Question

Chapter 16, Problem 63. A person is standing in a room at 18 ◦C. The exposed surface area and skin temperature of the person are 1.7 m2 and 32 ◦C, respectively, the convection heat transfer coefficient is 5 W/m2 ·K, and the emissivity of the skin and clothes is 0.9. Determine the total rate of heat transfer.

Answer 1

Answer:
`Q=248.011 W`

Step-by-step explanation:

Given

Temperature of Room
`T_(\infty )=18^(\circ)\approx 291 K`

Area of Person
`A=1.7 m^2`

Temperature of skin
`T=32^(\circ)\approx 305 K`

Heat transfer coefficient
`h=5 W/m^2.k`

Emissivity of the skin and clothes
`\epsilon =0.9`

`\Delta T=32-18=14^(\circ)`

Total rate of heat transfer=heat Transfer due to Radiation +heat transfer through convection

Heat transfer due radiation
`Q_1=\epsilon \sigma A(T^4-T_(\infty )^4 )`

where
`\sigma =stefan-boltzman\ constant`

`Q_1=0.9* 5.687* 10^(-8)* 1.7* (305^4-291^4)`

`Q_1=129.01 W`

Heat Transfer due to convection is given by

`Q_2=hA(\Delta T)`

`Q_2=5* 1.7* 14=119 W`

`Q=Q_1+Q_2`

`Q=129.01+119=248.011 W`