(Heat transfer) The transfer of heat energy through matter, referred to as heat conduction...

(Heat transfer) The transfer of heat energy through matter, referred to as heat conduction, is always from a region of higher temperature to one of lower temperature. It occurs by transferring energy from atom to atom within a substance. With uniform temperatures on either side of equal-sized surfaces, the rate of heat flow through a substance is provided by Fourier’s law of heat conduction, which becomes the following formula:

Q is heat per unit time per unit area (watts/m2 or BTU/hr-ft2).

k is the thermal conductivity, which is a property of a substance that indicates its capability to conduct heat (watts/m°K or BTU/hr-ft°F).

T2 is the hotter temperature (°F or °K).

T1 is the cooler temperature (°F or °K).

w is the width of the substance (ft or m).

a. Write, compile, and run a C++ program that calculates and displays the heat transfer through a substance. The inputs should be the substance’s thermal conductivity, its width, and temperatures on either side of it. Your program should determine which unit system is used, item by item, and then convert units as necessary so that a consistent unit system (SI or U.S. Customary) is used in the final determination of Q. The output should display the value of Q in both unit systems.

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b. Verify that your program is working by hand-calculating the heat transfer through a cement wall with a thermal conductivity of .29 watts/m°K and a thickness of 15 cm. One side of the wall is at a constant temperature of 32°C, and the other side is -7°C.

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c. After verifying that your program is working correctly, use the following chart of thermal conductivities to determine the heat transfer rate for the following:

i. A pane of glass that’s ½ cm thick and has an inside temperature of 24°C and an outside temperature of 15°C

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ii. A column of air 10 cm thick that’s held between two walls, one with a temperature of 23°C and the other of 14°C