Ht 031 Solution

CHEMICAL ENGINEERING SERIES: HEAT TRANSFER SOLVED PROBLEMS

The bottom face of a horizontal slab of thickness 6 mm is maintained at 300 °C. The top face is exposed to a flowing gas at 30 °C. The thermal conductivity of the slab is 1.5 W/m·K and the convective heat transfer coefficient is 30 W/m 2·K. At steady state, what is the temperature of the top face? Source: GATE 2014

SOLUTION:

For the heat of convection

q =h ( T 2 −T gas ) A q W = 30 2 ( T 2−30 ) A m ∙K

(

)

q =30T 2−900 eqn A A For the heat of conduction

T −T 2 q =k 1 A x 2−x 1 q W = 1.5 A m∙ K

(

() 300−T 0.006 m ) 2

q =75,000−250 T 2 eqn B A

ENGR. RONNIE V. FLORES

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CHEMICAL ENGINEERING SERIES: HEAT TRANSFER SOLVED PROBLEMS Equate

A

and

B

30 T 2−900=75,000−250 T 2 T 2 =271.07 ° C

ENGR. RONNIE V. FLORES

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