# What Is The Design Analysis Of The Surface Temperature Table

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Design Analysis of the Surface

Temperature Reference

The Design Analysis of the Surface Temperature Reference is divided in three main sub- section that deals with diﬀerent problem areas that can be summarized as follow.

Mathematical Model of the Thermal System to acquire a better understand- ing of the system in order to control the temperature.

Set-up Insulation Analysis in order to determine if the system can operate at high temperatures (500 [◦C]) without aﬀecting the normal performance of other equipments that have a restricted working temperature(Tmax = 50[◦C]).

Substrate Heat Transfer Analysis ,this study focuses on the eﬀect(temperature perturbations) on the substrate temperature at diﬀerent position and diameters of
the
Bi =
Rcond
Rconv

= hconvLc k (2.1)

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2.1. Mathematical Model of the Thermal System

where:
Rconv/cond : convective/conductive thermal resistance[◦C/W] hconv : heat convective coeﬃcient[W/m2K]
Lc : characteristic length[m](V/As[12](ch5)(pag.285)) k : thermal conductivity[W/m ◦C]

2.1.1 Model of the Thermal System

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b

Copper Cylinder

a

Copper Cylinder

a

Heater

Aluminum Substrate

Insulation

Figure 2.1: Simpliﬁcation of the Thermal System

The ﬁgure 2.1 (a) is a 2D representation of the actual system.It is composed by a copper cylinder and an aluminium substrate disk.This two components are placed in top of each other and surrounded by insulation material(mineral wool). The bottom element of the system is the heating element,that provide heat from electrical power.

Validity of the Lumped Method

It order to implement the lumped approximation of the system model it is required to check Biot Number Bi.The calculated Bi for the copper cylinder and aluminium substrate are values far below 0.1(0.0002 and 0.0003 respectively).This calculations are based on the estimation of the heat convective coeﬃcient hconv = 12[W/m2K] at 200◦C.[12].(for details in the calculation see appendix "Implemented Matlab Calculations"). In this case the thermal system fulﬁl the requirements (Bi < 0.1) in order to be considered as a lumped system. The entire set of assumptions to model the thermal