A short brass cylinder (rho = 8530 kg/m3, cp = 0.389 kJ/kg⋅K, k = 110 W/m⋅K, and α = 3.39×10−5 m2/s) of diameter 4 cm and height 20 cm is initially at a uniform temperature of 150°C. The cylinder is now placed in atmospheric air at 20°C, where heat transfer takes place from the cylinder 15 min after the start of the cooling by convection with a heat transfer coefficient of 40 W/m2⋅K. Solve this problem using the analytical one-term approximation method.

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

there are no atoms