22-Agric-B8 Food Process Engineering (Part 1) · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-B8 Food Process Engineering (Part 1), National Exams May 2014 — a three-hour open-book exam (any non-communicating calculator permitted). Ten questions are set in four sections (I–IV), each with a "do one/any N of M" instruction; a candidate following the choice rules answers six questions for a 100-mark paper. All ten are worked here so the set is a complete study resource.
Reference texts. R.T. Toledo, Fundamentals of Food Process Engineering, 3rd ed. (thermal-process lethality, D and z values, Ball/Stumbo process calculation, aseptic holding-tube residence time, evaporator design — this is the exam's own appendix source); C.J. Geankoplis, Transport Processes and Separation Process Principles, 4th ed. (evaporator heat and mass balances, multiple-effect steam economy); R.P. Singh and D.R. Heldman, Introduction to Food Engineering, 5th ed. (freezing-time estimation, modified Plank and Cleland-Earle equations, unsteady-state heat transfer in canned foods); A.C. Cleland, Food Refrigeration Processes: Analysis, Design and Simulation (Plank/Cleland-Earle freezing-time correlations); F.P. Incropera and D.P. DeWitt, Fundamentals of Heat and Mass Transfer (transient conduction, Heisler charts, composite-wall resistance).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Part (a) — Why cold product "sweats" in a warm room. A cold product carried into warm, humid air presents a surface that is well below the local dew point of the surrounding air, at least for the time it takes the surface to warm up. Because the boundary-layer air in immediate contact with the product is cooled below its saturation temperature, water vapour in that air condenses on the cold surface exactly the way a cold glass "sweats" on a humid day. This is a purely psychrometric effect of surface temperature lagging air temperature during the unsteady warm-up transient: as long as the product surface stays below the dew point of the surrounding air, moisture keeps condensing, and it only stops once the surface has warmed past the dew point (or once the product is enclosed in a vapour-tight wrap that isolates it from the room air). Sweating is therefore both a mass-transfer condensation problem and evidence of an unsteady thermal boundary layer at the product surface — it disappears once true steady state is reached because the driving temperature difference between surface and dew point vanishes.
Part (b) — transient or steady?
(i) Steady state. The problem states both surface temperatures of the oven wall are constant; with no time-varying boundary condition and no internal energy storage term of interest, the conduction rate through the wall is a classic Fourier steady-state resistance calculation \(q=kA\,\Delta T/L\) — there is no transient to solve.
(ii) Transient (unsteady). The question explicitly asks for the rate at which the milk's own temperature changes WITH TIME as it cools inside the tank; that is by definition an unsteady lumped- (or distributed-) parameter energy balance, \(mC_p\,dT/dt = -hA(T-T_\infty)\), not a fixed-boundary steady problem.
(iii) Transient (unsteady). "Instantaneous rate" at the moment of immersion in liquid nitrogen is asked for, and the fruit's surface and core temperatures are changing rapidly and non-uniformly right after immersion (this is exactly the kind of problem solved with the Heisler/Gurney-Lurie charts used elsewhere in this paper) — there is no steady thermal state until the fruit is fully frozen through.
Part (c) — procedure for the bologna centre-temperature history. The stick of bologna is treated as a finite (or, if its length is many diameters, an effectively infinite) cylinder of a known, homogeneous thermal diffusivity. The procedure is: (1) measure or estimate the product's density, specific heat and thermal conductivity (or its lumped diffusivity \(\alpha=k/\rho C_p\)); (2) measure or estimate the convective heat-transfer coefficient between the smokehouse air/steam and the casing surface, and compute the Biot number \(Bi=hr_0/k\) to confirm whether internal or surface resistance dominates; (3) record the initial (uniform) product temperature and the smokehouse dry-bulb temperature profile (ideally constant, or piecewise-constant if the smokehouse ramps); (4) compute the Fourier number \(Fo=\alpha t/r_0^2\) for each time of interest and read (or numerically evaluate, as in Question 1) the dimensionless centre temperature \(Y=(T_\infty-T_c)/(T_\infty-T_i)\) from the Heisler/Gurney-Lurie chart or series solution for a cylinder at that Biot number; (5) convert back to actual centre temperature \(T_c=T_\infty-Y(T_\infty-T_i)\) at each time step to build up the full time–temperature history; (6) validate the prediction against an actual inserted thermocouple reading at the geometric centre of a representative stick before relying on the calculation for process-lethality or food-safety sign-off, since casing shrinkage, internal fat pockets and smokehouse air-velocity non-uniformity are all real deviations from the idealized 1-D conduction model.
