22. Develop an algorithm, along with the program (preferably in python), to find thetemperature distribution in the example belowNOTE: Use the explicit finite differences methodEXAMPLE 5.9A fuel element of a nuclear reactor is in the shape of a plane wall of thickness2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². Kand T=250°C. At normal operating power, heat is generated uniformly within theelement at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-stateconditions associated with normal operation will occur if there is a change in thegeneration rate. Consider a sudden change to q₂ = 2 × 107 W/m³, and use theexplicit finite-difference method to determine the fuel element temperature distribu-tion after 1.5 s. The fuel element thermal properties are k = 30 W/m . K and a =5 × 10-6 m²/s.

import numpy as np # Constants and parameters L = 0.01 # Thickness of the wall (m) h = 1100 #…

Answered: 22. Develop an algorithm, along with…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.27P

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To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After the system had reached equilibrium, an operator recorded the thermocouple readings shown below for two different environmental conditions: Distance from the Surface (cm) Temperature (C) Test 1 0 40 5 65 10 97 15 132 Test 2 0 95 5 130 10 168 15 208 From these data, determine an approximate expression for the thermal conductivity as a function of temperature between 40 and 208C.
2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
1.)An aluminum tank with a volume of 1000 liters is filled with gasoline. Both are at a temperature of 12°C. The tank is transported to a place where the temperature is 37° and, due to the difference between the volumetric expansion coefficients of the metal and the liquid, the ebb of the tank. Assuming the tank expands like a massive volume of aluminum, how many liters of gasoline overflow from the tank? Data: βaluminum=7*10-5/ºC and βgas=9.5*10-4/ºC
Over the ocean surface, the Bowen ratio is estimated to be about 0.2. Estimate the sensible heat and latent heat fluxes to the atmosphere, as well as the rate of evaporation, in millimeters per day, from the ocean surface, when the net radiation received just above the surface is 800W per m^2 , the heat flux to the water below 55 m is negligible, the rate of warming of the 55 m deep oceanic mixed layer is 0.12 deg. Celsius per day, and the sea surface temperature is 27deg. Celsius.
A truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form D = ax3/2, where a = 2 m−1/2. The sides are well insulated, while the top surface of the cone at x1 is maintained at T1 and the bottom surface at x2 is maintained at T2. Conductivity k = 336 W/m-K (a) Obtain an expression for the temperature distribution T(x). (b) What is the rate of heat transfer across the cone if it is constructed of pure aluminum with x1 = 0.086 m, T1 = 113°C, x2 = 0.270 m, and T2 = 25°C?
Solve for the temperature distribution of a long, thin circular solid tube with a length of 10 cm (shown in Figure2), using the Finite Difference Method: Parabolic Equation (Explicit Method). The following values of the circular solid tube is as provided: k’= 0.49 cal/ (s · cm · oC), Δt = 0.1 s and Δx = 2 cm. When t = 0, the temperature of the circular solid tube is zero and the boundary conditions are fixed for all times at temperature T, at x = 0 cm is 100oC where as the temperature T, at x =10 is 50oC. From this information it is given that the circular solid rod is made of material with heat capacity, C = 0.2174 cal/(g· oC) and density (ρ) = 2.7 g/cm3. Use Explicit Method to solve this problem. Task: A Visual Basic of the FDM solution for (a) has been initially developed based on the required calculation of task Q2(a). The source code is as provided below (may need some minor tweak): Option Explicit Sub Explicit() Dim i As Integer, j As Integer, np As Integer, ns As Integer…
QUESTION-) 236 °C steam flows in a pipe which features are given below. Inner and outer diameters of pipe are 300 mm and 320 mm. Coefficient of heat transmission is 40 W/mK. It's external ambient is air and it's temperature is 20 °C. Take the temperature of the pipe's external surface 180 °C. It is known that the internal temp convection coefficient is 600 W/m^2K and external heat transfer coefficient is 5,9109 W/m^2K The pipe's length is 500 meter. You need to add the radiation in the calculation. The rate of the radiation emissivity is 0.85. You can take the environmental surface temp directly. a-) Please draw this question on the resistance network. b-) Please calculate the heat loss of pipe. c-) By applying insulation to this pipe, it is desired to reduce the heat loss to 20% of the uninsulated loss (option a). Calculate the insulation thickness accordingly. Take glass wool as insulation material.(Conductivity of glass wool = 0.040 W/mK.) Given, The temperature of steam inside the…
After the sinking of RMS Titanic, US operated the International Ice patrol with the purpose of monitoring the presence and movements of icebergs in the Atlantic and Arctic oceans. Once, they observed a unique tabular iceberg in a form of a rectangle (250 km x 50 km x 300 m). How many years would it take to melt the iceberg solely by heat from the sun if the ice absorbs a mean of 98 J/m2 -s, 12.5 hrs per day? Note: the exposed area for heating is 250 km x 50 km and the density is 920 kg/m3 . This is my solution.
QUESTION-) 236 °C steam flows in a pipe which features are given below. Inner and outer diameters of pipe are 300 mm and 320 mm. Coefficient of heat transmission is 40 W/mK. It's external ambient is air and it's temperature is 20 °C. Take the temperature of the pipe's external surface 180 °C. It is known that the internal temp convection coefficient is 600 W/m^2K and external heat transfer coefficient is 5.9109 W/m^2K The pipe's length is 500 meter. You need to add the radiation in the calculation. The rate of the radiation emissivity is 0.85. You can take the environmental surface temp directly. IMPORTANT NOTE: Hi. I sent this question to be solved 3 times. But I faced with different and wrong answers in all. What i want to ask is that doesn't all the resistances except conduction and convection resistances need to change after adding the insulation materials to the pipe? In the solution the people who solved this question took the external surface temp constant. Shouldn't the…
Question 2: The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA 20 W/m K and kC50 W/m K, and known thickness, LA 0.30 m and LC 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o 20°C, an inner surface temperature of Ts,i 600°C, and an oven air temperature of T 800°C. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of kB?
Steam is being transported in a pipe at a chemical production facility in Gebze, Kocaeli. Theouter diameter of the pipe is 8 cm, and the surrounding air temperature is 20 °C. On the surface of thepipe, the combined heat transfer coefficient is 35 W/m2*K. The surface temperature of the pipe is 150 °C.Steady-state conditions exist.(a) What is the rate of heat loss from the pipe to the surroundings?(b) The power used to generate the steam is obtained from natural gas. Perform an online search forapproximate values of the calorific value of natural gas, as well as the cost of natural gas per cubicmeter, and estimate the financial loss due to heat loss from this steam pipe within a period of oneyear. Indicate your sources clearly in your answer.
1. Residual oil, with a heating value of 18,480 BTU/bm, is used as a fuel in a power plant which produces 947,870 BTU/s of electricity. The overall efficiency of the power plant is 52 Determine the: a. Heat input, in BTUs b. Daily fuel consumption, in lbm C. Dimensions of the cylindrical storage (assuming length is equal to the diameter), in ft. d. Heat rejected the environment, in BTU/s. The density of the oil is 62 ID/ft.

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