How do you turn a proportionality between variables into an equation?

Answer. By adding the proportionality constant .

Explanation:

suppose 'x' a  is directly proportional to the 'y' , where x and y are variables:

x ∝ y

with an input of constant value 'K' proportionality relation gets converted into  an equation:

x = K y

For example : Gravitational force is directly proportional to the product of two masses and inversely proportional to the square of the distance between the two masses.

F ∝

To convert this proportionality relation constant 'G'  was introduced known as gravitational constant whose value remains constant under every conditions.

answer: semi-infinite solid initially at a uniform temperature of 400 ◦c is cooled at its surface by convection. the cooling fluid at a constant temperature of 200 ◦c has a convective coefficient (ha) of 250 w/m2.k. the physical properties of the solid: k = 20 w/m.k and α = 4 * 10-5  m2/s. using δx = 0.04 m and δt = 10 s. write the finite difference equations describing the transient heat transfer of the first five δx and the temperature profile after 30 s.