Thermal Interaction between Two Forced‐Convection Boundary Layers across a Conductive Solid Wall

Abstract

This paper presents an analytical model to the problem of thermal interaction between two forced convection layers of parallel flow on opposite wall sides. The problem is formulated in dimensionless terms to generalize the solution. The two convection layers are analyzed separately by employing the integral technique. The two analyses are then coupled by applying the solid-fluid interfacial conditions. The study indicates that the thermal interaction process is governed mainly by two dimensionless parameters relating the heat transfer effectiveness of two interactive convection modes and wall conduction. The effects of governing parameters on the flow and heat transfer characteristics of two coupled convection layers are documented. Results regarding mean conjugate Nusselt number are obtained for wide ranges of governing parameters. C⃝

Two Coupled Forced‐Convection Boundary Layers of Counter‐Flow

“…6. It is noted that the Nu number increases with an increase in the -parameter to approach the asymptotic result (24) as →Ý, while Nu decreases with a decrease in the -parameter to approach finally the asymptotic result (25) as goes to zero. This behavior is expected when considering the physical meaning of the -parameter defined by Eq.…”

“…The above result is also the same exact one of forced convection on an isothermal plane surface. Here, it is important to state that asymptotic results (24) and (25) prove the model's validity.…”

“…Hence, the solution trials are stopped. In preliminary solution tests, asymptotic results (24) and (25) were used as a reference to check the correctness of numerical results as well to adjust its accuracy. It has been found that the solution with step size ΔX = 0.005 gives stable and reliable results.…”

“…To overcome the singularity problem encountered in solving the resultant governing equations due to the elliptical nature of this counter flow problem, an efficient iterative numerical procedure is applied. This solution problem has not been encountered in our previous model [25] of parallel-flow arrangement due to its parabolic nature. The main advantage of such a semianalytical model is that the role of the derived dimensionless parameters controlling the conjugate heat transfer process becomes more evident than in a numerical model.…”

“…This is due to its significance for the design and operation of many types of heat transfer equipment, such as heat exchangers and electronic cooling systems. Several studies dealing with parallel flow [24,25] and counter-flow [26][27][28][29] arrangements have recently been reported. These studies indicated that the theoretical treatment of the counter-flow pattern yields a more complex mathematical problem compared to that of the parallel flow pattern, even with neglecting the longitudinal conduction in both fluid and solid domains.…”