Question

# A thin walled metal tank of surface area ( 5 mathrm{m}^{2} ) is filled with water and contains an immersion dissipating 1 ( mathrm{kW} ). The tank is covered with ( 4 mathrm{cm} ) thick layer of insulation whose thermal conductival is ( 0.2 mathrm{W} / mathrm{m} / mathrm{K} ). The outer face of the insulation is ( 25^{circ} mathrm{C} ). Find the temperature of the tank in the state

Solution

[

T_{i=?} quad T_{0}=298 mathrm{K}

]

(1) Rate of Heet pracusfin is giver by fourier ( varepsilon q^{4} ).

( therefore e_{i} frac{d Q}{d t}=frac{-k A d T}{d x} sigma_{i} )

( k= ) the mol conductivity

DT temperatur difforcin

( A= ) Area

( Rightarrow B )

( d x= ) thickness ( So: frac{d Q}{d t}=frac{0.2 times 5(T-25)}{0.04} )

( Rightarrow quad 1000=frac{0.2 times 5 times(T-.25)}{0.04}[because power frac{dδ}{dt})]

[

Rightarrow {T}=65^{circ} mathrm{C}

]