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 thermal_insolation [2015/07/21 19:58]ana thermal_insolation [2016/05/22 14:13] (current)sam 2016/05/22 14:13 sam 2015/07/21 19:58 ana 2015/07/21 19:57 ana 2015/07/21 19:28 ana 2015/07/21 19:27 ana 2015/07/08 21:31 ana 2015/07/08 21:12 ana 2015/07/08 20:50 ana 2015/07/08 20:49 ana 2015/07/08 20:49 ana 2015/07/08 20:49 ana 2015/07/08 20:48 ana 2015/07/08 20:48 ana 2015/07/08 20:48 ana 2015/07/08 20:46 ana 2015/07/08 20:46 ana 2015/07/08 20:40 ana 2015/07/08 20:33 ana 2015/07/08 20:33 ana 2015/07/08 20:33 ana 2015/07/08 20:32 ana 2015/07/08 20:32 ana 2015/07/08 20:31 ana 2015/07/08 20:31 ana 2015/07/08 20:30 ana 2015/07/08 20:30 ana 2015/07/08 20:29 ana 2016/05/22 14:13 sam 2015/07/21 19:58 ana 2015/07/21 19:57 ana 2015/07/21 19:28 ana 2015/07/21 19:27 ana 2015/07/08 21:31 ana 2015/07/08 21:12 ana 2015/07/08 20:50 ana 2015/07/08 20:49 ana 2015/07/08 20:49 ana 2015/07/08 20:49 ana 2015/07/08 20:48 ana 2015/07/08 20:48 ana 2015/07/08 20:48 ana 2015/07/08 20:46 ana 2015/07/08 20:46 ana 2015/07/08 20:40 ana 2015/07/08 20:33 ana 2015/07/08 20:33 ana 2015/07/08 20:33 ana 2015/07/08 20:32 ana 2015/07/08 20:32 ana 2015/07/08 20:31 ana 2015/07/08 20:31 ana 2015/07/08 20:30 ana 2015/07/08 20:30 ana 2015/07/08 20:29 ana 2015/07/08 20:28 ana 2015/07/08 20:13 ana 2015/07/08 20:09 ana 2015/07/08 19:47 ana created Line 1: Line 1: - ====== 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 |}} + - +