Question

In temperate countries,wood is sometimes used to panel the inside concrete wall in a house.A house is built 15cm thick concrete wall and paneled with 2.0cm thick wood.The thermal conductivities of concrete and wood are 1.0 and 0.1W/m.k respectively.Calculate the percentage reduction in the heat conducted per square meter by installing the wood panel.Assume that the concrete and wood panel are in perfect thermal contact.The temperature inside the house is 22°c when the outside is at 5°c.

Answer 1

First, find the heat flow thru the concrete wall without the wooden insulation:

$$q_c=\frac{\Delta T}{R_c}=\frac{\Delta Tk_cA}{L_c}.$$

Then calculate the heat flow with the insulation installed (series connection of thermal resistances):

$$q_{cw}=\frac{\Delta T}{R_c+R_w}=\frac{\Delta TA}{L_c/k_c+L_w/k_w}.$$

Finally, calculate the percentage reduction in the heat conducted per square meter by installing the wood panel:

$$\epsilon=\frac{q_c-q_{cw}}{q_c}\cdot100\%=\frac{L_wk_c}{L_ck_w+L_wk_c}\cdot100\%,\\\space\\ \epsilon=\frac{2\cdot1}{15\cdot0.1+2\cdot1}\cdot100\%=57\%.$$

Installation of wood will lead to a 57% reduction in heat loss.