1. Heat Conduction through a Slab with Energy Generation A solid slab of thickne

Question

1. Heat Conduction through a Slab with Energy Generation A solid slab of thickness d and infinite in extent in the lateral directions contains a source of heat which is producing energy at a rate per unit volume S=oz32, where z is the coordinate normal to the slab and z=0 is the lower face of the slab. The lower plate is maintained at a temperature To and at the upper face, z-d, air is blown over the slab at a temperature T) to keep the temperature in the slab below a critical temperature. The flow is fast enough so that a thermal boundary layer develops. The heat transfer to the air stream through the boundary layer can be described by a heat transfer coefficient h. (a) Use an energy shell balance to obtain a differential equation that describes the transport of heat within the slab. (b) Use the heat equation (equation of change of temperature) to obtain a differential equation that describes the transport of heat within the slab. Is this the same equation as the one that you derived in part (a)? (c) Obtain an expression for the temperature distribution within the slab. (d) What is the maximum temperature in the slab? Where is it located? (e) Calculate the temperature distribution for the case in which the lower plate is perfectly insulated rather than maintained at a temperature To. For which of the two cases is the maximum temperature the largest? Fluid at temperature To flows over inc. temp 1-10 Heat produced top s lower plate hear transfer through boundary layer desaribed by heat transfer coefficient h

Explanation / Answer

In this slab, both energy conduction as well as generation has been taken into account. From r an efficient and effective calculation, it is desirable that both factors needs it b considered.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.