Modified article based on submitted Proceedings of ASME

2005 ASME International Mechanical Engineering Congress & Exposition


Enhancement of heat transfer due to Plasma flow
in Material Processing Applications


Cincinnati, OH, USA


Convective heating is used in materials processing industry for heat treatment and melting applications.  Only recently, a new plasma device for convective heating at atmospheric pressure has become commercially available. In this paper, we have investigated heating of an aluminum sprue by conventional convective heating by air and by low ionized plasma flow.  Transient temperature measurements were made in the sprue interior and the overall heat transfer coefficient was computationally predicted in the two cases.  Results show that there is significant enhancement of heat transfer in convective plasma heating compared to heating due to unionized gas under identical flow and temperature conditions.  For the cases considered in this study, close to a 60% increase in the heat transfer rate was obtained.  The key scientific finding is that even small amount of ionization (~ < 1%) can lead to significant increase in heat transfer coefficient.


The research in industrial applications of Plasma has largely been concentrated on two types of systems, viz., thermal plasma at atmospheric or near atmospheric pressures and low pressure plasmas [1, 2].  Thermal plasmas are used extensively in applications such as plasma spray coatings and arc welding.  Typical temperature in such applications may be in the range of 5000-15000K and pressure is atmospheric.  In the second case, plasmas at low pressures are used for applications such as chemical vapor deposition and polymer processing.  These are generally cold plasmas as due to low collision coupling between electrons and heavy particles, the temperature of ions and neutral remains at room temperature [2].  Thermal Plasmas have received much attention in the literature.  Reviews [3] and a monograph [1] provide detailed reviews of the work published in literature.  Heat and momentum transfer to spherical particles in thermal plasma has been studied extensively for the application of plasma spray coating [4 and references therein]. It has been shown that the heat transfer to a surface of a solid introduced in thermal plasma flow is greater than that for flow of an unionized gas [5, 6].  Correlations for Nusselt number have been proposed for thermal plasma flow over spherical particles [7].  For plasma at low pressure, heat transfer to a solid has been investigated applying results from kinetic theory of rarefied gases [8, 9].  However, these two extremes (very hot plasmas at atmospheric pressure or cold plasmas at low pressures) are not best suited for metallurgical work.  For example, most of the aluminum melting or steel heat treatment is carried out between 600 oC and 1200 oC. The low pressure plasma posses very low energy density and can not be used for aluminum melting.  The very high temperature thermal plasmas result in significant heat losses and may result in poor efficiencies. 

Only recently, new mid temperature range (1200 K – 1600 K) convective plasma device has been patented and has become available commercially (PlasmaAirTorch [1] ) [10].  In this study, we have conducted experiments with two devices, PlasmaAirTorch1 and AirTorch1 to heat identical aluminum sprues to analyze the rate of heat transfer in the two cases.  Modeling of the flow and transient heat transfer was carried out using a Finite Volume method. Our results show that there is significant increase in heat transfer by plasma heating compared to heating by a unionized gas under identical flow and temperature conditions.  This finding has critical implications in metallurgical processing as the use of plasma heating can significantly increase productivity in such applications. Furthermore, the quality of the aluminum after melting was substantially better and much lower metal loss with plasma heating compared to conventional heating.



D             mass diffusivity

h              heat transfer coefficient

k              Boltzmann Constant

N             charged species (ion or electrons) number density

t               time

T              Temperature

V             Velocity

           Thermal Conductivity

           Thermal diffusivity



           Mass flux

e              Charge of an electron

Re           Reynolds Number

Sc            Schmidt Number

m             mass

Cp            Specific heat at constant pressure



g              gas

i               ion

e              electron

s              solid

w             wall


Experimental Set-up:


A schematic of the experimental set up is shown in Figure 1.  The set up consists of an insulted cylindrical chamber.  An Airtorch or a plasma torch is connected to the chamber on the left and the high temperature gas enters the chamber through the opening along the centerline of the chamber.  A thermocouple is placed at the entrance of the chamber to measure the temperature at the exit of the torch.  An aluminum sprue is placed in the chamber with a thermocouple attached to the sprue through a hole drilled from the back of the sprue along its centerline. The thermocouple is at a location, 12mm from the front surface, along the centerline. The K type thermocouple was used which can record up to 1500 K. The Airtorch exit temperature was measured with a B type thermocouple.   Both the thermocouples are connected to a data acquisition system for transient temperature measurements. An MHI DACs data acquisition system with a sampling rate of in excess of 1 per second was employed for the thermal measurements.

Temperature measurements were carried out with two identical aluminum sprues.  In the first case an air torch was used to provide the gas at 1573 K for convectively heating the sprue.  Transient temperature measurements were recorded.  In the second case, a Plasma Torch was used.  In this case, a weakly ionized gas from the torch provided the convective heating of the sprue.  Once again, transient temperature change was measured for the sprue interior.  In both cases, identical electric power was supplied to the torch. The sprue heated with the Plasma torch resulted in substantially higher heating rate compared to one heated with Air torch.  The experimental measurements are discussed later in detail with the computational predictions. 





Fig 1 : Schematic setup of the experiment




Computational Analysis for Neutral gas:


The flow and heat transfer in the chamber and conduction in the sprue were computationally modeled by solution of the continuity, momentum, and energy equations using commercially available software Fluent 6.2.16. The flow was considered steady and axi-symmetric.  However the temperature field was considered transient due to heating of the sprue.  The Reynolds number based on the inlet velocity and sprue diameter is about 120 and the flow is laminar.  Using Gambit2.1, a 2-D axi-symmetric mesh was generated using the dimensions given in the experimental set-up (see Figure 1). The mesh generated was highly refined in order to facilitate greater accuracy in the numerical solution and to account for steep gradients near the sprue. The grid was refined to obtain grid-independent solutions as described later in the paper.


The Governing equations in dimensionless form are:







The above continuity, momentum conservation and energy conservation equations were solved using commercially available Fluent flow/thermal solver. The SIMPLE algorithm for pressure correction was employed and descretization was carried out using the Power-law method. An under relaxation technique was used for both momentum and energy equations. The governing equations are solved subject to the following boundary and initial conditions.  The entire flow domain and the sprue were uniformly at room temperature at t = 0.  On the walls of the chamber and the surface of the sprue, no-slip boundary condition was applied.  As the walls and the sprue are not permeable to the gas, both the normal and the tangential components of the velocity were zero on the surface.  At the inlet, velocity was specified.  At the exit, the pressure outlet condition was used.  For the energy equation, the temperature was specified at the inlet and zero heat flux was considered at the insulated container walls.  As the formulation is axi-symmetric, only half of the domain was considered with symmetry condition of zero radial gradients of velocity and temperature at the centerline. On the surface of the sprue, condition of heat balance was applied, i.e. heat transfer from convection at each point on the surface must equal heat conduction in the interior of the solid.  This can be written as



where n is the direction normal to the surface.


Computational Analysis for the ionized species:


The conservation equations for charged particle densities and electric field can be written in non-dimensional form as 




Equation for Electrons:




Equations for Ions:




Laplace Equations for the electric field



The Ion and Electron flux is given by






 The following dimensionless parameters have been used


, , ,  

, , , 





 A  Tri- Diagonal system of equations was setup for each of the equations (5), (6) and (7) and was solved iteratively using Alternating Direct Implicit scheme. The convergence criterion was set at 1x 10-6 between to successive iterations at all points. The concentration of electrons, ions and the voltage field were found for different degrees of ionization by changing the initial condition for inlet. The flow field was obtained from the solution of the neural gas. Once the concentration of the electrons and ions are determined, the flux of these charged species near the surface of the sprue can be calculated using equations (9) and (10).


The above governing equations were set to the following boundary conditions. The sprue surface is a perfect sink for the charged species and so at the particle surface the appropriate continuum conditions are

at r = rp, Ni = Ne = 0

The electron and ion fluxes at the surface of the sprue are equal if the voltage there is set to the floating potential i.e.

                at r = rp,  if  V  = Vfloat


Once the flux at the surface in presence of floating potential is determined the energy transferred to the surface can be calculated by accounting for all the modes of heat transport to the surface. The convective heat transfer from the neutral gas is calculated from the temperature gradients evaluated at the sprue surface.  Additionally, the recombination of the ions and electrons at the surface provide energy equivalent to the ionization potential.

                at r =rp, q*r =


Results and Discussion

First we considered the flow from the Airtorch in the analysis.  The temperature at the exit of the torch, or inlet of the chamber, was measured as 1573 K and the inlet velocity was 0.44 m/s. The streamlines for the flow are shown in Figure 2.  It is clear from the figure that the as the flow goes around the sprue, a re-circulating flow pattern is obtained.  Due to the decrease in the cross-sectional area due to the presence of the sprue, the velocity increases as the gas moves along the container walls.

The temperature contours obtained for the flow domain are shown in Figure 3.  Most of the region in the upstream of the sprue the temperature is nearly uniform. Due to the re-circulating vortex patterns on the side and on the downstream region from the sprue, colder fluid from the sprue mixes with the hotter fluid away from the sprue. This is evident from the temperature contours. The temperature contours show that the heat transfer rate is maximum at the front surface of the sprue and hence there is a sharp change in gas temperature near the surface. As the flow proceeds toward the outlet there is decrease in the heat transfer rate on the top surface of the sprue. This is evident from the temperature contours showing temperature drop over a larger distance compared to the front surface. The heat transfer coefficient was obtained at all points along the surface of the sprue.  An area weighted average taken over the whole surface of the sprue for the surface heat transfer coefficient gave h = 26 w/m2K.  The total heat transfer rate over the surface of the sprue is then given by




The temperature contours in the interior of the sprue show only a small variation. The temperature difference within the solid is less than 0.5 degrees.  This is to be expected as due to the high thermal conductivity of aluminum (ks = 227 W/m K) the Biot number is very low and temperature distribution is nearly uniform and hence a lumped analysis can be performed for the sprue. The lumped analysis gives convective heat transfer as


  .                                                                    (12)

From the Figure 4 it can be seen that the slope  for plasma case is 60% higher than the non plasma case. With all other terms remaining constant in equation (9) this translates into 60 % increase in the heat transfer rate. This enhancement is due to recombination of electrons and ions at the surface where each recombination results in energy equal to ionization potential given to the surface. The motion of the charged particles to the surface is through convection and diffusion. Additionally a self-consistent electric field will affect the drift of the charged species. Runs were made with different values of inlet ion and electron concentration taking into the presence of this electric field, until the predicted values of the heat transfer rate to the sprue interior was obtained with the measurements with Plasma heating. In this case the inlet ionization was obtained as 0.64%. The following parameters were used 3.33x10-4, Vi = 14.5V.


Grid Independence:

 In a computational study, it is important to evaluate the effect grid spacing on the solutions to make sure that the results are grid-independent. The computations were carried with different grid sizes until the solution was insensitive to the grid size, the results are shown in Table 1. The asymptotic nature of results leading to grid-independent solution is evident from Table 1.




Grid spacing


Number of Nodes
























































Table 1: Grid Independence Study


Transient temperature measurements and computational simulation of convective heating of an aluminum sprue was carried out. Two cases were considered, one with Airtorch and the second with low amount of ionized Plasma heating.  In the first case, air at 1573 K from an non plasma Airtorch was used whereas in the second case slightly ionized air at 1573 K from a Plasma Torch.  From the temperature measurements and computational analysis, it was noted that the plasma heating results in 60% increase in heating rate for the sprue compared to that with unionized air at the same temperature. The degree of ionization was obtained as 0.64%.  This shows that even a small degree of ionization results in significant increase in the heat transfer coefficient. This finding also has significant implications in aluminum processing because of the increase in the heat transfer coefficient. Significant increase in productivity can be expected by use of plasma heating in metal processing.  The variation of the heat transfer rate with the degree of ionization is shown in fig 5.


Fig2: Stream lines in the flow field






Fig 3: Temperature Contours of Airtorch


                   Fig 4:Experimental Results for Temperature Variation 



Fig 5: Ratio of Ionization to Convection heat transfer Vs Degree of Ionization




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