Chapter 5, Problem 5.10P

A flaked cereal is of thickness $2L=1.2\text{mm}\text{.}$ The density, specific heat, and thermal conductivity of the flake are $\rho =700\text{}{\text{kg/m}}^{\text{3}},c_p=2400\text{J/kg}\cdot \text{K,}$ and $k=0.34\text{W/m}\cdot \text{K,}$ respectively. The product is to be baked by increasing its temperature from $T_i=20°\text{C}$ to $T_f=220°\text{C}$ in a convection oven, through which the product is carried on a conveyor. If the oven is $L_o=3\text{m}$ long and the convection heat transfer coefficient at the product surface and oven air temperature are $h=55{\text{W/m}}^{\text{2}}\cdot \text{K}$ and $T_{\infty }=300°\text{C,}$ respectively, determine the required conveyor velocity, V. An engineer suggests that if the flake thickness is reduced to $2L=1.0\text{mm}$ the conveyor velocity can be increased. resulting in higher productivity. Determine the required conveyor velocity for the thinner flake.