GATE Agricultural Engineering Dairy and Food Engineering Syllabus

State the LMTD design equation for a heat exchanger.

$$q=UA\,\Delta T_{lm},\qquad \Delta T_{lm}=\frac{\Delta T_1-\Delta T_2}{\ln(\Delta T_1/\Delta T_2)}$$ where $U$ is the overall heat transfer coefficient and $\Delta T_1,\Delta T_2$ are the terminal temperature differences.

How is the overall heat transfer coefficient $U$ related to individual resistances (plane wall)?

$$\frac{1}{UA}=\frac{1}{h_iA}+\frac{L}{kA}+\frac{1}{h_oA}$$ The total thermal resistance is the sum of inside convection, wall conduction, and outside convection resistances (plus fouling factors if present).

Define heat exchanger effectiveness $\varepsilon$ in the NTU method.

$$\varepsilon=\frac{Q_{actual}}{Q_{max}}=\frac{Q}{C_{min}(T_{h,in}-T_{c,in})}$$ where $C_{min}$ is the smaller of the two fluid heat-capacity rates ($\dot m c_p$). $NTU=\frac{UA}{C_{min}}$.

State Fick's first law of diffusive mass transfer.

$$J_A=-D_{AB}\frac{dC_A}{dx}$$ where $J_A$ is molar flux (mol/m²·s), $D_{AB}$ is the diffusion coefficient (m²/s), and $\frac{dC_A}{dx}$ is the concentration gradient. Mass diffuses from high to low concentration.

State the convective mass transfer rate equation.

$$N_A=k_c A (C_{A,s}-C_{A,\infty})$$ where $k_c$ is the convective mass transfer coefficient (m/s), analogous to Newton's law of cooling with concentration difference as the driving force.

Define the Sherwood and Schmidt numbers.

$$Sh=\frac{k_c L}{D_{AB}},\qquad Sc=\frac{\mu}{\rho D_{AB}}=\frac{\nu}{D_{AB}}$$ $Sh$ is the mass-transfer analogue of $Nu$; $Sc$ is the analogue of $Pr$, relating momentum to mass diffusivity.

State the Lewis number and its significance.

$$Le=\frac{\alpha}{D_{AB}}=\frac{Sc}{Pr}$$ It relates thermal to mass diffusivity. When $Le\approx1$ heat and mass transfer analogies (e.g. wet-bulb = adiabatic saturation) hold, important in simultaneous heat and mass transfer during drying.

Give an example of simultaneous heat and mass transfer in agricultural processing.

Drying of grains/foods, where heat is supplied to evaporate moisture (heat transfer) while the resulting water vapour diffuses away from the surface (mass transfer) simultaneously. Other examples: humidification, evaporation, and freeze-drying.

In drying, what is the relationship that defines the wet-bulb temperature via simultaneous heat and mass transfer?

A heat balance at the evaporating surface: heat supplied by convection equals heat used for evaporation: $$h(T-T_w)=k_c\lambda(C_{w}-C_\infty)$$ At equilibrium the surface stays at the wet-bulb temperature $T_w$ during the constant-rate period.

What does a material (mass) balance state in food processing?

Conservation of mass: total mass in = total mass out + accumulation. For steady state with no accumulation: $\sum \dot m_{in}=\sum \dot m_{out}$, and component balances apply to each constituent (e.g. solids, water).

Write the general energy balance for a steady-flow food process.

$$\sum \dot m_{in} h_{in}+Q=\sum \dot m_{out} h_{out}+W$$ Energy in (enthalpy + heat added) equals energy out (enthalpy + work done), with no accumulation at steady state.

In an evaporator, if a feed of mass $F$ with solids fraction $x_F$ gives product $P$ and vapour $V$, write the overall and solids balances.

Overall: $F=P+V$. Solids: $F\,x_F=P\,x_P$ (solute is non-volatile, so all solids leave in the product). These two equations let you solve for the product and vapour rates.

Define water activity $a_w$ and give its formula.

$$a_w=\frac{p}{p_0}=\frac{\text{ERH}}{100}$$ the ratio of the vapour pressure of water in the food $p$ to that of pure water $p_0$ at the same temperature; equals the equilibrium relative humidity divided by 100. It ranges $0$ to $1$.

Why is water activity important for food preservation?

It governs microbial growth and chemical reaction rates. Most bacteria need $a_w>0.91$, most molds $>0.80$; below $a_w\approx0.60$ no microbial growth occurs. Lowering $a_w$ (by drying, salting, or adding sugar) preserves food.

What is a moisture sorption isotherm?

A plot of equilibrium moisture content of a food versus water activity (or relative humidity) at constant temperature. It shows how a food gains/loses moisture and is typically sigmoidal (Type II).

Define sorption hysteresis.

The phenomenon where the adsorption (wetting) and desorption (drying) isotherms of a food do not coincide — at a given $a_w$ the desorption curve shows a higher moisture content than the adsorption curve, forming a loop.

Name a common model used to describe sorption isotherms.

The BET (Brunauer-Emmett-Teller) equation for the low-$a_w$ monolayer region, and the GAB (Guggenheim-Anderson-de Boer) model for a wider $a_w$ range. Both estimate the monolayer moisture content, important for storage stability.

What kinetic order describes microbial thermal death, and write its rate equation.

First-order (logarithmic) death: $$\frac{dN}{dt}=-kN\quad\Rightarrow\quad N=N_0e^{-kt}$$ The number of survivors decreases exponentially with time at constant lethal temperature.

Define the decimal reduction time $D$.

$D$ is the time at a given temperature required to reduce the microbial population by 90% (one $\log_{10}$ cycle, factor of 10). On a survivor curve, $$D=\frac{t_2-t_1}{\log N_1-\log N_2}$$

Define the thermal resistance constant $z$.

$z$ is the temperature increase required to reduce the $D$-value by a factor of 10 (one log cycle): $$z=\frac{T_2-T_1}{\log D_1-\log D_2}$$ It describes how the death rate changes with temperature.

Define the thermal death time $F$ and the $F_0$ value.

$F$ is the time needed to achieve a stated lethality (number of $D$ reductions) at a reference temperature. $F_0$ is the equivalent lethality time at $121.1^\circ$C ($250^\circ$F) with $z=10^\circ$C, the standard reference for low-acid canned foods.

Relate $D$, initial and final counts to the required thermal process time.

$$t=D\,(\log N_0-\log N)=D\cdot \log\frac{N_0}{N}$$ The process time equals the $D$-value multiplied by the number of decimal (log) reductions required.

What is pasteurization and what does it target?

A mild heat treatment (below 100°C) that destroys pathogenic (disease-causing) and most spoilage vegetative microorganisms while minimizing changes to flavour and nutrition. It does NOT kill all spores, so it extends shelf life but does not sterilize.

Give the temperature-time conditions for LTLT and HTST milk pasteurization.

LTLT (Low Temperature Long Time / batch): $63^\circ$C for $30$ min. HTST (High Temperature Short Time): $72^\circ$C for $15$ s. Both achieve equivalent lethality against target pathogens (e.g. Coxiella burnetii / Mycobacterium).

Define UHT processing of milk and its typical conditions.

Ultra-High Temperature processing: heating milk to about $135$–$150^\circ$C for $1$–$4$ s followed by aseptic packaging, producing commercially sterile milk with a long ambient shelf life.

Distinguish pasteurization from sterilization.

Pasteurization uses mild heat (<100°C) to kill pathogens and reduce spoilage organisms; product is not shelf-stable at ambient and must often be refrigerated. Sterilization uses higher heat (>100°C) to destroy all microorganisms including spores, giving commercial sterility and ambient shelf stability.

What enzyme test is used to verify adequate milk pasteurization?

The alkaline phosphatase test. Phosphatase is naturally present in raw milk and is inactivated by proper pasteurization; a negative phosphatase test indicates the milk was adequately pasteurized.

How does freezing preserve food?

By lowering temperature below the freezing point, it converts water to ice — reducing available liquid water (lowering $a_w$) and drastically slowing microbial growth and enzymatic/chemical reactions. Freezing is microbistatic (it halts, but does not kill, most microbes).

What is the difference between slow and quick (fast) freezing in terms of ice crystals?

Slow freezing forms large extracellular ice crystals that rupture cell walls and cause drip loss and texture damage. Quick freezing forms many small intracellular crystals, better preserving texture and quality. IQF (Individual Quick Freezing) is the commercial fast method.

State the coefficient of performance (COP) of a refrigerator.

$$COP_{R}=\frac{Q_L}{W_{net}}=\frac{Q_L}{Q_H-Q_L}$$ the ratio of useful refrigerating effect (heat removed from the cold space) to the net work input. For a Carnot refrigerator $COP=\dfrac{T_L}{T_H-T_L}$.

Name the four components of the vapour-compression refrigeration cycle and what each does.

1) Compressor — raises refrigerant pressure/temperature (work input). 2) Condenser — rejects heat $Q_H$, refrigerant condenses. 3) Expansion (throttle) valve — drops pressure and temperature. 4) Evaporator — absorbs heat $Q_L$ from the cold storage, refrigerant evaporates. Defines one tonne of refrigeration $=3.517$ kW.

What is cold storage and what conditions are controlled? Give the definition of a tonne of refrigeration.

Cold storage is refrigerated storage that preserves perishables by controlling temperature, relative humidity, and air circulation (and sometimes gas composition in controlled-atmosphere storage) to slow respiration, microbial growth and spoilage. One tonne of refrigeration = heat removal rate to freeze 1 short ton of water at 0°C in 24 h $=3.517$ kW $=3024$ kcal/h.