Estimate the time required to heat a cubical piece of chicken to \(120^{\circ} \mathrm{C}\). The temperature of the grill used for cooking is \(250^{\circ} \mathrm{C}\). The temperature of the air above the grill is \(50^{\circ} \mathrm{C}\). Assume lumped capacitance. The heat-transfer coefficient of between the grill and the chicken is \(200 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) and the heat-transfer coefficient between the chicken and air is \(15 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). Assume that one of the six faces of the chicken receives heat from the grill and the remaining five faces transfer heat to the air. The cross-section area of the piece is \(0.001 \mathrm{~m}^{2}\). The density of the chicken is \(800 \mathrm{~kg} / \mathrm{m}^{3}\) and the specific heat is \(2000 \mathrm{~J} / \mathrm{kg} \mathrm{K}\). The initial temperature of the chicken is \(30^{\circ} \mathrm{C}\).