A Dimensionless Empirical Model to Predict Heat Transfer Coefficients for Cooling High‐Moisture Meat Analog with Rectangular Dies

An empirical dimensionless relationship useful for estimating heat transfer coefficients during continuous cooling of high moisture meat analog (HMMA) in rectangular linear cooling dies is described here. This information is essential for designing better cooling dies, which is timely since the cooling rate has recently been demonstrated to be important in controlling the quality of HMMA. Wheat-based HMMA was extruded as per an experimental design that varied cooling media temperature (36-72°C), product mass flow rate (2.7-4.5 kg/h), and die aspect ratios (a* = 0.28 or 0.45). In situ product and cooling media temperatures and mass flow rates were measured continuously using penetrative thermocouples and flow meters, respectively. Dimensional scaling of the underlying differential equations governing heat transfer for this system demonstrated a relationship between dimensionless Nusselt ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mover><mml:mi>Nu</mml:mi> <mml:mo>¯</mml:mo></mml:mover> <mml:annotation>$\overline {{\mathrm{Nu}}}$</mml:annotation></mml:semantics> </mml:math> ), Graetz (Gz^-1), and conduit aspect ratio (a*) numbers. Values for these numbers derived from the described experimental data were fit via nonlinear regression to a dimensionless model of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mover><mml:mi>Nu</mml:mi> <mml:mo>¯</mml:mo></mml:mover> <mml:annotation>$\overline {{\mathrm{Nu}}}$</mml:annotation></mml:semantics> </mml:math> = A∙(Gz^-1)^B∙(C+D∙[1-a*]^E) with a high degree of quality (root mean square error = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mover><mml:mi>Nu</mml:mi> <mml:mo>¯</mml:mo></mml:mover> <mml:annotation>$\overline {{\mathrm{Nu}}}$</mml:annotation></mml:semantics> </mml:math> ± 4.9, p < 0.0001). The resulting fit parameters were deemed reasonable given that the model was logically bound within theoretical Nusselt number limits. The model documented here allows for the estimation of heat transfer coefficients relevant to HMMA cooling dies, while also illustrating the effect of altering cooling die aspect ratios and heat exchanger lengths as would be considered when scaling up an HMMA process. PRACTICAL APPLICATION: Carefully balanced cooling rates are essential for producing whole-cut type meat analogs with a desirable texture and fibrous quality at an economically feasible scale. This work presents a useful model for estimating the required cooling rates of whole-cut type meat analogs as a function of key processing criteria such as production rate and product size. Models like this would be useful for engineers and scientists attempting to optimize their meat analog processes, with such efforts ultimately resulting in reduced costs and improved quality associated with meat analog production.