An amount of fine coal powder has been stockpiled as the 2-m-deep layer shown be

Question

An amount of fine coal powder has been stockpiled as the 2-m-deep layer shown below. Due to a reaction between coal particles and atmospheric gases, the layer generates heat volumethcally at the uniform rate qm = 50 W/m3. The coal temperature is in steady state. The ambient air temperature is T infinity = 20 degreeree C, and the heat transfer coefficient at the upper surface of the coal stockpile is h = 5 W /m2-K. Calculate the temperature of the upper surface, Tw. b) Consider the case where the layer of coal loses heat to the ground at the rate of 30 W/m2. Calculate the temperature of the upper surface of the layer of coal.

Explanation / Answer

similar to your previous question

equate the heat transfer at the interfaces

q= 50W/m^3

considering heat transfer per unit area
A=1
heat tranfer through 2x1 m^3 coal = 50 x 2 x 1
= 100W

100 = h x A x T

100 = 5 x 1 x (Tw - 20)

20 = Tw - 20

Tw = 40 degrees

case 2

if heat is lost to the ground also at the rate of 30 W/m^2

so asthe heat transfer coeff of the groun is not given ,neither the temp of the ground is given

so this seems a bit incomplete still let me work out

the total amount of heat generated by the coal remains same as in case 1 but now heat transfer takes palce at both surfaces

so the effective heat transfer from upper surface = 100 +30

so h x A x T = 130

5 x 1x Tw - 20 = 130

Tw = 26 + 20

Tw = 46 degrees

please rate me!

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