Mathematical Expressions Mathematics Assignment Help

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Q1. An isothermal plate with a constant temperature of 17°C is placed at one end of a cooling plate. The isothermal plate acts as a cooling device for a battery module. The cooling plate is used to isolate the battery module from the cooling device as shown in Figure 1. In order to keep the isothermal plate to be maintained at 17°C, the plate is powered by an external electrical power. During discharging, the battery module will reject heat at a constant heat flux of 280 W/ m². The contact between isothermal plate, battery module and cooling plate are in a prefect contact. The cooling plate is made from pure copper and has a length of 15-cm and thickness of 30-cm and height of 15-cm. The top and bottom of the system are well insulated therefore, heat only travels in one direction.

a) State and write mathematical expressions to describe two boundary conditions for the cooling plate

b) Obtain an expression to describe temperature profile along the cooling plate

c) Determine the surface temperature of cooling plate which in contact with battery module

d) Calculate the heat transfer rate along the cooling plate.

e) Suggest two ways to keep the battery module to be at low temperature. Cooling plate Battery module Isothermal plate 15-cm Figure 1. Battery module cooling system



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