Question

Supplemental Problem 2.003 A large plate of thickness 2L is at a uniform temperature of Tỉ-190°C, when it is suddenly quenched by dipping it in a liquid bath of temperature To Heat transfer to the liquid is characterized by the convection coefficient h. Assume x = 0 corresponds to the midplane of the wall -20°C (a) If h = 100 w/m2, K, what is the heat flux atx = L and t = 0? If the wall has a thermal conductivity of k = 50 W/m-K what is the corresponding temperature gradient at x L? (b) Consider a plate of thickness 2L = 20 mm with a density of ρ = 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/m) that is transferred to the bath over the time required to reach steady-state conditions (c) 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, = A exp (-Bt), where t is in seconds, A = 1.7 x 104 W/m2, and B = 4.126 × 10-3 s-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 The temperature gradient at x = L and 1-0, in K/m: OT K/m dx し,0 The amount of energy per unit surface area of the plate that is transferred to the bath over the time required to reach steady-state conditions, in 1/m E out,stcady The energy per unit surface area of the plate that is transferred to the fluid during the quenching process, in J/m2 out,quench- Physical Properties Mathematical Functions

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Answer 1

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