Thermal Contact Resistance - MapleSim Help

Thermal Contact Resistance

Basic thermal contact resistance between two materials

 Description The Thermal Contact Resistance component models a heat transfer between two materials which have different thermal conductivities. The following image illustrates an example of apparent contact area of two materials.          Because of the surface roughness of both materials, the actual contact area of two materials becomes spots of contact. The other areas are regarded as the void space filled by fluid such as air. The following image illustrates the mechanism of jointed surface in more detail.          Then heat flow of the contact of two materials is regarded as the following image. This component is based on this. Using each option, you can control the apparent area size, area ratio, and the thickness of void space by real input signals.That makes it possible for you to change contact resistance value during simulation. For example, change by deformation of actual contact area size caused by joint pressure change.
 Equations   Fundamental equation is: ${Q}_{\mathrm{flow}}=\frac{1}{\mathrm{RC}}\cdot A\cdot \mathrm{dt}=\mathrm{hc}\cdot A\cdot \mathrm{dT}$ The equation for the areas is shown below: The equation for heat flow is as below:   ${Q}_{\mathrm{flow}}=\mathrm{Q__solid}+\mathrm{Q__fluid}=\frac{\mathrm{dT}}{\frac{\left(\frac{L}{2}\right)}{\mathrm{Material_a.k}\mathrm{Ac}}+\frac{\left(\frac{L}{2}\right)}{\mathrm{Material_b.k}\cdot \mathrm{Ac}}}+\frac{\mathrm{dT}}{\frac{L}{\mathrm{kf}\cdot \mathrm{Av}}}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}$
 References [1] : J. P. Holman. "Heat Transfer Ninth Edition", McGraw-Hill Higher Education.

Variables

 Symbol Units Description Modelica ID ${Q}_{\mathrm{flow}}$ $W$ Heat flow rate from port a to port b Q_flow $\mathrm{dT}$ $K$ Temperature difference between port a and port b dT $\mathrm{Rc}$ $\frac{{m}^{2}K}{W}$ Thermal contact resistance Rc $\mathrm{hc}$ $\frac{W}{{m}^{2}{K}^{}}$ Coefficient of thermal contact conductance, which is the inverse of Rc hc $A$ ${m}^{2}$ Apparent contact area A $\mathrm{Ac}$ ${m}^{2}$ Ac $\mathrm{Av}$ ${m}^{2}$ Area of void space Av $L$ ${m}^{}$ Thickness of the void space L

Connections

 Name Units Condition Description Modelica ID $\mathrm{port_a}$ - Thermal port a port_a $\mathrm{port_b}$ - Thermal port b port_b $\mathrm{A_input}$ - if use Apparent contact area input is true. Apparent contact area is defined by Real signal input. A_input $\mathrm{Aratio_input}$ - if use Area ratio input is true. Area ratio $\frac{\mathrm{A__c}}{A}$ is defined by Real signal input. Aratio_input $\mathrm{L_input}$ - if use Void space thickness input is true. Thickness of the void space is defined by Real signal input. L_input

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{Material_a}$ $\mathrm{SolidPropertyData}$ $-$ Solid material property data Material_a $\frac{W}{m\cdot K}$ Material_a.k is the thermal conductivity of the material of port_a Material_a.k $\frac{J}{\mathrm{kg}\cdot K}$ Material_a.cp is the specific heat capacity of the material of port_a Material_a.cp $\frac{\mathrm{kg}}{{m}^{3}}$ Material_a.rho is the density of the material of port_a Material_a.rho $\mathrm{Material_b}$ $\mathrm{SolidPropertyData}$ $-$ Solid material property data Material_b $\frac{W}{m\cdot K}$ Material_b.k is the thermal conductivity of the material of port_b Material_b.k $\frac{J}{\mathrm{kg}\cdot K}$ Material_b.cp is the specific heat capacity of the material of port_b Material_b.cp $\frac{\mathrm{kg}}{{m}^{3}}$ Material_b.rho is the density of the material of port_b Material_b.rho $\mathrm{k__fluid}$ $0.0241$ $\frac{W}{m\cdot K}$ The thermal conductivity of the fluid which fills void space kf $A$ $0.0001$ ${m}^{2}$ Apparent contact area between materials A_const $\frac{\mathrm{A__c}}{A}$ $-$ Area ratio $\frac{\mathrm{A__c}}{A}$ (between 0 and 1)  Aratio_const $L$ $m$ Thickness of the void space L_const

Initial Conditions

 Symbol Units Description Modelica ID ${Q}_{{\mathrm{flow}}_{0}}$ $W$ Initial heat flow rate Q_flow(0) ${\mathrm{dT}}_{0}$ $K$ Initial temperature difference dT(0)