Artificial Neural Network Modeling of Thermal Conductivity Changes in Milk during Mechanized Khoa Production
Abstract
An artificial neural network (ANN) approach was successfully deployed to model and predict the thermal conductivity of milk and concentrated milk systems during mechanized khoa production. Reliable data points (n=203) spanning wide operational boundaries of temperature (275.15–353.10 K), moisture content (48.82–92.00%), and fat content (0.00–11.17%) were compiled from established experimental studies to formulate and validate the model. A multi-layer feed-forward network optimized via the quasi-Newton algorithm using a 3:3:1 topology (three inputs, three hidden neurons with hyperbolic tangent activation functions, and a single linear output layer) demonstrated optimal predictive behaviour. The architecture yielded outstanding precision on independent testing subsets, demonstrating a strong correlation coefficient (R = 0.986), a minimal root mean squared error (RMSE = 0.0084 W/m•K), and a normalized squared error of 0.029 (normalized to the variance of the target data). Input sensitivity computations verified that product temperature (31.4% contribution) and moisture content (30.2% contribution) exert the highest thermodynamic control on thermal conductivity shifts, whereas fat content (4.4% contribution) exhibits a weaker but consistently inverse linear relationship. The resolved predictive equations were effectively embedded within a highly practical Microsoft Excel-based graphical user interface (GUI) to assist dairy process designers in real-time calculation, simulation, and industrial scaling of continuous scraped surface heat exchangers for indigenous milk confectionery manufacturing.
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Introduction
Khoa is one of the most prominent traditional indigenous dairy products in the Indian subcontinent. It is conventionally manufactured by the gradual heating, desiccation, and continuous concentration of whole milk in open kettles at atmospheric pressure, combined with continuous manual scraping and stirring until a dense, semi-solid dough-like consistency is achieved. Industrially, khoa serves as an essential intermediate base matrix for an extensive portfolio of traditional sweets including peda, burfi, milk cake, kalakand, and gulabjamun. Annually, approximately 600,000 metric tons of khoa are manufactured within India alone, representing a vital utilization channel for nearly 7% of the nation's total fluid milk production.
Driven by the growing urban and commercial demand for uniform-quality milk sweets, the dairy sector has progressively moved away from batch-oriented cottage-level preparation toward large-scale mechanized desiccation systems. Modern continuous machinery — specifically single and multi-stage inclined scraped surface heat exchangers (SSHE) and thin-film evaporation plants — has been developed to support industrial throughput. However, raw milk and its concentrated intermediates display non-linear, non-Newtonian behaviour and are highly susceptible to chemical degradation, thermal discoloration, and fouling if process heat flux is inappropriately regulated.
The rational design, computer-aided simulation, and precise control of modern high-efficiency heat exchange equipment depend fundamentally on accurate knowledge of the physical and thermodynamic properties of the milk matrix across the entire path of its concentration gradient. Among these properties, thermal conductivity (k) stands out as a critical parameter driving transient heat transfer and temperature distributions within the product film. Despite its obvious importance, historical data regarding the thermal conductivity of milk are often constrained to narrow temperature or solids ranges, typically treated as simple binary water-solid systems or presented solely in fragmented tabular or graphical formats that are cumbersome for continuous spreadsheet-based engineering calculations.
Furthermore, thermal conductivity is heavily influenced not only by gross moisture content but also by complex structural rearrangements among the constituent solids, including lipid state transformations and protein concentration cross-linking under elevated temperature kinetics. Because milk composition varies continuously across the multi-stage desiccation cycle of khoa, empirically measuring thermal conductivity across all prospective micro-states is practically unfeasible. Consequently, a reliable and mathematically robust predictive framework is required.
Artificial Neural Networks (ANN) represent a powerful class of data-driven computing models capable of learning intricate non-linear relationships directly from numerical examples without demanding precise prior physical formulations. ANNs excel at managing structural uncertainties and noisy experimental measurements. This study aims to develop, optimize, and deploy a compact, highly precise feed-forward ANN framework capable of accurately mapping thermal conductivity as a direct function of product temperature, moisture content, and fat content, thereby providing process engineers with an accessible, high-fidelity modelling tool for traditional dairy process scaling.
Conclusion
This study successfully developed and validated a compact 3:3:1 feed-forward artificial neural network optimized via the quasi-Newton algorithm to predict the thermal conductivity of milk during khoa production. The developed network achieved high predictive accuracy, demonstrating a strong testing correlation coefficient of 0.986 and a minimal RMSE of 0.0084 W/m•K across diverse operational ranges. Input sensitivity analysis revealed that product temperature and moisture content exert primary thermodynamic control over the system (31.4% and 30.2% contributions, respectively), while fat content serves as a secondary, inversely correlated structural variable (4.4% contribution), with the remaining variance attributable to non-linear interaction effects among the three inputs. By converting the trained network into explicit algebraic equations and embedding them within an accessible Microsoft Excel GUI, this research provides a practical, high-fidelity design tool. This framework can assist dairy process engineers in accurately simulating, sizing, and controlling automated heat exchange equipment, helping transition traditional indigenous dairy confectionery manufacturing toward efficient, modern industrial scales.
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