The steady-state temperature distribution in a one dimensional wall of thermal conductivity 50 W/m^2.K and thickness 50 mm is observed to be T(C) = a + bx^2, where a = 200 C, b= -3000 C/m^2, and x is in meters. Determine the heat fluxes at x = L Determine the heat fluxes at x = 0 What is the heat generation rate in the wall 15000 W/m^2 0 W/m^2 300000 W/m^3
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- 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.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 170The temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h? - Degree Celsius 200°C q" In- q'in q'out= h = Choose... Choose.... Choose... L₂x K = 2.5 W/m.k T(x)-200-200 x +30x² q" Out 142.7 C 11 L=0.25 m Fluid Too = 100 °C h
- The heat flow per unit length of a thick cylindrical pipe is 772 W per meter. The pipe has radii ri = 12 cm, ro = 24 cm, outside surface temperature, To = 95 deg C and k = 0.05 + 0.0008T where T is in deg C and k is in W/(m K). Find the inside surface temperature of the pipe, assuming steady state conditions and accounting for the variation of thermal conductivity with temperature. Also determine the temperature of a point midway to the inside and outside radius.ähäi 100 Q1: Consider a long resistance wire of radius r1 = 0.3 cm and thermal conductivity kwire = %3D 17 W/m•°C in which heat is generated uniformly as a result of resistance heating at a constant rate of q = 100 W/cm3 (see Figure below). The wire is embedded in a 1-cm- thick layer of ceramic whose thermal conductivity is kceramic =1 W/m.°C. If the center temperature of the resistance wire is measured to be Tc= 705°C, determine the temperatures at the surface of ceramic and the interface of the wire and the ceramic layer under steady conditions.under steady-state conditions. If you are given T1 = 200 °C and T2 = 164 °C, determine: a) the conduction heat flux, q,.cond, in m2 W from x = 0 to x = L b) if the dimensions of the triangle ares 15 mm and h 13 mm, calculate the heat transfer due to convection, q,y, in W at x = L Finsulation T2 T T = 20°C h = 500 W/m2.K Triangular Prism x L x 0 L= 50 mm k = 100 W/m-K
- Need help on the Q.Which formula is used to calculate the heat conduction in the AXIAL direction in a vertically located pipe segment whose inner and outer surfaces are perfectly insulated. Here r, is inner radius, r, outer radius, Tri pipe inner surface temperature, Tro pipe outer surface temperature, L is the length of the pipe, T the temperature on the lower surface, Ty the temperature on upper surface. Tu r; Tro rProblem 4 A cork board (k = 0.039W/m K) 3 cm thick is exposed to air with an average temperature T.. = 30°C with a convection heat transfer coefficient, h = 25 W/m².K. The other surface of the board is held at a constant temperature of 15°C. A volumetric heat generation of 5 W/m³ is occurring inside the wall. Assuming one dimensional conduction, write the governing equation and express the boundary conditions for the wall. (solve the equation is not required) Problom
- H.W.: Q1: Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures at the selected nodes and the thermal conditions at the boundaries are as shown. The thermal conductivity of the body is k = 45 W/m. °C, and heat is generated in the body uniformly at a rate of g = 6 x 106 W/m3. Using the finite difference method with a mesh size of Ax = Ay = 5.0 cm, determine (a) the temperatures at nodes 1, 2, and 3 and (b) the rate of heat loss from the bottom surface through a 1-m-long section of the body. . 200°C 5 cm 5 cm g=6x 10 W/m² 260 3 240 305 290 Insulation 1 Convection T₂= 20°C, h= 50 W/m² °C 350°C 325A certain material has a thickness of 30 cm and a thermal conductivity of 0.04 W/m- °C. At a particular instant in time, the temperature distribution with x, the distance from the left face, is T = 150x ^ 2 - 30x , where x is in meters. Calculate the heat-flow rates atx x = 0 and x = 30 cm . Is the solid heating up or cooling down?pls ans quickly