Consider steady-state conditions for one-dimensional conduction
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 50 W/m·K and thickness L = 0.35 m, with no internal heat generation
Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indicating the direction of the heat flux.
Homework Answers
A large plane wall has a constant thermal conductivity of 8.5W/(m·K), a surface area of 15...
A large plane wall has a constant thermal conductivity of 8.5W/(m·K), a surface area of 15 m² and a thickness L=25 cm. The temperature on the leftside of the wall (T0) is constant and measured at 0.0°C. A constant heat flux(푞̇H)of 450.0 W/m² entersthe rightside of the wall.a.Express the differential equation and the boundary conditions(mathematical formulation)for steady one-dimensional heat conduction through the wall.b.Obtain a numerical equationfor the variation of temperature in the wall by solving the differential equation. c.Evaluate the...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surfa...
need help with c and d
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the...
ncat transfer system. Question 3-30 points The steady-state temperature distribution in a one-dimensional wall of 20...
ncat transfer system. Question 3-30 points The steady-state temperature distribution in a one-dimensional wall of 20 W/m-K and thickness L 20 cm is of the form T(x) Ax Bx +Cx + D, where A 20 Crn, B-l 50°C/㎡, C =-120°C/m, D-200 ℃ Find (i) the heat generation rate per unit thermal conductivity, k
A plane wall with thermal conductivity of k, is insulated on one side and is exposed...
A plane wall with thermal conductivity of k, is insulated on one side and is exposed to ambient air at To and convection coefficient of h, on the other side. A heat source in the 3) wall is generating a uniform heat rate per unit volume of For one-dimensional steady-state conduction in the wall, derive a proper differential equation for the temperature by either using the heat equations or doing the energy balance. Identify proper boundary conditions and find the...
20) Me Steady-state temperature distribution in the s figure. The heat flow is one-dimensional. ibution in...
20) Me Steady-state temperature distribution in the s figure. The heat flow is one-dimensional. ibution in the sandwich of three materials (A, B, and C) is shown in the aterial B has volumetric heat generation à = 64,000 W/m. Material A has thermal conductivity of 10 W/ m K . Determine: a) The heat flux at the left side: b) The heat flux at the right side: c) The thermal conductivity of Material C: : - W/m2 W/m2 _W/mK T[deg.]...
Consider steady one-dimensional conduction in a slab having a thickness of L and a constant thermal...
Consider steady one-dimensional conduction in a slab having a thickness of L and a constant thermal conductivity of k. The two ends are maintained at temperatures T_0 (at x = 0), and T_L (at x = L). There is a heat source, with strength A(x/L)(1 - x/L) W/cm^3. a) Define a set of dimensionless independent variables (depending on position), and a dimensionless dependent variable. b) Obtain a differential equation in which each term is dimensionless. c) Define an appropriate dimensionless...
19. The temperature distribution in a plane wall will be during steady and one-dimensional heat transfer...
19. The temperature distribution in a plane wall will be during steady and one-dimensional heat transfer with non-constant wall thermal conductivity. a. Straight line b. Linear c. Non-linear
2. A one dimensional plane wall of thickness L=80 mm experiences uniform thermal energy generation of...
2. A one dimensional plane wall of thickness L=80 mm experiences uniform thermal energy generation of q = 1000 W/m and is convectively cooled at x=140 mm by an ambient fluid characterized by T=30°C. If the steady state temperature distribution within the wall is T(x)mall-x)+b where a=15°C/m and b=40*C, what is the thermal conductivity of the wall? L=80mm
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k...
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k = 2.5 W/m K and surface area A = 20.0 m². Both sides of the slab is maintained at a constant wall temperature of 358°K while it is subjected to a uniform but constant heat flux of 950.0 W/m2 Evaluate the temperature distribution/profile within the wall. Calculate the heat flux and temperature at location x = 0.1m. Problem 3: Consider a 10.0 m long...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
need help with c and d
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the...
ncat transfer system. Question 3-30 points The steady-state temperature distribution in a one-dimensional wall of 20 W/m-K and thickness L 20 cm is of the form T(x) Ax Bx +Cx + D, where A 20 Crn, B-l 50°C/㎡, C =-120°C/m, D-200 ℃ Find (i) the heat generation rate per unit thermal conductivity, k
A plane wall with thermal conductivity of k, is insulated on one side and is exposed to ambient air at To and convection coefficient of h, on the other side. A heat source in the 3) wall is generating a uniform heat rate per unit volume of For one-dimensional steady-state conduction in the wall, derive a proper differential equation for the temperature by either using the heat equations or doing the energy balance. Identify proper boundary conditions and find the...
20) Me Steady-state temperature distribution in the s figure. The heat flow is one-dimensional. ibution in the sandwich of three materials (A, B, and C) is shown in the aterial B has volumetric heat generation à = 64,000 W/m. Material A has thermal conductivity of 10 W/ m K . Determine: a) The heat flux at the left side: b) The heat flux at the right side: c) The thermal conductivity of Material C: : - W/m2 W/m2 _W/mK T[deg.]...
Consider steady one-dimensional conduction in a slab having a thickness of L and a constant thermal conductivity of k. The two ends are maintained at temperatures T_0 (at x = 0), and T_L (at x = L). There is a heat source, with strength A(x/L)(1 - x/L) W/cm^3. a) Define a set of dimensionless independent variables (depending on position), and a dimensionless dependent variable. b) Obtain a differential equation in which each term is dimensionless. c) Define an appropriate dimensionless...
19. The temperature distribution in a plane wall will be during steady and one-dimensional heat transfer with non-constant wall thermal conductivity. a. Straight line b. Linear c. Non-linear
2. A one dimensional plane wall of thickness L=80 mm experiences uniform thermal energy generation of q = 1000 W/m and is convectively cooled at x=140 mm by an ambient fluid characterized by T=30°C. If the steady state temperature distribution within the wall is T(x)mall-x)+b where a=15°C/m and b=40*C, what is the thermal conductivity of the wall? L=80mm
Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k = 2.5 W/m K and surface area A = 20.0 m². Both sides of the slab is maintained at a constant wall temperature of 358°K while it is subjected to a uniform but constant heat flux of 950.0 W/m2 Evaluate the temperature distribution/profile within the wall. Calculate the heat flux and temperature at location x = 0.1m. Problem 3: Consider a 10.0 m long...
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