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1. Boxes of hamburger are being cooled from an initial temperature of 25 C using

ID: 1718472 • Letter: 1

Question

1. Boxes of hamburger are being cooled from an initial temperature of 25 C using cold air at 0 C. The dimensions of the boxes are 12 cm height, 15 cm width and 18 cm length. The cooling occurs in a 10 m long tunnel with the boxes of product moving through a rate of 2 m/hr. The thermal diffusivity of the product is 1.2 x 10-7 m2/s, and the convective heat transfer coefficient is 450 W/m2K. The paperboard of the box has a thickness of 10 mm and a thermal conductivity of 0.04 W/mK.

a. Estimate the overall heat transfer coefficient for the box and air flow.

b. Determine the temperature of the product at the center of the boxes when the product reaches the exit from the cooling tunnel.

Explanation / Answer

Mean film temperature Tf = 0 +25 /2

Tf = 12.5 C

Re = VL /v

= 2 / 60 x 60 X 10 / 1.2 x 10^-7 = 462960

Re < 5 x 10^5

it is laminar flow

Nu = 0.332 x Re^0.5 Pr ^0.333

= 0.332 x462960^0.5 x 0.698 ^0.333

= 63.44

NU = h xL /k

h = k x NU /L = 0.04 x 63.44 / 10

= 0.253W/m^2 k

overall heat transfer coefficient U = Q /A x delta T

1 /U =(1 /h1 + x /k + 1 /h2 )

= 1/450 + 0.18 / 0.04 + 1 /0.253

= 0.022+4.5+3.95 = 0.118

U = Q / A x Delta T

Dt = Q / A xU

= 0.11