Thermal Analysis of Apparatus having Multiple Thermal Control Zones

Abstract

Systems and methods for conducting thermal analysis in materials and devices having multiple thermal control zones are provided. Modem apparatuses, such as manifolds, generally have several thermal devices that introduce or remove heat at different rates from several different regions. Previous attempts to determine a thermal profile required constant guessing and an unknown number of simulations to arrive at an acceptable result. Further, since the number of simulations required is not known from the onset of the operation, the duration is unknown, which is often unsatisfactory to manufacturing personnel. Disclosed embodiments include the use of FEA to aid in designing and/or evaluating manifold systems. In one embodiment, finite element analysis is conducted to determine the heat flux caused upon other control zone by a thermal device in a specified control zone.

1 . A method of determining a thermal parameter of an apparatus, the method comprising:
 (a) providing a model of an apparatus having a plurality of thermal control zones, each thermal control zone of the apparatus comprising a thermal controller and a thermal device, wherein the thermal controller of each thermal control zone is operative, in response to a thermal parameter at a location within that thermal control zone, to generate a control signal directly or indirectly to the thermal device of that thermal control zone;   (b) providing at least one input value that directly or indirectly corresponds to at least one thermal property of at least one material of the apparatus;   (c) defining a finite element analysis mesh having nodes for the model of the apparatus;   (d) applying at least one boundary condition value to at least one portion of the model of the apparatus;   (e) determining the thermal correlation among at least a selected plurality of the thermal control zones, comprising constructing an [n×n] influence matrix of matrix values, where n equals the number of selected thermal control zones, each matrix value corresponding to a value of a first thermal parameter selected from heat loss and temperature for a corresponding one of the thermal control zones, the constructing of the [n×n] influence matrix comprising conducting n finite element analysis simulations of the apparatus based on the finite element analysis mesh, the input value of (b) and the boundary condition value, each of the n finite element analysis simulations comprising determining a matrix value of the first thermal parameter for each thermal control zone by applying a value for the other thermal parameter selected from heat loss and temperature which is unknown to each boundary of a corresponding one of the thermal control zones; and   (f) using the finite element analysis influence matrix to determine the value of the second thermal parameter for each control zone for a desired value of the first of the first thermal parameter for each control zone included in the selected plurality of thermal control zones.   
     
     
         2 . The method of  claim 1 , further comprising:
 (g) applying the result obtained in (f) to a finite element analysis simulation the model of (a) to obtain a thermal parameter for the apparatus.   
     
     
         3 . The method of  claim 1 , further comprising:
 (g) applying the result obtained in (f) to an finite element analysis simulation the model of (a) to obtain a thermal profile for the apparatus.   
     
     
         4 . The method of  claim 3 , further comprising:
 (h) utilizing the thermal profile of (g) to evaluate a malfunction in an existing apparatus.   
     
     
         5 . The method of  claim 1 , wherein the thermal device is selected from the group consisting of: a heater, thermoelectric cooler, heat sink, heat pipe, and combinations thereof. 
     
     
         6 . The method of  claim 1 , wherein the apparatus is a manifold configured to transport a material that is a fluid. 
     
     
         7 . The method of  claim 6 , wherein the manifold comprises a plurality of components and wherein at least a portion of the plurality of components comprise one control zone. 
     
     
         8 . The method of  claim 1 , wherein Equation (1) is utilized in association with the influence matrix to obtain a linear thermal relationship, wherein the unknown thermal parameter for each thermal control zone is the heat flux and the known first thermal parameter is a temperature value at the thermal controller for each thermal control zone, thereby determining how much heat needs to come from a thermal device in a specific thermal control zone to get a certain temperature at the thermal controller in the same thermal control zone. 
     
     
         9 . The method of  claim 1 , wherein the input value of (b) further corresponds to a thermal property of a node of the mesh defined in (c). 
     
     
         10 . The method of  claim 1 , wherein the input value of (b) further corresponds to a thermal property of a thermal control zone of the apparatus. 
     
     
         11 . A method comprising:
 (a) receiving a model of an apparatus having a plurality of thermal control zones, each thermal control zone of the apparatus comprising a thermal device controlled by a thermal controller, wherein each thermal controller is configured to transmit, in response to a thermal parameter at a specific location within the apparatus, a control signal to the thermal device;   (b) providing at least one input value that directly or indirectly corresponds to at least one thermal property of at least one material of the apparatus;   (c) defining a finite element analysis mesh having nodes for the model of the apparatus;   (d) applying at least one boundary condition value to at least one portion of the model of the apparatus   (e) determining the thermal correlation among at least a selected plurality of the thermal control zones, comprising constructing an [n×n] influence matrix of matrix values, where n equals the number of selected thermal control zones, by applying a known thermal parameter for each control zone within the influence matrix and conducting n simulations, wherein the constructing of the [n×n] influence matrix comprising conducting n finite element analysis simulations of the apparatus based on at least the finite element analysis mesh and the input value of (b) and the boundary condition value; and   (f) using the influence matrix to obtain a result of the linear thermal relationship of an unknown thermal parameter for each control zone within the influence matrix   
     
     
         12 . The method of  claim 11 , wherein the thermal controller is within the same thermal control zone as the thermal device it is controlling. 
     
     
         13 . The method of  claim 11 , further comprising:
 (g) receiving at least one user input that modifies the mesh defined in (c).   
     
     
         14 . The method of  claim 11 , further comprising:
 (g) applying the result obtained in (f) to the model of (a) to obtain a thermal profile for the apparatus.   
     
     
         15 . The method of  claim 14 , further comprising:
 (h) utilizing the result obtained in (g) to evaluate a malfunction in an existing apparatus.   
     
     
         16 . The method of  claim 14 , further comprising:
 (h) utilizing the result obtained in (g) in designing a physical apparatus of the model received in (a).   
     
     
         17 . The method of  claim 11 , wherein the known thermal parameter for each thermal control zone comprises the temperature at the thermal controller. 
     
     
         18 . The method of  claim 11 , wherein the known thermal parameter for each thermal control zone comprises the heat loss across a boundary of the control zone. 
     
     
         19 . The method of  claim 11 , wherein Equation (1) is utilized in association with the influence matrix to obtain the linear thermal relationship, wherein the unknown thermal parameter for each control zone is the heat flux and the known thermal parameter is a temperature value at the thermal controller for each thermal control zone, thereby determining how much heat needs to come from a heater in a specific thermal control zone to get a certain temperature at the thermal controller in the same thermal control zone. 
     
     
         20 . The method of  claim 11 , wherein the apparatus is a manifold having a plurality of channels configured to transport a fluid. 
     
     
         21 . The method of  claim 11 , wherein the input value of (b) further corresponds to a thermal property of a node of the mesh defined in (c). 
     
     
         22 . A system comprising:
 a computing device having a computer-readable medium configured to receive computer-executable instructions that when executed provide a model of an apparatus having a plurality of thermal control zones, each thermal control zone of the apparatus comprising a thermal device controlled by a thermal controller, wherein each thermal controller is configured to transmit, in response to a thermal parameter at a specific location within the apparatus, a control signal to the thermal device;   an input device operatively coupled to the computing device configured to allow the reception of at least one input regarding at least one material of the apparatus and an input relating to at least one boundary condition;   a computer-readable medium having computer-readable instructions for defining a mesh having nodes for the model of the apparatus; and   a computer-readable medium having computer-readable instructions that when executed construct an [n×n] influence matrix, where n equals the number of selected thermal control zones, each matrix value corresponding to a value of a first thermal parameter selected from heat loss and temperature for a corresponding one of the thermal control zones, the constructing of the [n×n] influence matrix comprising conducting n finite element analysis simulations of the apparatus based on the finite element analysis mesh, the input value of (b) and the boundary condition value, each of the n finite element analysis simulations comprising determining a matrix value of the first thermal parameter for each thermal control zone by applying a value for the other thermal parameter selected from heat loss and temperature which is unknown-to each boundary of a corresponding one of the thermal control zones and using the finite element analysis influence matrix to determine the value of the second thermal parameter for each control zone for a desired value of the first of the first thermal parameter for each control zone included in the selected plurality of thermal control zones.   
     
     
         23 . The system of  claim 22 , further comprising:
 a computer-readable medium having computer-readable instructions that when executed apply the result of the linear thermal relationship to the model to obtain a thermal profile for the apparatus.   
     
     
         24 . The system of  claim 23 , further comprising:
 a display adapter operatively coupled to the computing device for displaying the thermal profile of the apparatus.   
     
     
         25 . The system of  claim 23 , further comprising:
 a computer-readable medium having computer-readable instructions that when executed analyze the thermal profile of the apparatus to evaluate any malfunctions of a physical apparatus having characteristics that are similar to the model.   
     
     
         26 . The method of  claim 25 , wherein the apparatus is a manifold having a plurality of channels configured to transport a fluid. 
     
     
         27 . The method of  claim 26 , wherein the apparatus is a manifold having a plurality of channels configured to transport a material that is a fluid at an elevated temperature and a solid at a lowered temperature. 
     
     
         28 . The system of  claim 23 , further comprising:
 a computer-readable medium having computer-readable instructions that when executed utilize the thermal profile of the apparatus in designing a physical apparatus having characteristics that are similar to the model.   
     
     
         29 . The system of  claim 23 , wherein the known thermal parameter for each thermal control zone comprises the temperature at the thermal controller. 
     
     
         30 . The method of  claim 23 , wherein the computer-readable medium having computer-readable instructions that when executed construct an [n×n] influence matrix comprises instructions for performing Equation (1) in association with the influence matrix to obtain a linear thermal relationship, wherein the unknown thermal parameter for each thermal control zone is the heat flux and the known first thermal parameter is a temperature value at the thermal controller for each thermal control zone, thereby determining how much heat needs to come from a thermal device in a specific thermal control zone to get a certain temperature at the thermal controller in the same thermal control zone.