Two approaches used in development of the thermal resistance network in the x-direction for multi-dimensional problems are to assume any plane normal to the x-axis to be isothermal and to assume any plane parallel to the x-axis to be adiabatic.
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- 1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.Drive an expression for heat transfer and temperature distribution for steady state one dimensional heat conduction in a plan wall. The temperature is maintained at a temperature Ti at x=0, while the other face X-L is maintained at temperature T2, the thickness of the wall may be taken as L and the energy equation is given by: d²T/dx² = 0. : Sketch a simple diagram for the temperature distribution in plane wall for a steady state one dimensional heat conduction, with heat generation. The surface temperature of the walls Ti and T2, for the cases Ti>T2, T1-T2, and T2>T1. The thickness of the wall may be taken as 2LA slender rod of length L, diameter d (L >> d) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2, to form a composite cylindrical rod oflength 2L. The heat transfer in radial direction and contact resistance are negligible. Find the effectivethermal conductivity of the composite rod.
- An annulus (e.g., a tube) has a temperature of Ti at the inner surface (at ri) and a temperature of To at the outer surface (at ro). Steady-state conditions prevail and there is not any heat generation in the annulus. However, the thermal conductivity k of the annulus is a strong function of temperature and can be described mathematically by the following function k(T) = a + bT + cT2. Calculate the total rate of heat flow (not heat flux) through the annulus if it is L long. Show steps to get to the answer attached.Write the finite difference form of the two dimensional steady state heat conduction equation with internal heat generation at a constant rate ‘g’ for a region 0.03m X 0.03m by using a mesh size ∆x=∆y= 0.01 m for a material having thermal conductivity 25 W/m.K and heat generation rate, 107 W/m3 . All the boundary surfaces are maintained at 10°C. Express the finite difference equations in matrix form for the unknown node temperatures.A composite wall is formed by sandwiching a 0.1 m thickness material between two steel slabs. The thermal conductivity of steel is 20 W/mK. We need to calculate the thermal conductivity of the material. The thickness of each steel slab is 0.4 m. The heat flux given at steady state is 20KW/m^2. The inner temperature of this composite wall is 700 K and the outer temperature is 200 K. Also calculate the temperature at the interface.
- A hollow cylindrical copper conductor 1.27cm. i.d. and 5.1cm. o.d. carries a current density 5000 amp/cm². For copper K = .38 kW/m°K and electrical resistivity = 2 x 10-6 ohm cm. Find the position and magnitude of the maximum temperature and the internal and external heat removal when (a) the outside temperature is 37.8°c and no heat removal occurs on the inside and (b) the outside is at 37.6°C and the inside at 27.2°C.Thermal Modeling The figure shows a thermal system involving two compartments with one containing a heater. The temperature of the compartment containing the heater is T1, the temperature of the other compartment is T2 and the temperature surrounding the compartment is T3, develop equations how temperatures T1 and T2 will vary with time. All the walls of the containers have the same resistance and negligible capacity. The two containers have the same capacity C. Also R1=R2=R Design the thermal modeling equation in chambers 1 and 2? CT CT, C T; TPlease provide accurate answer with proper steps The wall of the furnace is 30.48 mm thick and is insulated from outside. Thermal conductivity of the wall material is 0.1 W/m K and the insulation material is 0.01 W/m K. The furnace operates at 650 0C and the ambient temperature is 30 0 Allowable temperature on the outer side of the insulation is 1000C. Determine the overall heat transfer by conduction per unit area occurring across a furnace wall made from clay. If the air side heat transfer coefficient is 0.4 W/m2 K, calculate the minimum insulation thickness requirement.
- 2. The slab shown is embedded in insulating materials on five sides, while the front face experiences convection off its face. Heat is generated inside the material by an exothermic reaction equal to 1.0 kW/m'. The thermal conductivity of the slab is 0.2 W/mk. a. Simplify the heat conduction equation and integrate the resulting ID steady form of to find the temperature distribution of the slab, T(x). b. Present the temperature of the front and back faces of the slab. n-20- 10 cm IT- 25°C) 100 cm 100 cmA wall of a house is made from two layers of bricks enclosing a layer of insulation. A radiator is positioned to cover the whole internal surface, and used intermittently when the internal temperature is low. The external surface is exposed to the outside air. Which of the following assumptions could be used to identify the relevant reduced form of the conduction equation to find the temperature in the wall. a. Conduction is mainly in two directions. b. Conduction is mainly in one direction. c. The wall properties are homogeneous. d. Steady conditions exist. e. Unsteady conditions exist. f. There is an internal volumetric heat generation in the wall.A 1-D conduction heat transfer problem with internal energy generation is governed by the following equation: +-= dx2 =0 W where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that m-K T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the temperature at nodes 3 and 4. Insulated Ar , T For the answer window, enter the temperature at node 4 in Kelvin (K). Your Answer: EN SORN Answer units Pri qu) 232 PM 4/27/2022 99+ 66°F Sunny a . 20 ENLARGED oW TEXTURE PRT SCR IOS DEL F8 F10 F12 BACKSPACE num - %3D LOCK HOME PGUP 170