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thermal_insolation [2015/07/21 19:58]
ana
thermal_insolation [2016/05/22 14:13] (current)
sam
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-====== Thermal Conductivity ====== +this page has moved to [[orb:thermal_insulation]]
-To make an hypothesis of how the thermal conductivity in our insulated box will evolve, we're basing in Fourier'​s Law and the heat convection-diffusion equation. +
- +
-$\vec{q}=-\kappa \nabla T$ +
-$$$$ +
-$\frac{\partial Q}{\partial t}=-\kappa \oint \limits_S\nabla T \vec{dA}$ +
- +
-$_{General Fourier'​s law}$ +
- +
-Where for the first form, $\vec{q}$ is the local heat flux density, $\kappa$ is the material'​s conductivity,​ $\nabla T$ is the gradient of the temperature. And for the second form $\frac{\partial Q}{\partial t}$ is the amount of heat transferred per unit time, and $\vec{dA}$ is an oriented surface area element. +
- +
-$\frac{\Delta Q}{\Delta t} = -\kappa A \frac{\Delta T}{\Delta x}$ +
-$$$$ +
-$_{Fourier'​s law applied ​to an homogeneous material of 1D geometry between two endpoints at constant temperature}$ +
- +
-Where $\Delta T$ is the difference of temperature between the edges, and $\Delta x$ is the distance between them. +
- +
-$\frac{\partial T}{\partial t}=\nabla.(\frac{\kappa}{\rho c_{\rho}} \nabla T) - \nabla. (\frac{\partial T}{\partial x}) + R$ +
- +
-$$$$ +
-$_{heat convection-difussion equation}$ +
- +
-Where $\frac{\partial T}{\partial t}$ is the temperature transfer per unit time, $\rho$ is the density, $c_{\rho}$ is specific heat capacity, $\frac{\partial T}{\partial x}$ is the speed of the temperature transfer in the outside direction, and $R$ is the source of heat. $\nabla$ stands for the gradient and $\nabla.$ the divergence operators. +
-{{ :thermal_diffusion.png?​nolink |}} +
- +
-====== Experiment ====== +
- +
-Objective: We want to know the behavior of the rock wool and polyurethane foam used as insulation materials during a long period of time. +
- +
-Materials:  +
-Sensirion SHT21 +
-Cardboard box (20x20x14 cm) +
-Rock wool (density 50kg/m3, Thermal conductivity (R) =0.039, specific heat 1500 J/Kg°C) +
-{{ :​rock_wool.jpg?​nolink&​300 |}} +
-Polyurethane Foam (density 150kg/m3, Thermal conductivity (R) =0.04, specific heat 1500 J/Kg°C) +
-{{ :​polyurethane_foam.jpg?​nolink&​300 |}} +
- +
- +
-Procedure:​ +
-We cover the interior of the cardboard boxes with a 40mm homogeneous layer of the insulation material, the sensor inside will recovered the data (temperature,​ humidity, and time) +
- +
-Results: +
- +
-{{:​rock_temp.png?​nolink&​300 |}} +
- +