New Approaches to Improve Safety and Quality in Cooking of Hamburger Patties

Introduction

In recent years, the cooking process of hamburger patties has been brought to question due to several outbreaks of food poisoning (Ahmed et al., 1995; Goepfert, 1977; Hague et al., 1994; Jackson et al., 1996; and Rita et al., 1993). The primary method of destroying pathogens such as E. coli O157:H7 in hamburger patties is to cook them to a proper internal temperature. USDA and FDA recommend slowest heating points for hamburger patties of 71°C (USDA, 1998) or 68°C for at least 15 s, (FDA, 1999). However, implementation of these standards has been difficult because of the complexity of measuring the internal temperature of patties and the nonhomogenous composition of hamburger meat. As a result, hamburger patties often are overcooked, leading to deterioration in textural quality, or undercooked, which presents a potential safety problem. A fundamental understanding of the hamburger cooking process and its effect on textural quality and microbial lethality can lead to improved specifications and new design of equipment and sensors that ensure the safety and quality of cooked patties.

In a typical process, frozen or refrigerated hamburger patties are cooked by placement directly on either single-sided or double-sided contact grills. During a relatively fast cooking period, typically less than 2 min for a 1-cm-thick patty, several physical and chemical changes take place, such as the melting of ice and fat, evaporation of water, drainage of water with solutes and pigments, fat expulsion, and protein denaturation. The heterogeneous nature of hamburger meat, due to nonuniform distribution of fat, protein, and water, causes nonuniform rates of heat and mass transfer.

The denaturation of protein in hamburger meat during cooking results in major alterations in the structure of a patty. The most commonly observed dimensional change in hamburger patties during cooking is the decrease in diameter and thickness due to shrinkage. These physical changes are influenced by the product properties, rates of heat and mass transfer, and cooking conditions. Shrinkage of a patty results partly from the evaporation of water and drainage of melted fat and juices. These structural alterations influence the textural quality of cooked patties.

During cooking, the patty surface temperature exceeds 100°C, resulting in the formation of a thin crust layer. The thickness of the crust layer increases with cooking time. The physical and thermal properties of the crust layer are different from those of the internal core region. The crust layer, with its distinct porous structure, affects the rates of heat transfer and vapor and fat transport. In addition, the crust layer changes the textural quality of hamburger patties. The influence of crust layer on rates of the heat and mass transfer and textural quality needs to be quantified for designing improved cooking processes.

The setting of gap thickness between the two heating plates in a double-sided grill causes a certain pressure on hamburger patties as they are cooked from both sides. The application of pressure on the patty influences the contact heat transfer coefficient between the patty surface and the grill heating surface. This pressure also has an effect on the physical dimensions and cooking losses from the patties. Yet, little is known about the quantitative effects of pressure on heat and mass transfer during the cooking of a hamburger patty.

The heat and mass transfer processes occurring in a hamburger patty are complicated phenomena due to transient changes in physical and thermal properties. To improve the textural quality of cooked hamburger patties while ensuring food safety, it is necessary to systematically study the influence of process variables on physical properties, textural quality characteristics, and pathogen destruction under different cooking conditions. Use of predictive mathematical modeling can provide valuable insight to the sensitivity of various process conditions. Considerable progress has been made during the past year in modeling internal heat transfer in hamburger patties. The overall goal of this renewal proposal is to determine the textural properties of hamburger patties during cooking and incorporate them in a predictive model.

Objectives

The proposed research will specifically address the following objectives:

(1) Quantify changes in mechanical properties of hamburger patties as influenced by initial composition of hamburger meat, initial temperature, cooking temperature, and applied pressure, and determine their effects on the overall textural quality of patties during cooking.

(2) Determine the influence of fouling of the heating surface and applied pressure on the contact heat transfer coefficient during cooking of a hamburger patty.

(3) Extend the newly developed, one-dimensional predictive model of heat transfer to a two-dimensional axisymmetric model to predict the textural quality of patties.

(4) Incorporate textural properties and microbial lethality in optimization methods to develop new and improved cooking processes for hamburger patties that ensure a safe product with desirable levels of textural quality and yield.

Literature Review

The influence of the composition of hamburger patties on process conditions and product quality have been studied by Troutt et al. (1992b), who reported that high-fat hamburger patties require a longer cooking time to reach the desired center temperature. Others also have reported that physical properties of hamburger patties, such as thermal conductivity, density, and specific heat, are influenced by fat content (Baghe-Khandan et al., 1982; Baghe-Khandan and Okos, 1981; Dagerskog, 1979a; and Sörenfors and Dagerskog, 1978). A study of the thermal properties of hamburger meat as a function of temperature has been recently completed by Pan(1998) and is presented here in the Progress Report section.

The cooking process leads to shrinkage of hamburger patties accompanied by a decrease in water-holding capacity. This phenomenon results in cooking losses. Again, Troutt et al. (1992b) noted that the cooking losses in hamburger patties increased from 24.8 to 32.1% when the fat content increased from 5 to 30%. The heating of hamburger patties results in significant dimensional changes during contact cooking. Troutt et al. (1992a) and Lin and Keeton (1994) reported that the decreases in diameter and thickness were about 4.5 to 13% and 25%, respectively. Similar phenomena were also observed by Berry et al. (1981) and Berry (1996) for hamburger patties that were broiled in a conveyor oven or cooked on a double-sided grill.

The most dramatic changes in hamburger meat during heating, such as shrinkage, tissue hardening, juice release, and discoloration, are caused by changes in muscle protein denaturation. This is defined as a change in the specific steric conformation of a protein, i.e., a change in the secondary and tertiary structure without a chemical modification of the amino acids (Bouton et al., 1976; Bowers et al., 1987; and Hamm and Deatherage, 1960). Hamm (1977) reported that for beef muscle, changes in tenderness, rigidity, and water-holding capacity caused by heating occur in two phases, the first phase being between 30 and 50°C, and the second between 60 and 90°C. At a temperature between 50 and 55°C, negligible changes occur. Changes in the first phase are due to heat coagulation of the actomyosin system. Changes in the second phase are due to denaturation of the collageneous system (shrinking and solubilization of collagen) and/or the formation of new stable cross-linkages within the coagulated actomyosin system. The denaturation of protein in meat results in a decrease in water-holding capacity. A recently developed predictive model of heat transfer allows temperature mapping within a patty undergoing cooking (Zorrilla and Singh, 1999). This model can be adapted to identify the temperature-induced changes by location within the patty.

Martens et al. (1982) studied changes in the texture of meat during cooking as influenced by thermal denaturation of muscle proteins and reported that an optimal texture was obtained in the 60 to 67°C temperature region, implying denatured myosin and collagen. Troutt et al. (1992b) studied the effects of fat level and endpoint temperature on textural and sensory qualities and showed that cooking to 77°C accentuated physical and sensory differences between low- and high-fat patties, compared with cooking to 71°C. Low-fat patties had a firmer texture and were more crumbly, less juicy, and less flavorful. Hanenian et al. (1989) reported on the effects of prechilling, freezing rate, and storage time on beef patty quality.

Most of the research conducted measuring sensory and physical properties of beef patties has involved the addition of texture-modifying ingredients (Brewer et al., 1992; Troutt et al., 1992b), fat substitutes (Ju and Mittal, 1999), or changes in fat levels and cooking methods for the patties (Berry and Leddy, 1984; Troutt et al., 1992a; Berry, 1994).

Considerable effort has been focused on reducing the fat content of ground beef patties. However, their textural quality is highly dependent on the fat content, because fat contributes to increased flavor, tenderness, and juiciness of the product (Cross et al., 1980; Brewer, 1992). This effect may be partially due to the longer cooking times required for the lower-fat level patties to reach the equivalent internal temperature of high-fat patties (Troutt et al., 1992a,b). Ju and Mittal (1999) found that the fat level can be reduced without affecting tenderness and juiciness using proper fat-substitutes.

Beef patties are often frozen for purchasing and distribution requirements. Faster freezing has been found to improve tenderness, juiciness, and flavor of high-fat level beef patties (Berry and Leddy, 1984), as well as ensure tenderness for low-fat ground beef (Berry, 1993).

The relationship between the sensory and textural qualities of cooked patties has been studied by Berry and Bigner-George (1999), Berry (1996), Lin and Keeton (1994), and Cross et al. (1978). Cross and colleagues showed that the subjective panel evaluation of the amount of connective tissue and tenderness of cooked patties correlated well with the readings obtained with the Instron Universal Testing Machine. These studies emphasize the suitability of using instrumental methods for describing the textural quality of hamburger patties.

The overall contact heat transfer coefficient for double-sided cooking with 3.15 g/cm² of pressure on the top of the patty was determined by Dagerskog and Sörenfors (1978) to be 260 ± 50 W/m²°C. Dagerskog (1979a) calculated the heat transfer coefficient as 425 ± 33 W/m²°C when the distance between the two frying pan surfaces was constant. The difference between the two heat transfer coefficients was due to the higher contact pressure when the two heating surfaces were controlled at a constant distance. Housova and Topinka (1985) reported that the heat transfer coefficients were in the range of 200 to 1200 W/m²K, depending on product type, temperature (measured only at 115 and 140°C), pressure, and stage of the heat treatment. A complete description of how the contact heat transfer coefficient changes during the cooking cycle is unavailable, yet it is crucial for reliable prediction of heat transfer during cooking of patties.

Progress Report (1997-2000)

The three objectives of our current amended project are as follows:

(1) Determine changes in physical and thermal properties (thermal conductivity, specific heat, porosity, density) of hamburger patties as influenced by the initial composition of hamburger meat, initial temperature, cooking temperature, and applied pressure.

(2) Develop predictive mathematical models to describe heat transfer in hamburger patties involving dimensional changes, pathogen destruction, and textural modifications during cooking.

(3) Using optimization methods, develop new and improved cooking processes for hamburger patties that ensure a safe product with desirable levels of textural quality and yield.

Significant progress has been made in addressing the first two objectives during the first year of the project.

Physical and Thermal Properties: Hamburger patty meat was obtained from a commercial patty manufacturing plant. It had a moisture content of 59.9% and a fat content of 23.8%. Physical and thermal properties of the hamburger meat were measured at 30, 40, 50, 60, 70 and 75°C at holding periods of 2, 10 and 20 min. The density, volume, thermal conductivity, specific heat, and water and fat loss were measured. The lowest density of 1.01 g/cm³ was obtained for a temperature range of 50 to 60°C. The volume change of hamburger meat with an original weight of 11.5 g showed a significant decrease from 11.02 cm³ to 8 cm³ when the temperature was increased from 30 to 70°C, respectively. When the holding period was increased from 10 to 20 min, the volume change was insignificant. Water loss from the hamburger meat was about 30% when the meat was heated from 30 to 70°C. The fat content of hamburger meat decreased from 23.8% to around 19% at 70 °C. Thermal conductivity was measured using a line source probe. It varied from 0.35 to 0.41 W/m°C in the temperature range of 5 to 70°C (Pan, 1998; Pan and Singh, 1999).

Measurement of Patty Center Temperature as Influenced by Grill Operating Factors: A comprehensive experimental study was designed, based on the Taguchi method, to assess the influence of various process and product variables on the patty center temperature profiles. Five control factors were selected: clam-shell grill, top plate temperature, bottom plate temperature, gap thickness, and cooking time. Interactions between the aforementioned control factors were also considered. Patty variation was considered to be minimal, as all patties were obtained from the same lot from a commercial supplier. Two levels of each control factor were used; this required the use of clam-shell grills from two different manufacturers. The two manufacturers (Garland, Taylor) provided new commercial grills fully equipped with appropriate data gathering sensors. The total number of degrees of freedom for control factors and interactions amounted to 15; therefore, an orthogonal array (L₁₆) was used to design the experiment. For each trial, six replicates were used.

For each replicate, a total of six (113 g each) or nine (45.5 g each) hamburger patties were cooked. Two of the patties in each trial had thermocouples placed at their center locations. All experiments were conducted in a randomized manner. For this study, approximately 2,200 patties were cooked over a two-week period. The operating procedures as used in commercial practice were strictly enforced; this was ensured by the engineering staff of equipment manufacturers who were present for most of the experimental trials. Data analysis indicated that the most critical factor influencing the center temperature of patties was the cooking time, followed by gap thickness. The results showed that, although the plate temperatures were close to the set conditions, when a frozen patty is placed on the grill, the bottom plate temperature drops by almost 10.5°C and the top plate temperature by 8 to 10.5°C. The plate surface temperature returns to the set conditions only after 100 s or more, which is close to the end of the cooking cycle. Therefore, the plate surface temperature should be treated as a variable rather than a constant in mathematical modeling (Singh, 1998). Center temperature profiles were obtained from all trials. These data were later used in checking the validity of the predictive models.

Development and Validation of a Predictive Model: A computer-aided predictive model was developed to predict heat and mass transfer in hamburger patties during cooking. This model is based on a moving boundary problem and treats the patty as a one-dimensional object. The model uses the enthalpy method for solving the governing heat transfer equation.

Figure 1 shows the experimental and theoretical temperatures and the plate temperatures for each case. The bottom plate temperature was set at 204ºC and the top plate at 221ºC. A drop in the plate temperatures can be observed when frozen patties are placed on the grill. Excellent agreement between the predicted and experimentally measured center temperature was obtained.

Temperature profiles as a function of axial position for different times are shown in Fig. 2. As shown, the liquid-solid interface during the melting process moves inward faster than the crust-core interface.

Simulated center temperature profiles are shown in Fig. 3 for different heat transfer coefficients. The influence of this parameter is very important, but in most of the published studies a constant value has been assumed because of difficulty in obtaining experimental data. This value may depend on product type, contact plate temperature, contact pressure, and stage in the heat treatment. Thus, further studies are needed to obtain reliable values for how this coefficient changes during heating and its influence on the textural properties and the center temperature profile.

Simulated temperature profiles considering different gap thicknesses between plates are shown in Fig. 4. In this case, the same heat transfer coefficient is assumed, although there may be a relationship between gap thickness and heat transfer coefficient. When the patty is pressed more, the contact surface increases, which may improve the heat transfer. However, the fat and water release also increases, and the composition of the layer between the hamburger and the plate possibly changes and also affects heat transfer. These variables need further investigations (Pan et al., 1999; Zorrilla and Singh, 1999).

The predictive model was useful for identifying gap thickness as the most influential among various process conditions. A small change, on the order of 1 mm in gap thickness, can result in over 20°C difference in center temperature at the end of the cooking time (Fig. 4). Results from the predictive model showed that small variations in the plate surface temperature do not seriously influence the final center temperature. However, the quality characteristics at the surface of the hamburger patty may be affected by changes in plate surface temperature. The predictive model is also useful in determining the influence of changing initial fat levels and different holding periods after removal of a patty from the grill. The model has been extended to incorporate the kinetic parameters for E. Coli O157:H7. The integrated lethality at the center of a patty is readily predicted with the model.

The predictive model, initially written in Fortran, was rewritten using Visual Basic as a user-friendly, Windows-based program. This beta version of the model was distributed to grill manufacturers, hamburger patty manufacturers, and hamburger processors. The model is already being used by these commercial companies for improving grill design, assessing the effect of patty thickness on cooking times, and seeking new ways to process hamburgers.

Rationale and Significance

Beef continues to be the most popular meat in United States, with nearly nine out of ten U.S. households eating beef in a two-week period, generating more than $50 billion in beef sales annually. Hamburgers dominate the number of beef servings in food service, comprising 76.6 percent of total beef market (NCBA, 1999). U.S. companies benefit from the worldwide popularity of hamburgers; for example, McDonald’s has restaurants in 100 countries, serving several million hamburgers per day. To manufacture safe, high-quality products and introduce processing innovations in the prepared-food industry, a fundamental understanding of the cooking process is required.

The textural quality of cooked hamburger patties can be improved and the safety risk from undercooking can be minimized by (a) obtaining a fundamental description of the mechanisms of heat and mass transfer, (b) quantifying changes in textural quality characteristics, and (c) determining microbial lethality during the cooking process. To optimize the cooking conditions for achieving improved product quality, predictive models of heat and mass transfer coupled with textural quality are necessary. The results of predictive heat transfer models can help address food safety issues associated with the survival of pathogens such as E. coli O157:H7 in undercooked patties. Recent outbreaks of E. coli O157:H7 in undercooked hamburger meat (1993 and 1997 outbreaks in the United States) emphasize the significance of this study. It is obvious that these types of outbreaks bring to question the safety of the U.S. food supply chain. The negative consequences of such incidents are worldwide, with potential harm to the U.S. food industry. An increased level of understanding of the material science (in our case hamburger meat) and use of predictive modeling (of the cooking process of patties) can provide improved recommendations for the process and design of new equipment to alleviate such mishaps.

Optimization studies are necessary to obtain new information for designing the next generation of grills with dynamic controls to improve product quality and safety. The results of the proposed research are expected to provide new and useful information for food and equipment manufacturers, operators of restaurants and fast-food establishments, consumers, and regulatory agencies for future product development and quality control.

Research Methods

This research will involve both experimental investigations and modeling of the textural quality of hamburger patties. Experimental studies are necessary to obtain data on mechanical properties needed for the development and validation of models. The current predictive model for heat transfer will be improved by incorporating information on variable contact heat transfer coefficient and use of axisymmetric cylindrical geometry. The experimental plan will be aimed at addressing questions such as:

(1) What is the kinetic rate of change of mechanical properties of hamburger meat as a result of different cooking times and conditions?

(2) How do fouling of heat transfer surface, gap thickness and contact heat transfer coefficient influence the cooking of hamburger patties in double-sided grills?

(3) What is the sensitivity of various product and processing variables on the accuracy of heat transfer and textural quality models in predicting temperature profiles and quality of hamburger patties?

(4) What level of precision is required in controlling the product and process variables (such as gap thickness, patty thickness, grill temperature, and grill surface) in commercial operations to achieve consistency in textural quality and safety in cooking of hamburger patties.

Experimental Investigations: For cooking hamburger patties, commercial-scale double-sided grills will be used. Two double-sided grills (Welbilt Model MWE-9501, Garland, PA, and Taylor Model 32, Rockton, IL) are available on loan to the PI for the proposed duration of the project. Restaurants use these grills worldwide (including McDonald's, A&W, and Hardy's). The design of these grills allows the two opposite heating surfaces to be maintained at constant and/or variable temperatures. The gap thickness can be set to any desired value, and the grill can be programmed so that the gap setting can be varied during the cooking process.

Frozen patties will be obtained directly from a manufacturing facility and prepared according to industry and custom-specifications. These patties will be prepared using industrial forming equipment; therefore, the porosity and other physical characteristics of the patties will conform to industrial practice.

The temperature profiles within the patties during cooking will be measured using type T thermocouple probes of size 24 gauge. Before the patties are frozen at the commercial facility, 1-mm diameter needles will be inserted in patties in the radial direction so that their tip is at the axial center. The patties will be then frozen and shipped to our laboratory at UC Davis. Prior to cooking, needles will be extracted, and thermocouples will be inserted in their place. We have used this procedure for the current project and have found it to cause minimal disruption of the meat structure within the patty and provide reliable data.

Water, fat, and protein content of the patties will be determined immediately after cooking using AOAC (1990) methods. Cooking loss will be calculated based on the initial and final weights of hamburger patty samples taken from the patty center (Berry and Bigner-George, 1999).

For double-sided grills, the contact heat transfer coefficients between the patty and the heating surface, under different pressures, will be determined using a heat flux sensor (HFS-3, Omega Eng., Stamford, CT). The thin-film heat flux sensor will be placed between the heating surface and patty surface. The heat transfer coefficient will be determined as the ratio of the heat flux and the difference between the temperatures of the two adjacent surfaces. It is known that over long periods of use the roughness of the grill surface changes. To evaluate the influence of grill surface characteristics on the contact heating process, the heating plates used in the grill will be machined to different levels of roughness. The roughness of the heating plates will be measured with a surface roughness tester (Model TR 240, Qualitest International, Inc., Ontario, Canada), and the contact heat transfer coefficient obtained for each roughness will be measured. Any significant influence of the surface roughness on the contact heat transfer coefficient and its subsequent effect on center temperature profile will provide a basis for developing a sensor to evaluate the condition of grill surfaces.

The accumulation of meat residues and melted fat on the grill surface causes fouling of the heating surface. The effect of fouling on center temperature profiles will be assessed using the heat flux sensor. The development of the fouling layer in repeated cooking cycles will be determined with a video microscope (Olympus, OVM1000NM).

The effect of fat content and initial temperature of patties on the textural quality of the patties will be determined using ASMA (1995) guidelines. Patties with fat contents of 15, 20, 25, and 30% will be obtained. Initial temperature will be between -20° and 5°C. Frozen patties will be cooked directly by placing them on the heated grill, or the patties will be thawed first to a specified temperature just before cooking. The time needed to thaw the patties will be determined.

To characterize the texture of cooked hamburger patties, mechanical properties will be measured using two different procedures. In each case, the time elapsed between removal of the cooked patty from the grill and property measurement will be kept to a minimum. The temperature of the patty will be monitored during the time that it is evaluated for its mechanical properties. According to the first procedure, a 2.5-cm wide strip cut from the center of each patty will be sheared three times with a straight edge blade using a Texture Analyzer TA.TX2 (Texture Technologies Corp., Scarsdale, NY) similar to AMSA (1995) procedures. The data obtained from the shearing test will include peak load, peak energy, post peak energy, modulus, and displacement at the peak load (Berry and Bigner-George, 1999).

The second procedure will involve conducting texture profile analysis using the Texture Analyzer. The sensory process where human subjects evaluate food texture can be simulated by applying instrumental texture profile analysis (Szczesniak et al., 1963; Friedman et al., 1963; Bourne, 1978) to two successive compression cycles imposed on the food. Five cylindrical samples (diameter 23 mm) will be removed from each patty with a core borer. Each sample will then be compressed twice to 75% of its original height using a 40-mm diameter aluminum cylinder probe at a test speed of 5 mm/s. Analysis of the resulting two force deformation curves will be analyzed for several textural characteristics such as fracturability, hardness, cohesiveness, adhesiveness, springiness, gumminess, and chewiness.

A central composite design will be used to evaluate the effect of five independent factors (initial patty thickness, initial patty composition, grill surface temperature, cooking time, and pressure) on two dependent variables (textural quality and cooking loss) for patties cooked to a desired center temperature. The regression equations developed from the experimental results will be used to determine changes in textural quality and yields of patties for heat transfer calculations and process optimization.

For the current project, the information on lethality of pathogens in hamburger patties during cooking has been obtained from published data. Specifically, thermal lethality data in the form of D- and z-values for E. coli O157:H7, Listeria monocytogenes, and Salmonella spp. was obtained from Line et al. (1991), Carlier et al. (1996), and Goodfellow and Brown (1978). Pflug (1997) recently presented the use of D- and z-values in evaluating lethality of a hamburger patty cooking process. Juneja et al. (1997) provided results on internal temperature and survivor data for E. coli O157:H7 in hamburger patties undergoing a typical cooking process. These kinetic data of microbial lethality have been incorporated in the predictive heat transfer model to predict integrated lethality in cooking and holding periods typically used in clam-shell grills.

Mathematical Modeling: In the current study, a one-dimensional heat transfer model has been developed and validated with excellent agreement between experimental and predicted results (described in the Progress section). We would like to extend this model to an axisymmetric cylindrical object that is more representative of a patty. Although we do not expect any different results for the center temperature, due to the large ratio of diameter to thickness (usually above 8) in a hamburger patty, the temperature predictions for the peripheral regions of a patty are expected to be more accurate with the proposed cylindrical model. The higher temperatures reached in the peripheral regions, due to convection and radiation from the edge surfaces, have a profound effect on the textural quality of that region. Therefore, prediction of temperatures in the peripheral zones is necessary to accurately model the overall textural quality of the cooked patty.

The emphasis in mathematical modeling will be to develop predictive models based on physical mechanisms. This is in contrast to developing empirical models based on regression analysis. The predictive models require knowledge of physical and thermal properties and appropriate initial and boundary conditions to predict rates of heat and mass transfer for a given process and the subsequent changes in mechanical properties.

Similar to the development of the one-dimensional predictive model, heat transfer in hamburger patties will be treated as a problem of transient heat conduction with phase changes, including melting of ice and fat and evaporation of water. This type of problem is commonly referred to in the literature as the moving boundary problem. The boundary between two phases such as solid ice and melted water moves from the outside to the interior as initially frozen material is heated. Similarly, the evaporation front of water, which separates the patties into core and crust regions during cooking, moves from the surface toward the center.

In the core region, phase changes such as melting of ice and fat take place over a range of temperatures, during which the physical and thermal properties of patties change. The methods used for solving problems involving a single, discrete phase change temperature are not applicable for this situation. Therefore, the enthalpy method used previously in our laboratory for solving phase change problems in freeze/thaw and frying applications will be used (Mannapperuma, 1988; Mannapperuma and Singh, 1989; Vijayan, 1996; and Voller, 1985). In the enthalpy formulation, the enthalpy function H(T), which is the total heat content of the substance, enters the problem as a dependent variable along with the temperature. The governing equation of the heat conduction problem with phase change in cylindrical coordinates is given by:

(1)

where T = T{H}, k = k {H}, H = specific enthalpy (J/m³), t = time (s), T = temperature (°C), k = thermal conductivity (W/m°C) z = axial distance (m), and r = radial distance (m).

A moving interface separating two regions when the water vaporization temperature is reached and a third type boundary condition at the patty surface considering a contact heat transfer coefficient will be assumed in the axial direction. Furthermore, a boundary condition considering a combined heat transfer coefficient for radiation and convection at the peripheral edge and the symmetry condition in the center will be assumed in the radial direction. The governing equation (Eq. 1) will be solved using finite difference techniques that incorporate dimensional changes by recalculating the grid size at selected time intervals (Lang et al., 1994; Balaban, 1989).

The microbial lethality data will be incorporated as a separate subroutine within the program, so that integrated lethality may be predicted along with temperature for a patty during cooking.

Once the predictive heat transfer model in cylindrical coordinates is validated with experimental data on temperature profiles, the sensitivity of the process to various cooking conditions will be examined, and the most sensitive process variables will be identified.

The properties obtained for textural quality, using the procedures described earlier in this section, will be incorporated as a function of temperature in the predictive model. Thus, the model will predict temperature as well as textural quality characteristics. It is understood that the textural property data will be empirical in nature; therefore, sufficient trials must be carried out to obtain a wide range of process conditions such as grill temperature, gap thickness, cooking time, initial fat content, and patty thickness. It should be also noted that, although sensory studies to obtain textural properties would be useful, they are not being proposed at this stage in order to keep the overall cost of the project at a minimum. Instead, only instrumental procedures will be used to develop the required data. Several researchers have previously shown good agreement between sensory and instrumental measurements for hamburger cooking (Berry and Bigner-George, 1999; Cross et al., 1978; and Berry, 1996).

Optimization Studies: Although a limited number of optimization studies have been conducted in the current project, no work was performed to optimize for textural quality. The emphasis for the proposed work will be to incorporate textural quality along with an ensured level of safety in the optimization studies. For this purpose, an optimization procedure will be used. Banga et al. (1991) and Banga and Singh (1994) used an Integrated Controlled Random Search for Dynamic System (ICRS/DS) optimization method, which is based on the combination of robust parameterization of the control function and a computationally efficient, nonlinear programming algorithm of unconditional convergence. The ICRS/DS algorithm has been used successfully in optimizing the drying process of foods and thermal processing of canned foods. The ICRS/DS method will be used in this proposed research for optimization purposes.

For the double-sided grill, the objectives of the optimization will be to determine optimal processing conditions that can achieve the highest patty yield (minimum cooking losses) with required microbial destruction and textural quality. To fulfill these objectives, the following optimization problem will be studied:

Determine the grill temperature profile T(t) (control variable) for

0 £ t £ t_final to maximize patty yield (Y) subject to the constraints

(a) T_c(t = t_final) ³ T_rc

(b) CRC(t = t_final) ³ ln(`C<sub>0</sub>/`C_f)

(c) F(t = t_final) £ F_upper

(d) T_lower £ T(t) £ T_upper

(e) P_lower £ P £ P_upper

where T_c = center temperature of patties, T_rc = required minimum center temperature, t_final = total cooking time, CRC = required natural logarithm cycles of microbial reduction, F = textural quality index (such as area under force curve from textural quality measurement),`C<sub>0</sub> = initial average population of microbes in patties,`C_f = final average population of microbes in patties, T = grill temperature, P = pressure, and subscripts: lower, upper = lower and upper bounds of each variable.

The shortest cooking time will be determined based on the highest patty yield (Y) by using different t_final values in the optimization calculations. The optimal processing conditions will be those achieving the highest patty yield and ensuring required safety and quality using the shortest cooking time.

While the proposed studies involve modeling of complicated phenomena such as texture in a heterogeneous material, the expected success of the proposed experimental and mathematical methods is based on the experiences gained from the current USDA/NRIP-supported research on modeling heat transfer in hamburger patties and previous research on food frying. Most of the equipment needed for the proposed studies is available. The study of fouling and grill surface characteristics on contact heat transfer and inclusion of textural properties in the predictive model during cooking are examples of novel approaches necessary to make future advances. Although the focus of the proposed research will be on hamburger patties, the information to be gained in this research is expected to have wide applications in the manufacturing of prepared foods¾a rapidly expanding sector of the U.S. food industry.

References to Project Description

Ahmed, N. M., D. E. Conner, and D. L. Huffman. 1995. Heat-resistance of Escherichia coli O157:H7 in meat and poultry as affected by product composition. Journal of Food Science 60(3):606-610.

AOAC. 1990. Official methods of analysis. Association of Official Analytical Chemists, Washington, D.C.

Baghe-Khandan, M. S., and M. R. Okos. 1981. Effect of cooking on the thermal conductivity of whole and ground lean beef. Journal of Food Science. 46:1302-1305.

Baghe-Khandan, M. S., M. R. Okos, and V. E. Sweat. 1982. The thermal conductivity of beef as affected by temperature and composition. Transactions of the ASAE, 25:1118-1122.

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