1. Learning and Teaching Conference 2009 COMSOL Multiphysics for the teaching of design and innovation in food science Malcolm Povey School of Food Science and Nutrition 1

2. Learning and Teaching Conference 2009 2 Modelling of battered potato chip in oil by use of COMSOL Multiphysics File: battered potato chip in oil.mph

3. Cricket and Maths Students are used to seeing data tabulated and plotted during sports programmes and live competitive events. They are familiar with the idea of discretized descriptions of continua, although they may not realise it. A serious issue facing a multidisciplinary subject such as food science is difficulty students have in adopting abstract, quantitative, and mathematical understanding of problems. 3

4. Acknowledgements I would like to thank Dr Anna Akinshina and Dr Melvin Holmes for their help in preparing teaching materials used in this presentation and course I would also like to thank the ADF fund of the University of Leeds for financial support, without which the software necessary to deliver the course could not have been purchased and for support with teaching assistance. 4

5. 5 R3 rectangle − potato CO2 outer shell – batter r = 0 − axial symmetry 1 MODEL: Definition of the geometry: DRAW MODE a chip is modelled as a cylinder a cylinder is obtained as a rectangle rotating around z-axis (r =0) r = 0 R3 CO2 r = 0 The typical modelling steps include: 1 MODEL (Definition of the geometry: Draw, Draw mode) 2 PHYSICS (Definition of the equations, parameters of the matter and boundary conditions: Physics) 3 MESHING (Mesh Mesh mode ) 4 SOLVING (Solve ) 5 RESULTS (Postprocessing) 2D geometry oil R3 rectangle − potato: length 0.074m (7.4cm), width 0.006m (6mm) CO2 outer shell – batter: thickness of 0.001m (1mm) around the potato

6. 6 2 PHYSICS: Subdomain settings Equations: Heat transfer by conduction Two subdomains: batter and potato. All the physical properties of the potato and batter should be defined. Unknown (variable) is T(t): How temperature within the chip depends on the heating time Parameters for batter and potato are taken from the data base or experiments Food data base: www.nelfood.com Username: GClayton Password: 1ruebeanwww.nelfood.com parametersbatterpotato δ ts 11 k 0.40.6 ρ 600700 CpCp 3851900 Q 00 Initial conditions for temperature T Init T(t 0 ) = 293 (Temperature at the initial time t 0 (t = 0)) potatobatter

7. 7 2 PHYSICS: Boundary settings Boundaries: between potato and batter (inner) between batter and oil (outer) Boundary conditions: Temperature (T 0 ) T 0 = 293K (room temperature between potato and batter) T 0 = 443K (temperature of the hot oil between batter and oil) While heating the chip the temperature inside the chip should increase from T 0 min (room T) to nearly T 0 max (hot oil)

8. 8 Why do we need mesh? An Idea of finite elements is the follows: when it is impossible to solve the equations for a “big object”, the object is divided into small pieces and the problem is solved for each piece. Such division into small pieces called meshing. A Mesh is a partition of the geometry model into small units of simple shapes. For a 2D geometry the mesh generator partitions the subdomains into triangular or quadrilateral mesh elements. If the boundary is curved, these elements represent only an approximation of the original geometry. The sides of the triangles and quadrilaterals are called mesh edges, and their corners are mesh vertices. A mesh edge must not contain mesh vertices in its interior. Similarly, in 3D the mesh generator partitions the subdomains into tetrahedral, hexahedral, or prism mesh elements whose faces, edges, and corners are called mesh faces, mesh edges, and mesh vertices, respectively. Equations have to be solved for all the edges and vertices. 3 MESHING (Mesh) The coarser is the mesh, the faster are the calculations (less computation time), but the worse is the accuracy. Refine mesh – make the mesh cells smaller

9. 9 4 SOLVING (Solve) Solver parameters: one can modify time t Solve 2D surface plot: T(t)

10. 10 Surface plot can be saved as a picture file (jpg, tiff) File −> Export −> Image −> change plot parameters if you like −> Export −>choose appropriate folder and save file. 5 RESULTS: Postprocessing and saving your data 1. Save graphical solution (2D surface plot from the previous page) 2. Make a probe plot (T(t) for several probe points) Postprocessing −> Probe Plot Parameters −> Defined Plots −> New −> New Probe Plot −> Coordinate probe −> −> type probe name (choose name yourself) −>OK −>Coordinate −> type coordinates of the probe point. Repeat from “New” if you would like to have several probes in different locations. If you would like to have plots for several coordinate probes in the same graph, trick “Plot all plots in the same axis”

11. 11 Probe examples: Middle of the chip: r = 0, z = 0.037 at 3mm from the side: r = 0.003, z = 0.037 at 3 mm from the bottom: r = 0, z = 0.003 Edit plot In the Figure 1 COMSOL click on “Edit plot” icon Edit plot Title, Axis and Lines −> Apply −> OK Save plot Save data file: click on “ASC ||” icon and save *txt file Copy image: click on “Copy” icon and paste you file to Word or PowerPoint Export image: click on “Export Image” icon and save the graph as a picture file (jpg, tiff) Solve You need to solve the task again to obtain the data for a probe plot

12. 12 3. Make a cross section plot (T(r) for different heating time) Postprocessing −> Cross-Section Plot Parameters −> −> Line/Extrusion −> Line plot−> Cross-section line data −> −> Coordinates of the desired cross section. Example: cross section across the middle of the chip: x-axis data: r coordinates: r0 = 0 r1 = 0.006 z0 = 0.037 z1 = 0.037 −>Apply You will get a graph with 81 lines (a line per each time interval from 0 to 80) Select several time intervals Postprocessing −> Cross-Section Plot Parameters −> General −> Solutions to use −> select several time intervals like 5, 10, 20, 40, 80 sec by Ctrl+left-click Save plot Same as for 2.

13. 13 Examples of the graphs Generate report: You can also save some data by “producing a report” as: File −> Generate report −> Browse the directory and file name −> Generate The report would not contain postprocessing graphs you made (T(t), T(r)), but it contains other information which could be useful for your reports. Description of the model: Help −> Model Documentation

14. 14 Chip size modification: Increase (decrease) the chip thickness Note, that you should modify the thickness of the potato keeping the thickness of the batter fixed (at 1mm) Potato: Draw mode −> click on potato rectangle −> double click on the potato rectangle OR Draw −> Object properties −> change width from initial 0.006 to 0.012 Batter: Draw mode −> Click on the batter layer −> double click on the batter layer OR Draw −> Object properties −> Curve selection There are 8 connected lines in the batter boundaries, you should adjust the length/coordinates of those which increase with the chip width. Example: Increase the thickness twice 1 not changed 2 r2 = 0.007 −> 0.013 (0.012 + 0.001) 3 r2 = 0.006 −> 0.012 4 not changed 5 r2 = 0.006 −> 0.012 6 r2 = 0.007 −> 0.013 (0.012 + 0.001) 7 r1 = r2 = 0.006 −> 0.012 8 r1 = r2 = 0.007 −> 0.013 Repeat all the stages: meshing, solving, postprocessing z r

15. 15 Exercise 1: Battered potato chip in oil Describe the model and parameters Perform the calculations and save the graphical 2D plot of the temperature distribution inside the chip. Put a probe point in the middle of the chip and obtain the probe point plot. Save it. Make a cross section plot for a slice across the middle of the chip. Save it. Describe the results. Additional exercise if you have desire and time: Place several probes on the chip and make probe plots T(t) to investigate how different points within the chip are heated. Make a cross section plot T(r) for several time intervals to investigate how temperature across the chip varies with different heating time (choose several time intervals in Postprocessing −> Cross-Section Plot Parameters −> General) Modify time interval in Solving Parameters and get what happened if fry the chip longer Exercise 2: Thicker battered potato chip in oil Modify the thickness of the chip and compare the results with Exercise 1 It could be useful for your report if you Generate Report after all your calculations and save Model Documentation file Exercise 3: Model Validation Propose an experiment to validate your model ( half a page + diagram)