Heat transfer basics

a$)$

The RT$25$ phase$-$change material has the thermo$-$physical properties given in the Table below:

with Cp the mass heat capacity, k the thermal conductivity, $$ the density, $L_F$ the latent heat of fusion, $T_m$ the solid$-$

liquid phase change temperature $($melting$),$ the volume expansion coefficient and $v$ the kinematic viscosity.

Calculate the energy required to raise $2$ kg of RT$25$ material from $10C$ to $30C.$

Calculate the thermal power required to achieve this heat transfer in one minute.

Show the variation of the average temperature of the material as a function of time $($temperature on the $y-$axis,

time on the x$-$axis$).$ Indicate which type of heat transfer $($latent or sensible$)$ corresponds to each branch of the graph.

b$)$

Consider a wall made up of three homogeneous, isotropic layers: exterior rendering, insulation $($glass wool$)$ and

heavy concrete. The properties of each layer are as follows:

Heavy concrete: $L_c=20cm,k_c=2\frac{W}{m.K}$

Insulation $($glass wool$)$: $L_i=20cm,k_i=0\mathrm{.}04\frac{W}{m.K}$

Plaster: $e_p=1cm,k_p=1\mathrm{.}5\frac{W}{m.K}$

where $L$ is thickness and $k$ is thermal conductivity.

Outside and inside air temperatures are, respectively, $T_e=-7C$ and $T_i=19C.$ Exterior and interior surface heat

transfer coefficients are, respectively, $h_e=12\frac{W}{m^2(K)}$ and $h_i=5\frac{W}{m^2(K)}.$ Heat transfer by radiation is neglected.

Insulation is towards the outside, i$.$e$.$ the configuration is plaster on the outside $-$ insulation in the middle $-$ concrete

on the inside. Heat transfer is assumed to be one$-$dimensional.

Draw the complete electrical network corresponding to the wall.

Calculate the various thermal resistances of the layers and the total resistance of the wall.

Calculate the flux density through the wall.

Given a wall surface area of $9m^2,$ what is the total flux through the wall?

Calculate the external and internal surface temperatures, and all interface temperatures in the wall.

What is the shape of the isotherms in the wall?