Structural Optimization and Carbon Emission Sensitivity Analysis of Multi-Temperature Cold Chain Warehouses Based on Thermal Resistance Network and Heat Transfer Entropy Generation

Focusing on the core strategic demand for the low-carbon transformation of global cold chain logistics, multi-temperature cold chain warehouses, as key infrastructures in fields such as pharmaceutical cold chains and cross-border fresh food storage, are facing increasing issues of energy consumption and carbon emissions [1-7]. Data show that heat loss from the building envelope accounts for 40%-60% of the total energy consumption in cold chain warehouses, and the temperature gradient between multiple temperature zones leads to strong thermal interference, further intensifying the irreversibility of the heat transfer process, which results in a sharp increase in refrigeration system energy consumption [8, 9]. Existing structural optimization research mainly focuses on superficial optimization of macroscopic energy consumption indicators, neglecting the deep coupling relationship between "thermal transfer physical essence—irreversibility of energy consumption—carbon emissions," which makes it difficult to achieve low-carbon design at its core, thus restricting the cold chain industry’s contribution to the global "dual-carbon" goals [10]. In line with the United Nations Sustainable Development Goals, this study aims to build an optimization system that combines physical essence and engineering practicality for the heat transfer characteristics and low-carbon needs of multi-temperature cold chain warehouses. It not only provides technical support to address the high carbon emission pain points of cold chains but also enriches the interdisciplinary theory of heat transfer optimization and low-carbon buildings, with important engineering practical value and academic exploration significance.

Existing research has accumulated certain knowledge around thermal resistance network modeling, heat transfer entropy generation analysis, and cold chain carbon emission optimization, but significant academic gaps remain. In the field of thermal resistance network modeling, related methods have been widely applied to quantify building heat transfer, but most studies focus on steady-state heat transfer processes in single-temperature zones, without fully considering the complex characteristics of dynamic thermal interference and uneven heat flow distribution in multi-temperature zones. Additionally, they lack a quantitative link to irreversible energy consumption, making it difficult for the models to reflect the essential energy consumption characteristics of the heat transfer system [11-13]. Regarding heat transfer entropy generation analysis, entropy generation theory has been used to reveal the irreversibility of thermodynamic systems, but current research mostly stays at a qualitative description of macroscopic energy consumption, without establishing a quantitative model directly linked to engineering structural parameters, which hinders the provision of precise theoretical guidance for structural optimization [14-21]. In the research on cold chain carbon emissions and multi-objective optimization, existing models often focus on "energy consumption—cost" as the core optimization goal, neglecting the irreversibility of heat transfer as the fundamental driving factor of energy consumption. Moreover, carbon emission accounting is often indirectly derived from energy consumption, and lacks deep coupling with the heat transfer physical process, leading to insufficient low-carbon and scientific results from the optimization [22-26]. In summary, current research has three major core gaps: first, the lack of a quantitative coupling mechanism between thermal resistance networks and heat transfer entropy generation, making it difficult to unify the physical quantification of heat transfer processes and the quantitative irreversibility of energy consumption; second, the absence of a nonlinear mapping model between multi-temperature zone structural parameters, entropy generation, and carbon emissions, which results in a lack of deep theoretical support for structural optimization; third, the inefficiency of the multi-objective optimization algorithm system that adapts to the coupled model, which restricts the engineering applicability of the optimization results.

In response to the above research background and academic gaps, this study sets three core objectives: first, to reveal the physical coupling mechanism between thermal resistance networks and heat transfer entropy generation and establish a quantitative correlation model between the two; second, to construct a multi-objective structural optimization model that integrates "irreversibility of heat transfer—carbon emissions—economic cost"; third, to verify the reliability and superiority of the model in practical scenarios through numerical simulations and engineering experiments. Accordingly, the academic contributions of this study are mainly reflected in three aspects: first, the proposal of a "thermal resistance-entropy generation" bidirectional coupling modeling method, achieving the organic unification of physical quantification of the heat transfer process and the quantitative irreversibility of energy consumption, filling the research gap of the lack of physical essence in existing models; second, the establishment of a direct correlation path between multi-temperature zone structural parameters and carbon emissions, breaking the limitation of the traditional optimization "energy consumption mediator" and providing more precise parameter regulation for low-carbon design; third, the formation of a complete method system of "coupled modeling—surrogate optimization—global sensitivity analysis," providing a new paradigm for low-carbon optimization of cold chain buildings.

3.1 Design variable definition

This study selects design variables based on the core principles of "engineering operability + sensitivity potential," and divides the variables into two categories: structural parameters and boundary condition-related parameters, based on the heat transfer characteristics and structural optimization requirements of multi-temperature cold chain warehouses. The structural parameter category focuses on the core structural parameters that play a dominant role in the thermal resistance network and entropy generation characteristics, including the insulation thickness of the building envelope, the thermal conductivity of partition materials, the heat transfer coefficient of doors and windows, the length-width-height ratio of the warehouse, and the area distribution ratio of multi-temperature zones. Among these, the insulation thickness of the building envelope is set for three mainstream materials: polyurethane (80-200 mm), rock wool (120-250 mm), and vacuum insulation panels (30-80 mm). This range covers commonly used specifications and can significantly alter the thermal resistance of the building envelope through thickness adjustments. The thermal conductivity of partition materials is selected in the range of 0.024-0.042 W/(m·K), covering the performance range of typical partition materials such as polyurethane and rock wool. The heat transfer coefficient of doors and windows is controlled within 0.4-1.2 W/(m²·K), suitable for various insulation levels such as aluminum alloy thermal break, hollow Low-E glass, and color steel sandwich panels. The warehouse length-width-height ratio is set to (2-4):1:(0.8-1.2), balancing structural mechanical stability and warehouse space utilization. The area distribution ratio of multi-temperature zones, based on the freezer, refrigerated, and shaded areas, is set with the values of 10%-40%, 30%-60%, and 20%-40%, respectively, to meet the diverse storage requirements of fresh products, pharmaceuticals, etc. The boundary condition-related category includes key operational parameters directly coupled with the heat transfer load, including ventilation frequency and the coefficient of performance (COP) of the refrigeration system. The ventilation frequency is differentiated by temperature zone type, with the freezer set to 0.5-1.0 times/hour, the refrigerated zone to 1.0-2.0 times/hour, and the shaded zone to 2.0-3.0 times/hour, balancing preservation needs and heat loss control. The COP of the refrigeration system is set between 3.0-5.5, covering the performance range of mainstream refrigeration units such as screw-type and scroll compressors, and dynamically coupling with the heat transfer load calculated by the thermal resistance network. All variables are validated through pre-experiments and sensitivity analysis to verify their significant impact on entropy generation rate, carbon emissions, and costs, ensuring the optimization's relevance and efficiency.

3.2 Objective function construction

3.2.1 Core objective: Minimization of heat transfer entropy generation rate

This study sets "minimization of heat transfer entropy generation rate" as the core objective of the multi-objective optimization model. The essence of this objective is to reduce the irreversibility of the heat transfer process by adjusting structural parameters, thereby reducing the intrinsic energy consumption of the refrigeration system from the root cause. This objective acts as the core link between structural parameters and low-carbon requirements and forms a significant coupling conflict with the subsequent carbon emission and cost objectives. The mathematical expression for the core objective is derived based on the coupling mechanism between the thermal resistance network and entropy generation, comprehensively covering the key heat transfer processes in the multi-temperature warehouse. The total entropy generation rate is the sum of the conductive entropy generation rate of the building envelope, the convective entropy generation rate of the multi-temperature zones, and the radiative entropy generation rate of the doors and windows, and is expressed as follows: minṠ_total=Ṡ_cond+Ṡ_conv+Ṡ_rad, where Ṡ_total is the total heat transfer entropy generation rate of the system, directly representing the irreversibility of the heat transfer process. A smaller value indicates higher heat transfer efficiency and lower intrinsic energy consumption. Ṡ_cond, Ṡ_conv, and Ṡ_rad represent the conductive entropy generation rate of the building envelope, the convective entropy generation rate of the multi-temperature zones, and the radiative entropy generation rate of the doors and windows, respectively.

The calculation formulas for each component strictly follow the second law of thermodynamics and the output parameters of the thermal resistance network model: ① The conductive entropy generation rate of the building envelope is calculated as: Ṡ_cond=∑_i=1ⁿ(Q_cond,i·ΔT_i/T_i²), where Q_cond,i is the conductive heat flux of the i-th building envelope unit, ΔT_i is the temperature difference between the inner and outer surfaces of the unit, T_i is the average temperature of the unit, and n is the total number of envelope units, this component quantifies the irreversibility of solid conduction processes. ② The convective entropy generation rate of the multi-temperature zones is calculated as: Ṡ_conv=∑_j=1^m(Q_conv,j/T_env,j)−Q_conv,j/T_zone,j, where Q_conv,j is the convective heat flux of the j-th temperature zone, T_env,j is the environmental temperature corresponding to that zone, and T_zone,j is the set temperature for that zone, and m is the number of temperature zones. This component represents the entropy generation of fluid convection processes. ③ The radiative entropy generation rate of the doors and windows is calculated as: Ṡ_rad=∑_k=1^p[Q_rad,k·(T_out,k⁴−T_in,k⁴)/T_out,k⁴·T_in,k⁴]·T_avg,k, where Q_rad,k is the radiative heat flux of the k-th door/window, T_out,k and T_in,k are the exterior and interior surface temperatures of the door/window, T_avg,k is the average temperature of the door/window, and p is the number of doors/windows, this component quantifies the irreversibility of radiative heat transfer processes.

The physical significance of this core objective is to transform the "structural parameters → heat transfer process → irreversible energy consumption" coupling relationship into an optimizable mathematical indicator through the model quantification, overcoming the limitation of traditional optimization that only focuses on macroscopic energy consumption. All heat flux and temperature difference parameters in the formulas are directly taken from the output of the thermal resistance network model, ensuring the deep coupling of the objective function with the physical heat transfer process.

3.2.2 Secondary objectives

The secondary objectives of this study are set as "minimization of total carbon emissions over the entire lifecycle" and "optimization of total construction and operational costs over the entire lifecycle." Both objectives have significant coupling conflicts with the core objective—such as increasing the insulation thickness can reduce entropy generation and carbon emissions but will increase material costs; improving the COP of the refrigeration system can simultaneously optimize both entropy generation and carbon emissions, but will increase equipment procurement costs. Scientific optimization needs to achieve a balance among the three. The first secondary objective, "minimization of total carbon emissions over the entire lifecycle," follows the latest IPCC accounting guidelines and ISO 14064 standards to construct a quantitative model, covering both direct energy consumption carbon emissions and indirect carbon emissions. The mathematical expression is as follows: minC_carbon=C_direct+C_indirect, where C_direct represents direct energy consumption carbon emissions, which are primarily associated with the energy consumption of the refrigeration system. Based on the coupling relationship between entropy generation rate and energy consumption, it is derived as: C_direct=(Ṡ_total·T_ref/η_COP)·t·λ_elec, where Ṡ_total is the total entropy generation rate from the core objective, T_ref is the reference temperature for the refrigeration system, η_COP is the coefficient of performance of the refrigeration system, t is the annual operating time, and λ_elec is the regional average carbon emission factor for electricity consumption, while also accounting for auxiliary energy consumption carbon emissions from ventilation, lighting, and other sources. C_indirect represents indirect carbon emissions, quantified using the lifecycle assessment method, covering the entire process of building envelope material production, transportation, construction, and end-of-life recycling, directly related to the design variables.

The second secondary objective, "optimization of total construction and operational costs over the entire lifecycle," is constructed from a lifecycle perspective, covering all stages of construction, operation, and maintenance. The mathematical expression is as follows: minC_total=C_construction+C_operation+C_maintenance, where C_construction represents the construction cost, which is primarily associated with structural parameter design variables. The construction cost of the building envelope is determined by the insulation layer thickness, material density, and unit price. The partition cost is positively correlated with the material thermal conductivity and partition area. The door and window costs are determined by the heat transfer coefficient corresponding to the profile and glass unit prices. C_operation represents operational costs, focusing on the energy consumption costs of the refrigeration system, while also accounting for ventilation, lighting, and equipment depreciation. C_maintenance represents maintenance costs, associated with material durability, and includes periodic expenses such as sealing and insulation layer aging repairs. The quantitative models for both secondary objectives are calibrated with industry measurement data and validated with international cost/carbon emission accounting standards, responding to the global "dual-carbon" strategy while considering engineering economic factors.

3.3 Constraints

The constraints in this study are centered on the three core dimensions of "thermal reliability—structural safety—operational compliance." All indicators are calibrated based on authoritative standards such as GB50072-2010 Standard for Design of Cold Store, ASHRAE 90.1 Energy Standards, and ISO 14067 Product Carbon Footprint, and embedded into the optimization model using quantitative mathematical inequalities to ensure the engineering feasibility and operational stability of the optimization results. Thermal constraints focus on the core functionality of cold chain storage, with clear quantitative thresholds for temperature fluctuations in multi-temperature zones: freezer zone fluctuations ≤ ±1K, refrigerated zone ≤ ±0.5K, shaded zone ≤ ±1K. These thresholds are strictly compatible with pharmaceutical GSP certification and fresh food cold chain HACCP system storage requirements to ensure stable product quality. At the same time, a surface dew point prevention constraint for the building envelope is set, where the inner surface temperature T_s, calculated from the thermal resistance network model, must satisfy T_s≥T_dp+1.5K, where T_dp is the corresponding dew point temperature of the temperature zone, calculated from indoor temperature and humidity, to avoid issues such as moisture penetration causing failure of the insulation layer and corrosion of structural steel. Structural constraints are set with the goal of balancing safety load-bearing capacity and space utilization. The upper limit for the insulation thickness is set differently based on the type of primary structure: for steel structure warehouses, due to component load-bearing characteristics, the maximum insulation thickness is set to ≤250mm; for concrete frame structures, which have stronger load-bearing capacity, the upper limit is set to ≤300mm. This constraint is calibrated through material density and structural mechanical finite element calculations to ensure overall structural stability. The warehouse space utilization rate is constrained to ≥80%, with the quantification relation η_space=V_totalV_storage×100%≥80%, where V_storage is the effective storage volume and V_total is the total warehouse volume. This constraint is controlled by the design variables of the length-width-height ratio and the area distribution ratio of the multi-temperature zones, balancing heat transfer optimization and storage functional requirements. Operational constraints ensure the system's long-term compliance and stable operation. The maximum refrigeration load Q_max must satisfy Q_max≤0.9×Q_rated, where Q_rated is the rated capacity of the refrigeration equipment, leaving a 10% load redundancy to accommodate extreme environmental temperature fluctuations. The carbon emission intensity constraint must comply with China's Assessment Standard for Green Building for a two-star rating or higher, quantified as C_intensity ≤ 8.0 kgCO₂/(m²·a), and also be compatible with the latest energy efficiency level thresholds of the EU's Energy Performance of Buildings Directive to ensure international compliance of the optimization results. All constraints are designed with explicit quantitative relationships and physical logic, linking design variables and the objective functions to form rigid boundary conditions, preventing the optimization results from deviating from engineering practice and standard requirements.

3.4 Mathematical expression of the coupled optimization model

This study presents the coupled optimization model in a structured form of “design variable vector → objective function vector → constraint condition matrix,” clearly defining the mathematical essence and coupling characteristics of the model. The complete mathematical expression is as follows:

(1) Design variable vector: Integrating the structural parameter category and boundary condition-related variables, an 11-dimensional decision vector X=[x₁,x₂,x₃,x₄,x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁]^T is constructed, where: x₁ is the thickness of the polyurethane insulation layer, x₂ is the thickness of the rock wool insulation layer, x₃ is the thickness of the vacuum insulation panel, x₄ is the thermal conductivity of the partition material, x₅ is the heat transfer coefficient of the doors and windows, x₆ is the length-to-width ratio of the warehouse, x₇ is the height-to-width ratio of the warehouse, x₈ is the area proportion of the freezer zone, x₉ is the area proportion of the refrigerated zone, x₁₀ is the ventilation frequency, x₁₁ is the COP of the refrigeration system. The value range of each variable meets the engineering boundaries set in Section 3.1.

(2) Objective function vector: A 3-dimensional minimization vector minF(X)=[f₁(X),f₂(X),f₃(X)]^T is constructed in the order of "core objective - secondary objectives," where: f₁(X)=Ṡ_total represents the heat transfer entropy generation rate, f₂(X)=C_carbon represents the total carbon emissions over the entire lifecycle, f₃(X)=C_total represents the total lifecycle construction and operational costs. The three objectives are intrinsically related through the thermal resistance - entropy generation coupling mechanism.

(3) Constraint condition matrix: The thermal, structural, and operational constraints are quantified into an inequality matrix form, with the equality constraint being the conservation of the area proportions of the multi-temperature zones, i.e., x₈ + x₉ + x₁₂ = 100%, where x₁₂ is the shaded zone proportion. The inequality constraint matrix is as follows:

$\mathrm{x} G(X)=\left[\begin{array}{l}T_{\text {zone }, i}-\Delta T_i-T_{\text {zone }, i, \min } \geq 0 \\ T_{\text {zone }, i, \max }-\left(T_{\text {zone }, i}+\Delta T_i\right) \geq 0 \\ T_s-T_{d p}-1.5 \geq 0 \\ x_1 \leq 250, x_2 \leq 250, x_3 \leq 80 \text { (Steel structure) } \\ x_1 \leq 300, x_2 \leq 300, x_3 \leq 80 \text { (Concrete structure) } \\ \eta_{\text {space }}-80 \% \geq 0 \\ 0.9 Q_{\text {rated }}-Q_{\max } \geq 0 \\ 8.0-C_{\text {intensity }} \geq 0 \\ x_j-x_{j, \min } \geq 0, x_{j, \max }-x_j \geq 0(j=1, \mathrm{~L}, 11)\end{array}\right]$.

where, T_zone,i and ΔT_i represent the design temperature and fluctuation threshold for the i-th temperature zone, and x_j,min and x_j,max represent the upper and lower limits of the j-th variable. Each row of the matrix corresponds to one constraint, ensuring that the model meets engineering and standard requirements.

To further verify the reliability of the model in actual engineering scenarios, this study conducted online monitoring over a 30-day period at an operating multi-temperature cold chain logistics center in Europe. As shown in Table 2, the root mean square error (RMSE) for entropy generation rate, energy consumption, and carbon emissions is 0.012-0.021 W/K, 10.5-15.3 kWh/d, and 0.55-0.85 kgCO₂/d, respectively, with a mean absolute percentage error (MAPE) of ≤ 4.8%, which is much lower than the acceptable threshold in international similar studies. Analyzing by scenario, during the daytime, the exterior surface temperature of the building increased by 5-8℃ due to solar radiation, resulting in a deviation of 4.8% in the predicted entropy generation rate, which is caused by the model's calculation of solar radiation heat flux density based on meteorological station average data, differing from the actual local shading conditions. However, this deviation is still within an engineering acceptable range. During nighttime conditions, the error is lowest because of stable ambient temperatures with no solar radiation interference, and the model's prediction of steady-state heat transfer for the envelope structure is more accurate. From the full-cycle trend, the deviation between the model's predictions and actual values for monthly cumulative energy consumption and carbon emissions is only 3.2%, indicating that the model is reliable for long-term performance prediction. Combined with experimental heat transfer measurements and model validation in accordance with international standards, this experimental verification proves that the coupled model can accurately predict entropy generation characteristics, energy consumption, and carbon emissions for multi-temperature cold chain warehouses, providing direct support for the engineering applicability of the research conclusions.

To analyze the coupled impact of design variable optimization on heat transfer irreversibility, carbon emissions, and economy from a mechanism perspective, this study combines the thermal resistance network model with lifecycle assessment methods for quantitative analysis, as shown in Figure 4. From the heat transfer mechanism perspective, the optimization of the design variable groups from Group 1 to Group 5, i.e., increasing the polyurethane insulation layer thickness from 80 mm to 160 mm and reducing the partition material thermal conductivity from 0.042 W/(m·K) to 0.024 W/(m·K), enhances the thermal resistance of the envelope structure and weakens the thermal disturbance between temperature zones. This reduces the conduction entropy generation rate by 45.1%, the convection entropy generation rate by 38.7%, and ultimately reduces the total entropy generation rate from 0.82 W/K to 0.55 W/K. Based on the coupling relationship between entropy generation rate and refrigeration energy consumption, carbon emissions decrease by 22.2% as energy consumption decreases. The increase in costs is mainly due to the purchase cost of high-performance insulation materials and increased construction complexity. By calculating the Pearson correlation coefficient, the correlation coefficient between entropy generation rate and carbon emissions is 0.98 (p < 0.001), and the correlation coefficient between entropy generation rate and cost is -0.95 (p < 0.001), statistically confirming the strong coupling conflict between the three, providing a quantitative basis for weight distribution in multi-objective optimization.

To systematically assess the quality and engineering applicability of the multi-objective optimization Pareto solution set, this study conducts experimental analysis. As shown in Figure 5, from the quantitative characteristics of the Pareto front, the entropy generation rate decreases linearly from 0.80 W/K to 0.40 W/K, carbon emissions decrease from 124×10⁴ kgCO₂ to 92×10⁴ kgCO₂, and the total cost increases from 1.78 million CNY to 2.4 million CNY, showing a strict "entropy generation - carbon emissions" coordinated reduction and a "cost" monotonous increase trade-off. By calculating the marginal substitution rate, it can be concluded that for every additional investment of 10,000 CNY, the entropy generation rate can be reduced by 0.0035 W/K, and carbon emissions can be reduced by 318 kgCO₂. This threshold provides a clear economic-environmental trade-off benchmark for engineering decisions: If the carbon tax is higher than 31.4 CNY/kgCO₂, the low-carbon-oriented solution should be prioritized; if cost constraints are strict, the cost-oriented solution should be chosen. Based on typical fresh food and pharmaceutical cold chain scenarios, Solution 2, which achieves the best balance between "low-carbon and cost," can be recommended as a general engineering solution.

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Figure 4. Line chart of multi-objective optimization objective function values for different design variable combinations

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Figure 5. Multi-objective optimization pareto front line chart

To quantify the main effects, interaction effects, and total impact of design variables on carbon emissions from a global perspective, this study employs the Sobol method, which is commonly used in the field of heat transfer optimization. As shown in Table 3, the total effect of insulation layer thermal conductivity is the highest, making its overall impact on carbon emissions the most significant, due to its main effect as well as its interaction effect with the partition thermal conductivity. From a heat transfer mechanism perspective, thermal conductivity directly determines the thermal resistance of the envelope structure, where increased thermal resistance reduces heat flux, entropy generation rate, and, subsequently, refrigeration energy consumption and carbon emissions. The total effect of partition thermal conductivity comes second, highlighting the critical role of controlling thermal interference between temperature zones in system entropy generation and carbon emissions. The second-order interaction effect between insulation layer thickness and window/door heat transfer coefficient indicates a strong coupling optimization potential for these two variables along the thermal loss path of the envelope; their simultaneous adjustment can generate a "1+1>2" effect in emissions reduction. The total effects of multi-temperature area ratio and refrigeration system COP are relatively low, indicating that the envelope structure parameters are the primary regulatory factors for carbon emissions, and equipment and layout optimization should be conducted based on improvements in envelope performance. Overall, the Sobol global sensitivity analysis identifies the priority of carbon emission impact as "Insulation Layer Thermal Conductivity > Partition Thermal Conductivity > Insulation Layer Thickness," providing a quantitative basis for parameter weight distribution and engineering decision-making in multi-objective optimization.

To reveal the internal mechanisms of how key parameters affect carbon emissions and clarify the optimization priorities, this study combines the Sobol analysis results with a mechanism breakdown (see Table 4). The results show that envelope parameters account for over 90% of the total effect on carbon emissions, which aligns with the heat transfer principle that "the envelope structure is the primary carrier of building energy consumption and entropy generation." Among these parameters, insulation layer thermal conductivity ranks first with a total effect of 0.38. Its mechanism can be explained by the "thermal resistance-entropy generation-energy consumption" coupling relationship: for every 0.01 W/(m·K) reduction in thermal conductivity, the thermal resistance of the envelope increases by 41.7%, which leads to a 18.3% decrease in entropy generation rate and a 15.6% reduction in carbon emissions. The total effect of partition thermal conductivity is 0.31, mainly due to its control over the thermal interference between temperature zones. For every 0.01 W/(m·K) reduction in cross-temperature zone thermal conductivity, the heat flux decreases by 22.5%, and the entropy generation rate decreases by 16.2%. The interaction effect between insulation layer thickness and window/door heat transfer coefficient suggests that engineering optimization needs to consider these two variables together. For example, increasing insulation thickness while reducing window/door heat transfer coefficient can reduce total thermal loss by 35.2% and decrease entropy generation by 28.7%. In contrast, the effects of multi-temperature area ratio and refrigeration system COP are weaker, indicating that equipment and layout optimization must be based on improvements in envelope structure performance. Overall, low-carbon design for multi-temperature cold chain warehouses should prioritize optimizing the thermal conductivity of the insulation layer and partition, along with coordinated adjustments in insulation thickness and window/door heat transfer coefficient. This conclusion provides both academic innovation and engineering practicality for material selection and structural design in cold chain buildings.

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Figure 6. Sensitivity analysis line chart for key design variables

To explore the sensitivity mechanism of insulation material and thickness on heat transfer irreversibility and carbon emissions, this study analyzes the coupling between material thermal physical properties and the thermal resistance network model. In Figure 6, Materials 11-33 correspond to the following insulation layer scenarios: Polyurethane 80 mm, Polyurethane 120 mm, Polyurethane 160 mm, Rock Wool 80 mm, Rock Wool 120 mm, Rock Wool 160 mm, Vacuum Insulation Panel 80 mm, Vacuum Insulation Panel 120 mm, and Vacuum Insulation Panel 160 mm. From the material performance differences, the thermal conductivity of vacuum insulation panels is only 1/3 that of polyurethane and 1/5 that of rock wool, resulting in significantly higher thermal resistance for the same thickness, leading to a much greater reduction in entropy generation rate compared to other materials. Regarding the marginal benefits of thickness, when the vacuum insulation panel thickness increases from 80 mm to 160 mm, the entropy generation rate reduction increases from 22.3% to 48.2%, but the marginal reduction decreases from 22.3% → 13.3% → 12.6%, which can be explained by the series connection mechanism of thermal resistance: as the total thermal resistance increases, the incremental contribution of insulation layer thermal resistance to the total thermal resistance gradually decreases. In line with international research, this study further quantifies the optimal thickness range of vacuum insulation panels in cold chain warehouses as 120-160 mm. This range achieves more than 40% reduction in entropy generation rate while avoiding excessive thickness that leads to cost waste.

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(a) Unit area heat transfer entropy generation rate

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(b) Unit area full lifecycle carbon emissions

Figure 7. Analysis of heat transfer entropy generation rate and carbon emissions for different design variable combinations

To reveal the coupling effect of insulation layer and partition parameters on heat transfer irreversibility and full lifecycle carbon emissions, and to provide a quantitative basis for low-carbon structural design of multi-temperature cold chain warehouses, this study conducts a systematic experimental analysis. The results are shown in Figure 7. In the figure, the baseline design corresponds to Polyurethane 80 mm + Rock Wool partition, with partition thermal conductivity λ = 0.042, and Scenarios 1-3 correspond to Polyurethane 120 mm + Polyurethane partition, Rock Wool 120 mm + Polyurethane partition, and Vacuum Insulation Panel 80 mm + Polyurethane partition, with partition thermal conductivity λ = 0.024 in each case. From the perspective of the coupling between the thermal resistance network mechanism and lifecycle evaluation, vacuum insulation panels, compared to the baseline design, result in the maximum reduction in unit area heat transfer entropy generation rate by 43.8% and the maximum reduction in unit area full lifecycle carbon emissions by 46.7%. This significant advantage arises from two aspects: first, the ultra-low thermal conductivity of vacuum insulation panels greatly improves the thermal resistance of the envelope structure, and according to the entropy generation rate calculation from the thermal resistance network model, its contribution to conduction entropy generation rate decreases from 62.3% in the baseline design to 31.5%; second, the "thickness reduction - high thermal resistance efficiency" synergy in the material lifecycle, despite vacuum insulation panels having higher carbon emissions per unit mass compared to polyurethane, results in a 40% reduction in material usage at 80mm thickness, and the reduction in carbon emissions from refrigeration energy consumption completely offsets the increase in carbon emissions from the material production stage. Comparing Scenario 1 and Scenario 2, their reductions in entropy generation rate and carbon emissions are only 21.9%-28.6% and 17.1%-25.3%, respectively, and Scenario 2 has clear performance bottlenecks due to the high thermal conductivity of rock wool. Through variance analysis, it was confirmed that material type has a much higher significance (p < 0.001) on entropy generation rate and carbon emissions than thickness, statistically confirming that thermal conductivity is the core regulatory factor. Therefore, low-carbon structural design for multi-temperature cold chain warehouses should prioritize using vacuum insulation panels with low thermal conductivity partition materials, as this combination has both academic innovation and engineering practicality in suppressing heat transfer irreversibility and reducing full lifecycle carbon emissions, providing a mechanism support and quantitative design benchmark for the application of ultra-insulation materials in cold chain buildings.