Power supply thermal analysis

The article provides an analysis of heat removal from power elements in a low-power power source. The efficiency of cooling fuel elements using the free convection method without additional inclusion of active cooling is considered due to design limitations of the overall dimensions of the source. Calculation estimates were made using numerical modeling of the temperature regime of the source. The object of the study is an intrinsically safe power supply with size restrictions of 200×160×65 mm with an aluminum housing. The main heat-generating elements are power transistors with a power of 1 to 6 W, mounted on the heat-dissipating parts of the housing through an insulating gasket. For stable operation of semiconductors, a temperature regime is required without exceeding the transistor temperature of 85 ° C under standard environmental conditions at an air temperature of 20 ° C and a relative humidity of 20%. The authors analyzed the heat exchange between the model of the designed power supply housing and the air environment according to the parameter of the limiting temperature of heat-generating semiconductors in a steady state. Conclusions about whether the thermal operating conditions are adequately ensured for this case are made.


Introduction
Temperature control is an important task in the design and operation of power electronics.Reducing volume while maintaining efficiency is an important consideration in today's portable power supplies.With increasing density, heat dissipation by power elements also increases.Losses in electronic components generally increase with increasing temperature, so it is necessary for the electronic system to be kept as low as possible.The maximum operating temperature of the source power transistors should not exceed 85°C, which makes it necessary to maintain the temperature regime using a cooling system, otherwise this may lead to failure of the circuitry part of the device [1,2].It is necessary to select a cooling method that is not redundant, without increasing the weight and size parameters, and also without unnecessary addition of cooling elements.
In the practice of operating electronics, there are many methods of heat removal, but most of them are based on the principle of heat removal to the environment by convection and heat removal using housing design elements according to the principle of thermal conductivity [3,4].Article [5] describes the influence of various coolants and cooling methods on the heat transfer coefficient.Natural convection using air is the basic method, but gives the lowest heat transfer coefficient; using water instead of air increases this parameter, but complicates the design of the device.Forced air convection increases the heat transfer parameter of the system, increasing from 10 -4 to 10 -3 W/(cm 2 •°С), but requires the additional inclusion of elements of this convection.In this case, the joint use of water flowing in the radiator tubes as a coolant and air participating in heat exchange with the radiator is used.Many types of active cooling are built on this principle in the case where there are no design restrictions [6].The temperature is also affected by the material of the elements, solder, design, material and shape of heat sinks for heat removal, as well as the presence of thermal contacts.
Natural cooling is used in devices with a power of up to 50 W, but it is also applicable to systems of higher power with limitations in forced cooling systems or the ability to realize a large heat dissipation area [7,8].Radiators are made from economically available materials with high thermal conductivity, such as aluminum and copper.They also have an increased ability to dissipate power by radiating thermal energy into the air.When using radiators, the most preferable design is one with a massive base and large space between the fins for better air circulation.Also, the height of the fins should be as accessible as possible to increase the dispersion area.Thus, 70% of heat is transferred into the air through convection heat exchange, and 30% through radiation.For a passive cooling system, it is necessary to achieve a large volume of dissipation with an appropriate thermal resistance, so to reduce the thermal resistance by 1.5 times, it is necessary to increase the volume by 4 times with other parameters unchanged [9].To increase heat transfer, modification of the radiator design is also used, adding passive conductive elements with heat pipes.

Research methodology
It is necessary to evaluate the effectiveness of the passive method of cooling the power elements of the power source with size restrictions and the absence of active cooling systems under convection cooling conditions in the absence of external air flows (wind).
The description of the laws of physics for problems that depend on space and time is usually expressed using partial differential equations (PDEs).For most geometries and problems, these equations cannot be solved by analytical methods.An alternative is to approximate the equations, usually based on various types of discretization of space.These discretization methods approximate PDEs using numerical model equations that can be solved using numerical methods.To calculate such approximations, the finite element method (FEM) is used.One of the advantages of using the finite element method is that it offers greater freedom in the choice of discretization, both in terms of the elements that can be used to discretize the space and in terms of the basic functions.This allows you to divide a three-dimensional model of a complex shape into discrete elements and determine the basic functions at the nodes of the elements [10,11].The power supply is housed in an aluminum case with dimensions of 200×154×65 mm.On the top of the case there is a radiator of 9 fins with dimensions of 5x170 mm and a depth of 10 mm.The main heat sources for this source are transistors with power output from 1 to 6 W: • 2 pcs.with a power of 1 W; • 4 things.with a power of 2 W; • 2 pcs.with a power of 1 W; • 1 pc.with a power of 6 W. The contacts of the power transistors are fixed on the source board, and the housing is screwed to the heat-conducting element of the radiator to remove the generated heat.An insulating gasket 0.2 mm thick is installed between the power element and the radiator.
The thermal properties of the model materials are shown in Table 1.The analysis is carried out based on the following environmental conditions: air temperature 20 ° C, relative air humidity 20%, pressure 1 atm., type of cooling -free convection.Movement of air by wind is not considered.There are no elements of forced air circulation from the external environment inside the housing.And heat transfer also involves free convection.Air properties for convection cooling analysis: dynamic viscosity μ=8•10 - 6 Pa•s; isobaric heat capacity Cp=1006 J/(kg K); density ρ=1.2041 kg/m³; thermal conductivity k=0.018W/(m•K); temperature T=20°C; relative humidity φ=20%.The model is located on the surface inside an area of air with dimensions of 250×350×250 mm with open boundaries.The source is located on a solid surface.The source has a closed convection system in its internal part without ventilation elements and holes.The analysis of heat generation and removal was performed using the finite element method, which allows one to solve differential equations that describe heat transfer in continuous and moving media of complex shape, as well as combine them with the air flow inside and outside the power source housing.
Application of the method allows one to calculate the temperature and velocity fields in a solid and a moving medium (air).The analysis considers the dependence of air density on temperature and pressure.
Heat transfer in solid and moving media is described through the equation [10]: where ρdensity (kg/m 3 ), Cpspecific heat capacity at constant voltage (J/(kg K)); Tabsolute temperature (К); utranstranslational velocity vector (m/s).qheat flow due to thermal conductivity (W/m 2 ).qrradiant heat flux (W/m 2 ); αcoefficient of thermal expansion (1/K); Ssecond Piola-Kirchhoff stress tensor (Pa); Qcontains additional heat sources (W/m 3 ) The first term on the right side of the equation describes thermoelastic damping, which describes thermoelastic effects in solids: Heat transfer in moving media, such as air, is determined according to a different principle, reflected in the equation [10]: where ρ (kg/m 3 )fluid density; Cp (J/(kg•K)heat capacity of liquid at constant pressure; k (W/(m•K) -thermal conductivity of the fluid (scalar or tensor if thermal conductivity is anisotropic); u (m/s)this is the fluid velocity field, either an analytical expression or a velocity field; Q (W/m 3 )heat source (or sink); The first term on the right side of the equation describes the work done due to variable pressure as a result of heating during adiabatic compression: The second term describes viscous dissipation in the liquid: In the problem, the heat sources are power transistors with power output P0 of 1, 2, 3, 6 W. The heat source in this case is calculated through the ratio of power and volume V: The thermal pad between the radiator and the thermal element is described through a series of thermal contact equations designed to describe processes in thin films between contacting bodies [10].Thermal conductivity h participates in the distribution of heat flow according to the equations: ( ) ( ) ; h=heq+hr; her=keq/ds; keqlayer thermal conductivity; dslayer thickness; hrradiation conductivity; Heat transfer by air inside the source body is described by the principle of free convection: where Hheat exchange space length (200 mm); ΔT -temperature gradient during air convection.Heat transfer in air from the external boundaries of the source is determined by the Navier-Stokes equations, which determine the field of air velocities and pressure [10]: where uvelocity field vector; ppressure; gacceleration of gravity; Iidentity matrix; K=μ(∇u+(∇u) T )-(2/3)μ(∇•u)I; μdynamic viscosity.To analyze the flow of a moving medium, the properties of which depend on temperature, it is necessary to use equations connecting the velocity field and the temperature-dependent properties of air.This shows the work done by the change in pressure resulting from heating during adiabatic compression: where coefficient of thermal expansion; Qvd=τ:∇u; τviscous stress tensor.

Results and discussion
In the process of numerical analysis, the temperature distribution in the source model in the air section was analyzed.Figure 2 shows the temperature distribution over the areas of the fuel elements and the housing, as well as the process of convection cooling through a radiator.The analysis was carried out by simulating the operation of the source for 10 hours of continuous operation until a steady-state heat transfer regime.In steady state, the temperature of the stoker fluctuates between 59-67 C°.Convection currents in the absence of external air movement make it possible to obtain transistor temperatures below the limit.Heat radiation is concentrated in the area with the highest concentration of fuel elements.Figure 3 shows the distribution of heat generated by the transistors throughout the source body and radiator.The distribution pattern also indicates the concentration of the generated heat at the top of the source on the radiator fins, which allows energy to be effectively dissipated in the air.This shows that the height of the radiator fins is sufficient to effectively cool the elements.Analysis of changes in the temperature of transistors indicates a direct dependence of the element's fashionability on the heat generated and its volume (6).Thus, elements with a power output of 1 and 2 W reach a temperature of 62°C, 3 W -64°C, 6 W -68°C.When operating continuously at the specified power, the source enters steady state after 3 hours of operation, after which the temperature does not change.From the graph we can conclude that the temperature of the elements does not exceed the maximum operating temperature.Thus, the source does not require additional cooling elements, such as active elements inside the housing, or increasing the cooling surface area by increasing the height of the radiator fins.Convection air flows inside the case and natural cooling are sufficient when the source is constantly operating in active mode.

Conclusion
A simulation mathematical model has been developed showing the process of heat exchange between power elements, the power supply housing and the surrounding air.It can be concluded that the system enters steady state after 3 hours of continuous operation of the power source at rated load.In this case, the power elements reach a maximum temperature of 62-68 °C, which corresponds to the operating temperature range; the developed power supply housing reaches 63 °C, when the source is operated in conditions of no air flow.The developed model allows us to evaluate the possibility of using a power source in various operating modes and environmental conditions.

Figure 1 .
Figure 1.Model of the power supply housing and location of power elements.

Figure 2 .
Figure 2. Temperature distribution in the power source model and in the surrounding air: a -ZX plane; b -ZY plane.

Figure 3 .
Figure 3. Temperature distribution in the source body: a -ZX plane; b -ZY plane; c -XY plane.

Figure 4 .
Figure 4. Dependence of temperature of fuel elements on time.

Table 1 .
Model material properties.