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Question-136487




Question Number 136487 by physicstutes last updated on 22/Mar/21
Commented by physicstutes last updated on 22/Mar/21
The figure above shows a system of two slaps with a space inbetween them  ,given that the respective thermal conductivities of the slap−space−slap system  is k_1 ,k_2  and k_3 . and thier lenght (or thickness) are y_1 ,y_2  and y_3 . Write  an equation for the rate of heat transfer through each surface with reference to  the temperatures on the diagram. Hence arrange the  equations above to   give the overall rate of heat flow equation.
$$\mathrm{The}\:\mathrm{figure}\:\mathrm{above}\:\mathrm{shows}\:\mathrm{a}\:\mathrm{system}\:\mathrm{of}\:\mathrm{two}\:\mathrm{slaps}\:\mathrm{with}\:\mathrm{a}\:\mathrm{space}\:\mathrm{inbetween}\:\mathrm{them} \\ $$$$,\mathrm{given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{respective}\:\mathrm{thermal}\:\mathrm{conductivities}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slap}−\mathrm{space}−\mathrm{slap}\:\mathrm{system} \\ $$$$\mathrm{is}\:{k}_{\mathrm{1}} ,{k}_{\mathrm{2}} \:\mathrm{and}\:{k}_{\mathrm{3}} .\:\mathrm{and}\:\mathrm{thier}\:\mathrm{lenght}\:\left(\mathrm{or}\:\mathrm{thickness}\right)\:\mathrm{are}\:{y}_{\mathrm{1}} ,{y}_{\mathrm{2}} \:\mathrm{and}\:{y}_{\mathrm{3}} .\:\mathrm{Write} \\ $$$$\mathrm{an}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{transfer}\:\mathrm{through}\:\mathrm{each}\:\mathrm{surface}\:\mathrm{with}\:\mathrm{reference}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{temperatures}\:\mathrm{on}\:\mathrm{the}\:\mathrm{diagram}.\:\mathrm{Hence}\:\mathrm{arrange}\:\mathrm{the}\:\:\mathrm{equations}\:\mathrm{above}\:\mathrm{to}\: \\ $$$$\mathrm{give}\:\mathrm{the}\:\mathrm{overall}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{flow}\:\mathrm{equation}. \\ $$

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