Heat Chap03-039

# Heat Chap03-039 - Chapter 15 Steady Heat Conduction Thermal...

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Chapter 15 Steady Heat Conduction Thermal Contact Resistance 3-39C The resistance that an interface offers to heat transfer per unit interface area is called thermal contact resistance , R c . The inverse of thermal contact resistance is called the thermal contact conductance. 3-40C The thermal contact resistance will be greater for rough surfaces because an interface with rough surfaces will contain more air gaps whose thermal conductivity is low. 3-41C An interface acts like a very thin layer of insulation, and thus the thermal contact resistance has significance only for highly conducting materials like metals. Therefore, the thermal contact resistance can be ignored for two layers of insulation pressed against each other. 3-42C An interface acts like a very thin layer of insulation, and thus the thermal contact resistance is significant for highly conducting materials like metals. Therefore, the thermal contact resistance must be considered for two layers of metals pressed against each other. 3-43C Heat transfer through the voids at an interface is by conduction and radiation. Evacuating the interface eliminates heat transfer by conduction, and thus increases the thermal contact resistance. 3-44C Thermal contact resistance can be minimized by (1) applying a thermally conducting liquid on the surfaces before they are pressed against each other, (2) by replacing the air at the interface by a better conducting gas such as helium or hydrogen, (3) by increasing the interface pressure, and (4) by inserting a soft metallic foil such as tin, silver, copper, nickel, or aluminum between the two surfaces. 3-45 The thickness of copper plate whose thermal resistance is equal to the thermal contact resistance is to be determined. Properties The thermal conductivity of copper is given to be k = 386 W/m °C (Table A-2). Analysis Noting that thermal contact resistance is the inverse of thermal contact conductance, the thermal contact resistance is determined to be C/W . m 10 556 . 5 C . W/m 000 , 18 1 1 2 5 2 c ° × = ° = = - h R c For a unit surface area, the thermal resistance of a flat plate is defined as R L k = where L is the thickness of the plate and k is the thermal conductivity. Setting R R c = , the equivalent thickness is determined from the relation above to be L kR kR c = = = ° × ° = = - ( . 386 10 0 0214 5 W / m. C)(5.556 m . C / W) m 2 2.14 cm Therefore, the interface between the two plates offers as much resistance to heat transfer as a 2.14 cm thick copper. Note that the thermal contact resistance in this case is greater than the sum of the thermal resistances of both plates. 3-23

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Chapter 15 Steady Heat Conduction 3-46 Six identical power transistors are attached on a copper plate. For a maximum case temperature of 85 ° C, the maximum power dissipation and the temperature jump at the interface are to be determined.
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