Define three mechanisms of the heat transfer process.

$[2$ MARKS$]$

Define Newton's law of cooling.

$[2$ MARKS$]$

Define Fourier's law for a steady, one$-$dimensional conduction.

$[2$ MARKS$]$

Write the general equation of heat conduction process.

$[2$ MARKS$]$

a$)$ Explain lumped capacitance approximation for a unsteady heat transfer process,

b$)$ Write the equation for the calculation of lumped capacitance time constant,

c$)$ Write the general equation that provides the correlation between temperature and time for zero$-$dimensional transient problem.

$[6$ MARKS$]$

$6.$ A $0\mathrm{.}1m-$thick wall is exposed to cold air at $270K$ through a convection heat transfer coefficient of $40W{m}^{-2}{K}^{-1}.$ The thermal conductivity of the wall is $k=0\mathrm{.}7W{m}^{-1}{K}^{-1}.$ On the opposite side of the wall is air at a temperature of $330K,$ and a convective heat transfer coefficient is $10W{m}^{-2}{K}^{-1}.$ Calculate the heat flux assuming steady$-$state conduction.