Question

A 1-in. thick steel plate measuring 10 in. in diameter is heatedfrom below by a hot plate, its upper surface exposed to air at80^oF. The heat-transfer coefficient on the upper surfaceis 5 Btu/h ft^oF and k for steel is 25 Btu/hft^oF.

a.) How much heat must be supplied to the lower surface of thesteel if its upper surface remains at 160^oF? (includeradiation)

b.) What are the relative amounts of energy dissipted from theupper surface of the steel by convection and radiation?

Here is the answer Ifound.

a.)q=(pi/4)(10/12)² *[(5)(80) + (0.1714)(6.2)⁴] = 356 Btu/hr

b.)q_conv=(pi/4)(10/12)²(5)(80)=218.2Btu/hr

q_rad=(pi/4)(10/12)²(0.1714)[6.2⁴ -5.4⁴] = 58.6 Btu/hr

I need help understanding wheresome of the variables came from.

I think the equation for a.) isq=A[h(ΔT)+σ(T)⁴].........so could you please tell mewhere the 12 and the 6.2 came from?

and for part b.)....where did the5.4 come from?