Blazon Portable Heater (Blazon Heaters Confidential)

Electrothermal Analysis

Version 1

Presented by Michael Salter

Overview

The Blazon heater utilizes bottled propane as an energy source to provide radiated heat and to convert heat to electricity for driving a fan and an auxiliary USB charging circuit.  The transducer used to convert heat to electricity is a thermoelectric generator (TEG) which produces electric power in proportional to the temperature difference across the TEG.  The fan provides warm air flow while at the same time cooling one side of the TEM to establish and maintain the necessary temperature difference to power the fan and the USB charging circuit.

Electrothermal Model¨

A simplified electrothermal model can be derived from steady state, coupled thermal and electrical circuits.  The thermal circuit can be modeled such as:

Where:

Th:  TEG hot side temperature ()

Tc:  TEG cold side temperature (Celsius)

Ta:  Ambient air temperature surrounding the heatsink which is attached to the cold side of the TEG.

Rth_tem:  thermal resistance to heat flow across the TEM

Rth_hs:  thermal resistance of the heat sink (as a function of airflow)

Qth: Heat flow from the heat souce (hot side of the TEM heated by the burning propane

An additional thermal resistance from Ta to To (outside temperature) could be added to model the complete heat flow/thermal characteristic for different operating environments (e.g. winter/summer).  Given a hot side temperature (fixed by the intensity of the burning propane flame), Ta, and the physical and material parameters of the TEG and heatsink, Qth and Tc can be established with the equation:

1       Qth=(Th-Ta)(Rthtem+Rthhs)

2    Tc=Th-Qth* Rth_tem

The temperature difference across the TEG (Th-Tc) causes it to produce an open circuit voltage (Vtem) and, when connected to drive the electrical circuit (fan and USB charger), an internal resistance (Rc) and a current flow based on the topology of the circuit connections.  The generated voltage and internal resistance are given by the TEG manufacturers data sheet as a function of the hot and cold side temperatures.  The graphical data in the spec sheet has been fit to a 2-dimensional linear model:

3    Vtem=k1* Tc+k2*Th+b1

4       Rc=k3*Tc+k4*Th+b2

where k1, k2, b1, k3, k4 and b2 are the parameters of the curve-fitted equations to the graphical data given by the TEG manufacturer.

The thermal resistance of the heat sink is also taken from the manufacturers data sheet where a logarithmic equation was fit to the graphical data:

5        Rthhs=k5*ln Af +b3

Where k5 and b3 are parameters of the curve fitted equation to the graphical data given by the heatsink manufacturer.

The airflow created by the fan is dependent on the voltage applied to the fan terminals which powers the motor, turns the fan and creates the airflow.  The airflow as a function of fan terminal voltage (Vf) was experimentally measured and a non-linear equation was extracted:

6   Af=k6*Vf+k7*Vf2+b4

The fan and USB voltages (Vf and Vusb) as well as the currents (and power) supplied to the fan and USB are dependent on the wiring of the electrical circuit which is shown below:

Linkage of the thermal and electrical models/circuits occurs through the fan, which converts fthe electrical voltage provided by the TEM (Vtem) to fan speed and air flow which in turn determine Rth_hs and Tc. 

Using standard circuit analysis, the expressions for all currents and voltages of the circuit can be written as a function of Vtem and Rtem (which are dependent on the thermal circuit and temperatures, Tc and Th).  There are two sets of equations depending on whether the USB circuit is active by engaging the switch.  When the switch is off (no USB charging), the 2 equations below can be written for the circuit voltage (Vf) and current (If):

7      If= Vtem(Rtem+Rf)        (If=It, No USB charging)

8           Vf=Vtem-If*Rtem        (No USB charging)

This results in a set of 8 equations that can be simultaneously solved for the steady state values of the 8 unknowns in the thermal and electrical models (Qth, Rth_hs, Tc, Vtem, Rc, Af, Vf, If).

When the USB charging switch is engaged, equations (7) and (8) are replaced with 3 equations (7), (8) and (9) with the additional variable Iusb:

7           Vf= (Rusb*Rf)Rf+Rtem*Rtem+Rusb+Rtem*Rf*Vtem

8         If= VfRf

9           Iusb= Vf+VtemRtem+Rusb

The 8 or 9 non-linear equations are solved in an accompanying spreadsheet to give the steady state values of the 8 or 9 variables for the charging and non-charging case.