22-Agric-A6 Physical Properties of Biological Materials and Food Products · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A6 Physical Properties of Biological Materials and Food Products, National Exams May 2015 — a three-hour closed-book exam (approved calculator permitted; one aid sheet, both sides). Nine questions are set and candidates answer any five, each worth 20 marks, for a 100-mark paper. All nine are worked here so the set is a complete study resource.
Reference texts. M.A. Rao, S.S.H. Rizvi, A.K. Datta and J. Ahmed, Engineering Properties of Foods, 4th ed. (rheology of fluid and semisolid foods, particle size, optical and dielectric properties); N.N. Mohsenin, Physical Properties of Plant and Animal Materials, 2nd ed. (thermal and rheological properties of biological materials, surface heat transfer coefficient measurement, stress relaxation); R.P. Singh and D.R. Heldman, Introduction to Food Engineering, 5th ed. (freezing/thawing rates and shape factors, unsteady-state heat transfer, screen analysis); J.F. Steffe, Rheological Methods in Food Process Engineering, 2nd ed. (viscoelasticity, generalized Maxwell model, time-dependent flow behaviour); R.L. Earle, Unit Operations in Food Processing, 2nd ed. (specific surface and particle number from sieve/screen data).
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.
Given. A packaged product held at some initial uniform temperature is exposed to a sudden (step) change in ambient temperature Ta during distribution (e.g. loaded from a chiller onto an uninsulated truck, or from a warm dock into a cold store), and the product's viscosity/texture depends on its own local temperature.
Find. (1) The environmental, surface, and package structure/size attributes that govern the resulting temperature and texture response; (2) an analysis approach for the temperature/texture history; (3) approximate sketches of those histories.
Attributes needing control. Environmental: ambient temperature Ta and its rate of change, air (or medium) velocity past the package (sets the convective coefficient h), and relative humidity/radiative exchange where surface moisture or solar/radiant loading matters. Surface: the package's exposed surface area A, its surface finish/colour (emissivity, for any radiant component), and orientation relative to the airflow (which changes the local convective coefficient over the surface). Package structure and size: wall material and thickness (thermal conductivity k and resistance L/k), any air gaps or insulating layers, the package's characteristic dimension/volume V (which sets thermal mass ρVc), and the resulting Biot number Bi = hLc/k, which determines whether internal temperature gradients inside the package are significant or whether the whole package can be treated as a single lumped temperature.
Analysis approach. (1) Establish or estimate the governing heat-transfer parameters — the external convective coefficient h (from correlations for the flow past the package geometry) and the package wall/product thermal resistance (k, L). (2) Compute the Biot number; if Bi < 0.1 the package can be treated as a lumped thermal mass and its centre/bulk temperature follows the classical first-order exponential response to the Ta step, (T(t) − Ta)/(Ti − Ta) = exp(−t/τ), with time constant τ = ρVc/(hA); if Bi is not small, solve the unsteady conduction problem for the package's actual shape (slab/cylinder/sphere Heisler-chart or series solution) instead, which adds an internal-gradient lag on top of the lumped response and is slower for a thicker/lower- conductivity package (a larger Bi). (3) Map the resulting local temperature history T(t) to a texture/viscosity history through the product's own temperature dependence, typically an Arrhenius-type relation μ(T) = μ0exp(Ea/RT); because this relationship is strongly non-linear, the texture/viscosity response to the same T(t) history is delayed and steeper than the temperature response itself — it changes little while T is far from the temperature range where the product's structure is sensitive, then changes rapidly once T passes through that range.
