Heat Transfer Coefficient
Practice Problems Set – 1 MEC301: Heat Transfer
Q.1 The slab shown in the figure is embedded on five sides in insulation materials. The sixth side is exposed to an ambient temperature through a heat transfer coefficient. Heat is generated in the slab at the rate of 1.0 kW/m3. The thermal conductivity of the slab is 0.2 W/m-K. (a) Solve for the temperature distribution in the slab, noting any assumptions you must make. Be careful to clearly identify the boundary conditions. (b) Evaluate T at the front and back faces of the slab. (c) Show that your solution gives the expected heat fluxes at the back and front faces.
Q.2
Compute overall heat transfer coefficient U for the slab shown in the figure.
Given: Ls = 2 mm = 0.002 m Lc = 3 mm = 0.003 m ks = 17 W/m-K kc = 372 W/m-K Q.3 A 4 mm diameter spherical ball at 50oC is covered by a 1 mm thick plastic insulation (k = 0.13 W/m-K). The ball is exposed to a medium at 15oC, with a combined convection and radiation heat transfer coefficient of 20 W/m2-K. Determine if the plastic insulation on the ball will help or hurt heat transfer from the ball. Q.4 Prove that if k varies linearly with T in a slab, and if heat transfer is one-dimensional and steady, then q may be evaluated precisely using k evaluated at the mean temperature in the slab.
Q.5 Layers of equal thickness of spruce and pitch pine are laminated to make an insulating material. How should the laminations be oriented in a temperature gradient to achieve the best effect? Given: kspruce = 0.11 W/m-K ; kpine = 0.14 W/m-K. Q.6 Consider the composite wall shown in figure. The concrete and brick sections are of equal thickness. Determine T1, T2, q, and the percentage of q that flows through the brick. To do this, approximate the heat flow as one-dimensional. Draw the thermal circuit for the wall and identify all four resistances before you begin.
Q.7 A furnace wall slab is constructed with fire clay of thickness 90 mm (L1) inside and red brick of thickness
Q.1 The slab shown in the figure is embedded on five sides in insulation materials. The sixth side is exposed to an ambient temperature through a heat transfer coefficient. Heat is generated in the slab at the rate of 1.0 kW/m3. The thermal conductivity of the slab is 0.2 W/m-K. (a) Solve for the temperature distribution in the slab, noting any assumptions you must make. Be careful to clearly identify the boundary conditions. (b) Evaluate T at the front and back faces of the slab. (c) Show that your solution gives the expected heat fluxes at the back and front faces.
Q.2
Compute overall heat transfer coefficient U for the slab shown in the figure.
Given: Ls = 2 mm = 0.002 m Lc = 3 mm = 0.003 m ks = 17 W/m-K kc = 372 W/m-K Q.3 A 4 mm diameter spherical ball at 50oC is covered by a 1 mm thick plastic insulation (k = 0.13 W/m-K). The ball is exposed to a medium at 15oC, with a combined convection and radiation heat transfer coefficient of 20 W/m2-K. Determine if the plastic insulation on the ball will help or hurt heat transfer from the ball. Q.4 Prove that if k varies linearly with T in a slab, and if heat transfer is one-dimensional and steady, then q may be evaluated precisely using k evaluated at the mean temperature in the slab.
Q.5 Layers of equal thickness of spruce and pitch pine are laminated to make an insulating material. How should the laminations be oriented in a temperature gradient to achieve the best effect? Given: kspruce = 0.11 W/m-K ; kpine = 0.14 W/m-K. Q.6 Consider the composite wall shown in figure. The concrete and brick sections are of equal thickness. Determine T1, T2, q, and the percentage of q that flows through the brick. To do this, approximate the heat flow as one-dimensional. Draw the thermal circuit for the wall and identify all four resistances before you begin.
Q.7 A furnace wall slab is constructed with fire clay of thickness 90 mm (L1) inside and red brick of thickness