Temperature imposed at the surface of soil initially at 20C. (a) Calculate and plot the temperature...

    

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Temperature imposed at the surface of soil initially at 20°C. (a) Calculate and plot the temperature history at the burial depth of 0.68 m for selected soil thermal diffusivity values, ax 107 = 1.0, 1.38, and 3.0 m²/s, (b) Plot the temperature distribution over the depth 0 ≤ x ≤ 1.0 m for times of 1, 5, 10, 30, and 60 days with a = 1.38 x 107 m²/s, (c) Plot the surface heat flux, qx (0,t), and the heat flux at the depth of the buried main, qx (0.68m, t), as a function of time for a 60 day period with a = 1.38 x 107 m²/s. Compare your results with those in the Comments section of the example. Use the IHT Models | Transient Conduction | Semi-infinite Medium model as the solution tool. SCHEMATIC: Xm = 0.68 m Ts = -15°C Soil, T₁ = 20°C ax107 = 1.0,1.38, or 3.0 m²/s k = 0.52 W/m-K Water main ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Soil is a semi-infinite medium, and (3) Constant properties. ANALYSIS: The IHT model corresponds to the case 1, constant surface temperature sudden boundary condition, Eqs. 5.57 and 5.58. Selected portions of the IHT code used to obtain the graphical results below are shown in the Comments. (a) The temperature history T(x,t) for x = 0.68 m with selected soil thermal diffusivities is shown below. The results are directly comparable to the graph shown in the Ex. 5.5 comments. x=0.68 m, T(0,1)=Ts = -15C, T(x0)=20C T(0.68 m.) (C) 20 10 -10 0 15 alpha= 1.00e-7 m^2/s alpha= 1.38e-7 m^2/s alpha=3.00e-7 m^2/s 30 Time,t (days) 45 60 Continued..... (b) The temperature distribution T(x,t) for selected times is shown below. The results are directly comparable to the graph shown in the Ex. 5.5 comments. T(x) (C) 20 15 10 5 0 -5- -10 -15 0 alpha= 1.38e-7 m2/s. T(0,1)=-15C, T(x0)=20 C 1 day 5 days 10 days 30 days 60 days 0.25 0.5 Depth, x(m) 0.75 (c) The heat flux from the soil, qx (0,t), and the heat flux at the depth of the buried main, qx (0.68m, t), are calculated and plotted for the time period 0 ≤t≤ 60 days. Heat flux, q"(x,t) (W/m^2) -50 -100 -150 -200 alpha = 1.38e-7 m ^2/s, k = 0.52 W/m -K, T(0,t) = -15 C 0 30 Time,t (days) Surface heat flux, x = 0 Buried-main depth, x = 0.68 m 15 45 60 Temperature imposed at the surface of soil initially at 20°C. (a) Calculate and plot the temperature history at the burial depth of 0.68 m for selected soil thermal diffusivity values, ax 107 = 1.0, 1.38, and 3.0 m²/s, (b) Plot the temperature distribution over the depth 0 ≤ x ≤ 1.0 m for times of 1, 5, 10, 30, and 60 days with a = 1.38 x 107 m²/s, (c) Plot the surface heat flux, qx (0,t), and the heat flux at the depth of the buried main, qx (0.68m, t), as a function of time for a 60 day period with a = 1.38 x 107 m²/s. Compare your results with those in the Comments section of the example. Use the IHT Models | Transient Conduction | Semi-infinite Medium model as the solution tool. SCHEMATIC: Xm = 0.68 m Ts = -15°C Soil, T₁ = 20°C ax107 = 1.0,1.38, or 3.0 m²/s k = 0.52 W/m-K Water main ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Soil is a semi-infinite medium, and (3) Constant properties. ANALYSIS: The IHT model corresponds to the case 1, constant surface temperature sudden boundary condition, Eqs. 5.57 and 5.58. Selected portions of the IHT code used to obtain the graphical results below are shown in the Comments. (a) The temperature history T(x,t) for x = 0.68 m with selected soil thermal diffusivities is shown below. The results are directly comparable to the graph shown in the Ex. 5.5 comments. x=0.68 m, T(0,1)=Ts = -15C, T(x0)=20C T(0.68 m.) (C) 20 10 -10 0 15 alpha= 1.00e-7 m^2/s alpha= 1.38e-7 m^2/s alpha=3.00e-7 m^2/s 30 Time,t (days) 45 60 Continued..... (b) The temperature distribution T(x,t) for selected times is shown below. The results are directly comparable to the graph shown in the Ex. 5.5 comments. T(x) (C) 20 15 10 5 0 -5- -10 -15 0 alpha= 1.38e-7 m2/s. T(0,1)=-15C, T(x0)=20 C 1 day 5 days 10 days 30 days 60 days 0.25 0.5 Depth, x(m) 0.75 (c) The heat flux from the soil, qx (0,t), and the heat flux at the depth of the buried main, qx (0.68m, t), are calculated and plotted for the time period 0 ≤t≤ 60 days. Heat flux, q"(x,t) (W/m^2) -50 -100 -150 -200 alpha = 1.38e-7 m ^2/s, k = 0.52 W/m -K, T(0,t) = -15 C 0 30 Time,t (days) Surface heat flux, x = 0 Buried-main depth, x = 0.68 m 15 45 60

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To solve this problem we will use the transient conduction semiinfinite medium model The temperature distribution and heat flux at different depths an... View the full answer