid (specific) volume of moist air.

Humid volume $v_{H}$ is the volume of moist air per unit mass of dry air: $$v_{H} = \left(\frac{1}{29} + \frac{W}{18}\right)\frac{R\,T}{P}$$ approximately $v_{H} = (0.00283 + 0.00456\,W)\,T\ (\mathrm{m^{3}\,kg^{-1}\ dry\ air})$, with $T$ in kelvin. It increases with temperature and humidity ratio.

On a psychrometric chart, what process is represented by a horizontal line, and what by a constant-enthalpy line?

A horizontal line (constant humidity ratio $W$) represents sensible heating or cooling — only dry-bulb temperature changes. A constant wet-bulb / constant-enthalpy line (sloping down to the right) approximates an adiabatic saturation/evaporative-cooling process, where dry-bulb falls as humidity rises at nearly constant enthalpy.

State Rittinger's law for energy in size reduction and the property it assumes.

Rittinger's law: energy required is proportional to the new surface area created, i.e. proportional to the increase in specific surface (inverse of particle size): $$E = K_{R}\left(\frac{1}{d_{2}} - \frac{1}{d_{1}}\right)$$ where $d_1,d_2$ are feed and product sizes. Best suited to fine grinding.

State Kick's law of size reduction.

Kick's law: the energy required is proportional to the logarithm of the size-reduction ratio (energy per unit mass is constant for a given reduction ratio): $$E = K_{K}\,\ln\!\left(\frac{d_{1}}{d_{2}}\right)$$ where $d_1$ and $d_2$ are initial and final particle sizes. Best for coarse crushing.

State Bond's law and define the work index.

Bond's law: $$E = K_{B}\left(\frac{1}{\sqrt{d_{2}}} - \frac{1}{\sqrt{d_{1}}}\right)$$ The work index $W_{i}$ is the energy (kWh per tonne) needed to reduce material from theoretically infinite size to 80% passing $100\ \mu\mathrm{m}$. Bond's law is intermediate between Kick's and Rittinger's, used for intermediate grinding.

Show that Kick's, Rittinger's and Bond's laws are special cases of the general (Walker) differential equation $dE = -C\,\frac{dx}{x^{n}}$.

Integrating $dE=-C\,x^{-n}\,dx$: for $n=1$ gives Kick's law (energy $\propto \ln(d_1/d_2)$); for $n=2$ gives Rittinger's law (energy $\propto 1/d_2 - 1/d_1$); for $n=1.5$ gives Bond's law (energy $\propto 1/\sqrt{d_2}-1/\sqrt{d_1}$). Thus the exponent $n$ distinguishes the three laws.

Define the reduction ratio in a size-reduction (comminution) operation.

Reduction ratio is the ratio of a characteristic feed size to the corresponding product size: $$R = \frac{d_{feed}}{d_{product}}$$ Often based on 80%-passing sizes ($d_{80}$). It measures how much the material has been reduced in one pass.

Define mean particle diameters used in particle-size analysis of comminuted solids: the surface-volume (Sauter) mean.

The Sauter (surface-volume) mean diameter is $$D_{sv} = \frac{\sum n_{i} d_{i}^{3}}{\sum n_{i} d_{i}^{2}} = \frac{1}{\sum (x_{i}/d_{i})}$$ where $x_i$ is the mass fraction in size interval $i$ with mean diameter $d_i$. It is the diameter of a sphere having the same surface-to-volume ratio as the whole sample, important for surface-area-controlled processes.

Define the fineness modulus and uniformity index obtained from sieve analysis of ground feed.

Fineness modulus (FM) is obtained by summing the cumulative percentages of material retained on a standard set of sieves and dividing by 100; higher FM means coarser product. The uniformity index expresses the proportions of coarse, medium and fine fractions (often as a three-figure ratio) describing the spread of the size distribution.

In screening, define screen effectiveness (efficiency).

Screen effectiveness measures how well a screen separates oversize from undersize. A common overall form is the product of recovery of undersize in the underflow and rejection of oversize: $$E = E_{o}\,E_{u}$$ where each term compares actual mass of correctly sorted material to the amount in the feed. Higher feed rate generally lowers effectiveness.

Write the material balance for an ideal screen separating feed $F$ into overflow $D$ (oversize) and underflow $B$ (undersize).

Total: $F = D + B$. Component (fraction of material finer than the cut, $x$): $$F\,x_{F} = D\,x_{D} + B\,x_{B}$$ Solving gives $\dfrac{D}{F} = \dfrac{x_{F}-x_{B}}{x_{D}-x_{B}}$ and $\dfrac{B}{F} = \dfrac{x_{D}-x_{F}}{x_{D}-x_{B}}$.

What is the relationship between mesh number and aperture size in standard screens?

Mesh number is the number of openings per linear inch of screen. As mesh number increases, the aperture (opening) size decreases, so higher mesh numbers pass finer particles. Aperture also depends on wire diameter: $\text{aperture} = \frac{1\ \text{inch}}{\text{mesh}} - (\text{wire diameter})$.

Name and distinguish the common industrial screening equipment by motion.

Grizzly: static inclined parallel bars for coarse scalping. Trommel: rotating cylindrical screen. Vibrating screen: high-frequency vibration for efficient sizing. Gyratory/oscillating screen: gyratory horizontal motion for fine separation. They differ in the motion imparted (none, rotation, vibration, gyration) and the size range handled.

What is the terminal velocity of a particle and its role in pneumatic/aspiration separation of grains?

Terminal velocity is the constant velocity a particle attains in a fluid when gravity balances drag and buoyancy: $$v_{t} = \sqrt{\frac{4\,g\,d\,(\rho_{p}-\rho_{f})}{3\,C_{D}\,\rho_{f}}}$$ Particles with different terminal velocities are separated in an air stream (aspiration), e.g. cleaning grain from chaff and light impurities.

In the constant-rate drying period, why does the surface stay at the wet-bulb temperature of the drying air?

During the constant-rate period the surface is fully wetted, so all sensible heat supplied by the air is consumed as latent heat of evaporating free water. This dynamic equilibrium between convective heat gain and evaporative cooling holds the surface at the air's wet-bulb temperature until the critical moisture content is reached.

What is hysteresis in moisture sorption isotherms of grains?

Sorption hysteresis is the phenomenon where the equilibrium moisture content at a given relative humidity is higher along the desorption (drying) isotherm than along the adsorption (wetting) isotherm. The two curves form a loop, attributed to capillary condensation, pore-shape ('ink-bottle') effects and structural changes.

Give the Brunauer (BET) interpretation relevant to sorption isotherms of foods.

The BET equation describes multilayer moisture sorption and is used to estimate the monolayer moisture value $M_{0}$: $$\frac{a_{w}}{(1-a_{w})M} = \frac{1}{M_{0}C} + \frac{C-1}{M_{0}C}\,a_{w}$$ where $a_{w}$ is water activity, $M$ moisture content, and $C$ a constant. The monolayer value indicates the moisture for maximum storage stability.

Define water activity and its significance in drying and storage of foods.

Water activity $a_{w} = \dfrac{p_{v}}{p_{vs}} = \dfrac{\mathrm{ERH}}{100}$ is the ratio of the vapour pressure of water in the food to that of pure water at the same temperature (equal to equilibrium relative humidity/100). It governs microbial growth, enzymatic and chemical reactions; lowering $a_w$ by drying improves shelf stability (most bacteria need $a_w>0.9$).

Differentiate the through-flow and cross-flow (parallel) air patterns in tray dryers.

In cross-flow (parallel-flow) tray dryers heated air passes horizontally over the surface of the product on the trays. In through-flow tray dryers air is forced vertically through perforated trays and the bed of product, giving greater contact area, faster and more uniform drying, but higher fan power.