In many thermal processes, all-metal vacuum furnaces offer a variety of technological benefits compared to furnaces with non-metallic (e.g., graphite) hot zones. Specifically, metal hot zones enable higher vacuum levels, quicker pump-down, cleaner atmosphere, no carbon contamination and higher quenching rates.


Due to increasing demands for energy efficiency, advanced furnace concepts are being developed. In the building industry, for example, energy-reducing measures require advanced equipment, which often means additional initial investment costs. When these additional costs are more than paid for by the achieved energy savings, the measures are economically justified. Therefore, the total cost of ownership (TCO) is reduced. With metal hot zones, the TCO benefit of different measures was rarely judged in the past with sufficient accuracy since the design of metal hot zones was often based on best-practice experience.

    In the interest of examining the energy-consumption efficiency of different hot-zone designs under operational loads, PLANSEE has recently developed an advanced numerical-modeling approach based on the finite element method (FEM) specifically aimed at predicting temperature distributions and energy balances in vacuum furnaces with all-metal hot zones. It is worth noting that the present model explicitly addresses the design problem of thermal insulation systems as an integral part of the hot zone.

    Under strict consideration of the TCO aspect and utilizing the FEM model, PLANSEE has developed the ENERZONE® where several measures contribute to a potential total energy savings of up to 35% compared to industry standards, which paid less attention to energy-saving potentials and, therefore, potentially precluded their effective use.


Heat Transfer in Radiation Shieldings

The design of the hot zone of the furnace has a high impact on the energy demand for an operational heat-treatment cycle with two key parameters being identified within this context:

•   Design of a thermal insulation system that primarily consists of radiation shielding, which governs energy losses due to radiation

•   Weight of the hot zone influencing the thermally transient characteristics of the furnace, which consequently affects the minimum possible cycle time


    In general, the radiative heat flux q¢rad [W m-2] between two parallel, diffuse, gray and infinite surfaces is given by:

                                 q'rad = σ ( ε1-1 + ε2-1 - 1)-1 A (T14 - T24)           (1)


where s= 5.6704 x10-8 [W m-2 K-4] is the Stefan-Boltzmann constant, unitless ε1and ε2 represent the emissivities of the respective surfaces, A [m-2] stands for the heat-exchanging area, and T1 [K] and T2 [K] represent the temperatures of the respective radiating surfaces.

    In the past, a simple one-dimensional model had been used in order to estimate the heat loss of different radiation shielding types of the hot zone. This model adopts the mathematical description of radiative heat exchange between two surfaces as given in equation 1, which implies some restrictions with respect to its practical applicability. The most important are thermal steady-state condition (thermal mass of hot zone, workload, etc. not accounted for), vacuum condition or an atmosphere with low gas pressure (convective heat transfer not accounted for), and thin-walled shields (conductive heat transfer not accounted for). The schematic working principle of this model is shown in Fig. 1.

    The total heat loss at the heating elements is equal to the total heat radiation of the heating elements towards the workload and the hot face:

                                           Q'loss = Q'H1 + Q'H2          (2)


    It should be noted that Q'lossdoes not necessarily correspond to the total heat loss of the furnace. In the thermal steady-state condition, the heat transfer from the heating elements toward the workload is equal to the heat transfer from the workload to the hot face (otherwise the temperature of the workload would change).

                                               Q'H1 = Q'L  (3)


    Due to its intrinsic limitations, it was discovered that this basic model for heat-loss calculations no longer kept up with the increasing demands of the design of hot zones. Therefore, an FEM-based modeling approach was developed to explicitly account for real features of the furnace such as the three-dimensional shape of the hot zone, including the gaps, corners and feed-throughs.


FEM Model for Thermal Furnace Simulations

Recently, the PLANSEE FEM engineering team developed a customized FEM modeling approach within the commercial FEM suite (Abaqus®) specifically intended for batch vacuum furnaces. It is suited to describe radiative and conductive heat transfer in the furnace. Thanks to its specific parametrical setup in view of geometry parameters, material characteristics, boundary and loading conditions, it can easily be applied to different furnace sizes and types (from small to large), from circular-vertical to rectangular-horizontal, and with variable setups of radiation-shielding layers with respect to number, material, thickness and surface conditions. Examples of such typical hot zones can be seen in Fig. 2.

    First, the geometry for the furnace model is constructed using a table of geometrical features comprising the overall layout of the complete furnace (Fig. 3). As this occurs, the individual components of the hot zone are geometrically defined. Second, assignments of material characteristics and surface properties to the components are made. It is worth noting that temperature dependencies of thermo-physical material parameters as well as the thermal surface properties are accounted for. Third, thermal loading and boundary conditions are assigned to the heating elements and the vessel. Finally, finite element meshing is done and simulation runs are performed.

    Thermal simulation results of this FEM approach comprise temperatures and heat fluxes and their corresponding temporal evolutions and spatial distributions. From this, overall energy balances and measures for overall thermal uniformity can be derived, and local parasitic heat fluxes can be identified. For optimization purposes, the parametric FEM model setup easily allows efficient performance of sensitivity analyses, thus enabling the customer to choose the best solution based on different design options.

    As an example, Figure 4 demonstrates the possibilities for investigating local thermal conditions. Here, the gap between the top shielding and the side shielding leads to both a parasitic heat loss and an increase of the temperature of the vessel. The effect of different gaps can easily be studied via parametric FEM analyses, and recommendations can be derived for the hot-zone design and installation instructions.

    For operational cases where convective and conductive heat transfer may play a role, a similar modeling approach is currently being developed on the basis of the commercial CFD suite FLUENT®.


Total Cost of Ownership (TCO) Consideration

The main design methods of reducing energy consumption of a vacuum furnace with an all-metal hot zone include:

•   Lightweight shielding

•   Lightweight hearth assembly (Fig. 2a)

•   Additional layers of shielding

•   Shielding on corners, gaps and feed-throughs

    Every measure impacts the cost of the hot zone (additional investment) on one hand but reduces energy consumption (lower operating costs) on the other hand. The TCO leads to the most economical solution. Additional benefits not yet considered in the TCO are:

•   Lower dependence on potentially increasing costs for electrical energy

•   Shorter cycles due to less mass being heated up and cooled down (i.e. high productivity)

•   Improved product quality via improved temperature uniformity


    Figure 5 shows the result of an FEM investigation of a horizontal metal hot zone of 24 x 24 x 36 inches in size. In the case of applying the listed measures, the heat loss is reduced by 35%, whereas the investment costs rise by 14%.

    Following the TCO concept, cost savings through lower energy consumption are compared to the additional investment costs. Table 1 demonstrates the result of a TCO consideration by assuming a hot-zone price of $100,000 (for reference only).

    The model leads to a cost savings of $8,404 per year, or 16.4% total savings, of the hot-zone investment and energy costs. The initial additional investment cost of $14,269 is paid back in less than two years just by cutting the energy costs. The TCO model can then be customized to individual requests and extended by additional parameters (e.g., interest, longer ENERZONE lifetime, ENERZONE cycle-time savings due to faster heating and cooling). This way, the TCO model allows for the determination of the most economic setup. As an example, the percentage of savings for the selected case, depending on the number of molybdenum shields being used, can be seen in Fig. 6.

    It can be concluded that – for the chosen example – using five molybdenum shields leads to the best financial benefit.



A powerful FEM modeling approach has been developed in order to investigate energy consumption and the heat loss of all-metal hot zones. Thanks to its parametrical model setup, different hot-zone types, shielding concepts and materials can be compared to each other. The efficiency of specific energy-saving measures via the ENERZONE concept can be analyzed easily by the TCO approach, which allows the economy of such measures to be judged by comparing the additional investment costs to the lower operating costs. In the end, the TCO approach in combination with the FEM modeling approach represents a powerful tool to determine the most suitable and cost-effective hot-zone design while still in the early project stage. It also helps to estimate the return time of financial efforts, which are put into power-saving technologies of all-metal hot zones. IH


For more information:  Contact Ray O’Neill, product manager – furnace components, Market Unit Thermal Processes; PLANSEE USA LLC., 115 Constitution Blvd., Franklin, MA 02038; tel: 508-918-1234; fax: 508-553-3823; e-mail:; web: