B: Set an expression for heat transfer rate through plane wall with thickness L and thermal conductivity k-ko (1+BT) where ko and ß are constant. The general heat equation can be taken as d/dx(k dT/dx)=0 and the boundary conditions are: X-0 T-T₁1 x=L_T=T₁2 9
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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 plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.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.
- Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are p=(1200*32)kg/mº, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux 9" =1000 W/m² is applied to the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated. 9" (W/m) T=0°C T=0°C W=(10*32)cm B=(30*32)cmThe 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.Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are p= 62400 kg/m', k-400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q%=1000 W/m² is applied to 2. the upper surface. The right and left surfaces are also kept at 0°C. Bottom surface is insulated. 9% (W/m³) y4 T = 0 °C T = 0°C W= 520 cm B=1560 cm
- Find the two-dimensional temperature distribution T(x,y) and midplane temperature T(B/2,W/2) under steady state condition. The density, conductivity and specific heat of the material are ρ =1200 kg/m 3, k=400 W/m.K, and cp=2500 J/kg.K, respectively. A uniform heat flux q =1000 W/m 2 is applied to the upper surface. The right and left surfaces are also kept at 0oC. Bottom surface is insulated.Qi: (50 marks) Find the total heat flux of the composite wall when: B KA = KC = KF = 15 m. K KB = KD = 10 m. K KE = KG = 20 %3D m. K D. Height of B = C = D 4 cm 3 cm 4 cm 6 cm Height of F = G AT = 30 KHeat flows through the wall in the following figure from the warm inside T, to the cooler The outside T, . In the center of the wall is a glass block of thickness t and thermal resistance R, . 2 thermal resistance of the wood and brick are R ,R, respectively. (a) wall, qw· The remainder of the wall is composed of two layers (wood and brick) each of thickness Find an expression for the steady state heat flow through the wood layer of the Determine the total resistance. (b) brick wood Rb Rw L glass Rg To TA
- 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 rDerive the general heat conduction equation in Cartesian coordinates. b) Electric heater wires are installed in a solid wall having a thickness of 8 cm and k =2.5W/m ◦C.The right face is exposed to an environment with h=50W/m2◦C and T∞ = 30°C, while the left face is exposed to h=75W/m2◦C and T∞ =50◦C. What is the maximum allowable heat-generation rate such that the maximum temperature in the solid does not exceed 300◦C?3.10 By neglecting lateral temperature variation in the analysis of fins, h,T. 木 H two-dimensional conduction is modeled as a one-dimensional H problem. То examine this T, h,T. approximation, consider a semi- infinite plate of thickness 2H. The base is maintained at uniform temperature T,. The plate exchanges heat by convection at its semi- infinite surfaces. The heat transfer coefficient is h and the ambient temperature is T.. Determine the heat transfer rate at the base.