Transient Heat Conductionkitchen are like mine, it is sonietimes more of a mystical, elusive art form. Thankfully, science also has much tocontribute in the kitchen as well as the laboratory.Cooking a Thanksgiving turkey is an art form and, if your skills in theLet us consider the change in temperature of a common, 20-lb holiday fowl as it is cooked in a convection oven.To simplify the analysis, let's assume the bird can be modeled as a uniform sphere of radius 7.0 in. with aspecific heat of 3.53 kJ/kg-K. Moreover, the turkey will be assumed to have a uniform temperature, T,throughout that will change with time as it is cooked according to the following relationship:-hAstT(t) = T + (To – T»)ePCpVwhere To is the initial temperature of the turkey, T», is the oven temperature, V is the volume of the turkey, As isthe surface area of the turkey, and h is the convection coefficient for the scenario which is 11.3 W/m2-K. If theoven is set to 325 °F and the initial temperature of the turkey is 50 °F, calculate how much time it takes for theturkey to reach 170 °F.

Write the expression for the temperature in a convection oven as follows: Tt = T∞ +T0-T∞exp-hAρcpVτTt-T∞T0-T∞ = exp-hAρcpVτ ......1Given, The radius of the sphere, r = 7.0 in×0.0254 m1 in = 0.1778 m Mass, m = 20 lb×0.453592 kg1 lb = 9.07184 kg Specific heat, cp = 3.53 kJ/kg·K Convection coefficient, h = 11.3 W/m2·K Oven temperature, T∞ = 325 °F Initial temperature, T0 = 50 °F Final temperature, T = 170 °FCalculate the volume of the sphere as follows: V = 43πr3= 43π0.17783= 0.0235 m3 Surface area, As = 4πr2= 4π0.1778 m2= 0.3974 m2 Calculate the density as follows: ρ = mV= 9.07184 kg0.0235 m3= 386 kg/m3Substitute the corresponding values in equation(1) and calculate the time. Tt-T∞T0-T∞ = exp-hAρcpVτ170°F-325°F50°F-325°F = exp-11.3 W/m2K×0.3974386 kg/m3×3.53 kJ/kgK×0.0235 m3×1 kJ1000 J×τ0.563 = exp-0.00014τ-0.00014τ = ln0.563τ = 4100 s Therefore, the required solution is 4100 s.