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13. (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 srfaces, the rate of heat flow through a substance is provided by Fouriers law of heat conduction, which becomes the following formula: T-T) 0 0 is heat per unit time per unit area (Watts/m2 or BTU/hrft) k is the thermal conductivity, which is a property of a substance that indicates its capability to conduct heat (Watts/m K or BTU/hrft F) T, is the hotter temperature "F or K). r, is the cooler temperature ( orK). a is the width of the substance (ft or m). a. Write, compile, and exccute a C++ program that calculates and displays the heat transfer through a substance. The inputs should be the substance's thermal conduc- tivity, 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 English Engineering) is used in the final determination of 0. Tike output should display the value of Q in both unit systems. 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