University Of Texas At Tyler Operations And Supply Chain Management Assignment Help - A large plate of thickness 2L

Question - A large plate of thickness 2L is at a uniform temperature of T; = 200°C, when it is suddenly quenched
by dipping it in a liquid bath of temperature T8 = 20°C. Heat transfer to the liquid is characterized by
the convection coefficient h.
(a) If x = 0 corresponds to the mid plane of the wall, on T – x coordinates, sketch the temperature
distributions for the following conditions: initial condition (t = 0), steady-state condition (t ? 8 ), and two
intermediate times.
(b) On coordinates, sketch the variation with time of the heat flux at x = L.
(c) If h = 100 W/m2 · K, what is the heat flux at x = L and t = O? If the wall has a thermal conductivity
of k = 50 W/m' K, what is the corresponding temperature gradient at x = L ...Read More ?
(d) Consider a plate of thickness 2L = 20 mm with a density of p = 2770 kg/m3 and a specific heat cp
= 875 J/kg · K. By performing an energy balance on the plate, determine the amount of energy per
unit surface area of the plate (J/m2) that is transferred to the bath over the time required to reach
steady-state conditions.
(e) From other considerations, it is known that, during the quenching process, the heat flux at x = + L
and x = - L decays exponentially with time according to the relation, q" = A exp (- Bt), where t is in
seconds, A = 1.80 X 104 W/m2 · and B = 4.126 X 10- 3s -1. Use this information to determine the
energy per unit surface area of the plate that is transferred to the fluid during the quenching process. ...Read Less

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