A hot sphere is cooled by forced convection from its initial temperature to ambient conditions. The...

 

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A hot sphere is cooled by forced convection from its initial temperature to ambient conditions. The temperature of the sphere is calculated as a function of time. The following initial conditions are provided: Item Value Unit h 40 Ti T... D 473 293 1 W/K/m K K cm Description Convection heat transfer coefficient Initial temperature of the sphere Ambient temperature Diameter of the sphere Use MATLAB to calculate and plot the temperature of the sphere based on the following equation: T-T = exp[-(A)] Ti-Too Calculate and show the Biot number (Bih x Lc/k) for your sphere following these steps: o Provide the surface area of the sphere (As) and include the units o Provide the volume if the sphere (Vs) and include the units o Provide the characteristic length of the sphere (Lc) and include the units o Include the convection heat transfer coefficient (h) and include the units o Include the conduction heat transfer coefficient for Copper (k) and include the units This is obtained from SolidWorks o Calculate the Biot number (Bi) o Is Bi smaller or larger than 1? Should the temperature variation inside the sphere be large or small? Use the following MATLAB script to calculate the temperature in the sphere o The variables shown equal to a question mark are to be changed to match your SolidWorks calculations o The material of the sphere is Copper. o Density, rho = 8900 Kg/m o Specific Heat, cp = 390 J/kg-K 0 Thermal Conductivity, k = 390 W/m-K clear variables; close all; clc; format compact; syms t; h = ?; I Editor - C:\Users\Jasly\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\TAW2980C\script.m [Read Only] first.mxscript.mx + clear variable; close all; 1 2 3 4 5 6 7 8 9 PENGASAANN27227 10 11 12 13 14 15 16 17 18 19 20 21 23 24 25 26 clc; format compact; t = linspace(0, 2000, 50); h = 40; Ti = 473; Tinf = 293; D = 1; D = D / 100; rho = 8900; cp = 390; k = 390; % W / K / m^2 % K % K % cm % m % Kg/m^3 % J / Kg-K % W / m-K As 4* pi (D/2)^2; Vs = 4/ 3* pi * (D/2)^3; Lc = Vs / As; Bi h Lc / K; * = % m2 (suface area of the sphere) % m3 % m % non-dimensional Biot Number T = (Ti - Tinf) *exp(-h * As *t / rho/Vs/ cp) + Tinf; % include the equation for T plot (t, T); title('Temperature'); xlabel ('time (s)'); ylabel ('T (K)'); grid on; box on; legend('equation'); Command Window Too many input arguments. Error in script (line 18) As = 4 * pi (D/2)^2; fx >> % m2 (suface area of the sphere) Zoom: 100% UTF-8 CRLF script x Workspace X > Name F cp D Hih k rho Hit Ti Tinf Value 390 0.0100 40 390 8900 1x50 double 473 293 Ln 27 Col SOLIDWORKS a E 98 PI Study Apply Simulation Thermal Connections Material Evaluator Loads Features Sketch Markup Evaluate 7 E 7. Sphere (Default < _Displ History Sensors Annotations Surface Bodies Solid Bodies(1) Revolve LOrigin Revolve Material a E 2378 PI G Study Apply Simulation Thermal Connections Shell Run Results Deformed Compare Material Evaluator Loads Manager Results 8 Features Sketch Markup Evaluate MBD Dimensions SOLIDWORKS Add-Ins Simulation MBD SOLIDWORKS CAM SOLIDWORKS CAM TBM Analysis Preparation Model name Sphere P54106 Study name: Initial Value(-Default) Plot type: Thermal Thermall Time step: 10 time: 1,000 Seconds < Sphere (Default < _Displ History Sensors Annotations 7. Surface Bodies Solid Bodies(1) Revolve Material Transient Sensor Graph File Options Help Temp (Kelvin) 400.00 380.00 360.00 340.00 320.00 300.00 280.00 100.00 Transient Sensor Graph 280.00 460.00 640.00 820.00 1,000.00 Time (sec) Thermal -38.6792, 408.067 X A hot sphere is cooled by forced convection from its initial temperature to ambient conditions. The temperature of the sphere is calculated as a function of time. The following initial conditions are provided: Item Value Unit h 40 Ti T... D 473 293 1 W/K/m K K cm Description Convection heat transfer coefficient Initial temperature of the sphere Ambient temperature Diameter of the sphere Use MATLAB to calculate and plot the temperature of the sphere based on the following equation: T-T = exp[-(A)] Ti-Too Calculate and show the Biot number (Bih x Lc/k) for your sphere following these steps: o Provide the surface area of the sphere (As) and include the units o Provide the volume if the sphere (Vs) and include the units o Provide the characteristic length of the sphere (Lc) and include the units o Include the convection heat transfer coefficient (h) and include the units o Include the conduction heat transfer coefficient for Copper (k) and include the units This is obtained from SolidWorks o Calculate the Biot number (Bi) o Is Bi smaller or larger than 1? Should the temperature variation inside the sphere be large or small? Use the following MATLAB script to calculate the temperature in the sphere o The variables shown equal to a question mark are to be changed to match your SolidWorks calculations o The material of the sphere is Copper. o Density, rho = 8900 Kg/m o Specific Heat, cp = 390 J/kg-K 0 Thermal Conductivity, k = 390 W/m-K clear variables; close all; clc; format compact; syms t; h = ?; I Editor - C:\Users\Jasly\AppData\Local\Microsoft\Windows\INetCache\Content.Outlook\TAW2980C\script.m [Read Only] first.mxscript.mx + clear variable; close all; 1 2 3 4 5 6 7 8 9 PENGASAANN27227 10 11 12 13 14 15 16 17 18 19 20 21 23 24 25 26 clc; format compact; t = linspace(0, 2000, 50); h = 40; Ti = 473; Tinf = 293; D = 1; D = D / 100; rho = 8900; cp = 390; k = 390; % W / K / m^2 % K % K % cm % m % Kg/m^3 % J / Kg-K % W / m-K As 4* pi (D/2)^2; Vs = 4/ 3* pi * (D/2)^3; Lc = Vs / As; Bi h Lc / K; * = % m2 (suface area of the sphere) % m3 % m % non-dimensional Biot Number T = (Ti - Tinf) *exp(-h * As *t / rho/Vs/ cp) + Tinf; % include the equation for T plot (t, T); title('Temperature'); xlabel ('time (s)'); ylabel ('T (K)'); grid on; box on; legend('equation'); Command Window Too many input arguments. Error in script (line 18) As = 4 * pi (D/2)^2; fx >> % m2 (suface area of the sphere) Zoom: 100% UTF-8 CRLF script x Workspace X > Name F cp D Hih k rho Hit Ti Tinf Value 390 0.0100 40 390 8900 1x50 double 473 293 Ln 27 Col SOLIDWORKS a E 98 PI Study Apply Simulation Thermal Connections Material Evaluator Loads Features Sketch Markup Evaluate 7 E 7. Sphere (Default < _Displ History Sensors Annotations Surface Bodies Solid Bodies(1) Revolve LOrigin Revolve Material a E 2378 PI G Study Apply Simulation Thermal Connections Shell Run Results Deformed Compare Material Evaluator Loads Manager Results 8 Features Sketch Markup Evaluate MBD Dimensions SOLIDWORKS Add-Ins Simulation MBD SOLIDWORKS CAM SOLIDWORKS CAM TBM Analysis Preparation Model name Sphere P54106 Study name: Initial Value(-Default) Plot type: Thermal Thermall Time step: 10 time: 1,000 Seconds < Sphere (Default < _Displ History Sensors Annotations 7. Surface Bodies Solid Bodies(1) Revolve Material Transient Sensor Graph File Options Help Temp (Kelvin) 400.00 380.00 360.00 340.00 320.00 300.00 280.00 100.00 Transient Sensor Graph 280.00 460.00 640.00 820.00 1,000.00 Time (sec) Thermal -38.6792, 408.067 X