First Temperature Derivatives Research Articles

The Thermal Absorption/Generation on Ferro-fluid Combined Convective Flow Over Curvilinear Porous Surfaces

In the influence of fluid buoyancy forces, the ferrofluid combined convective flow in porous curvilinear surfaces is studied with thermal generation/absorption effect. In the ambient flow conditions, the pressure gradient terms and ferrofluid buoyancy forces are replaced by the free steam velocity . The governing equations of the present problem are converted to ODEs by introducing non-dimensional functions and similarity variable. Boundary conditions of first derivative of velocities and temperature of our problem were constructed by the initial value problem, also the unknown initial conditions are found by shooting methods, and then a set of ODEs is solved numerically by the integration scheme of the six-order Range-Kutta method. The results of the solutions are presented graphically of velocity and thermal profiles with the help of MATLAB for different values of suction parameter and heat absorption parameter . Finally, the comparisons of the results highlight the justification of the numerical calculation accepted in the presence study. The problems in curvilinear surface study of boundary layer flow are complicated in fluid mechanics with applications of natural science and engineering.

Approximate analytical treatment of annular fins of rectangular profile for teaching fin heat transfer: Utilization of the mean value theorem for integrals

In the teaching of annular fins of rectangular profile, the main obstacle lies in solving the quasi one-dimensional heat conduction equation, the modified Bessel equation of first kind. In the modified Bessel equation, the variable coefficient [Formula: see text] multiplying the first order derivative of temperature [Formula: see text] is problematic. The principal objective of the present paper on engineering education is to solve the modified Bessel equation of first kind in approximate analytical form. Specifically, we seek to apply the mean value theorem for integrals to the variable coefficient [Formula: see text], viewed as an auxiliary function in the domain of the annular fin extending from the inner radius [Formula: see text] to the outer radius [Formula: see text]. It is demonstrated in a convincing manner that approximate analytical temperature distributions having exponential functions are easy to obtain without resorting to the exact analytical temperature distribution embodying four modified Bessel functions of first kind. Furthermore, the easiness in calculating heat transfer rates in annular fins of rectangular profile for realistic combinations of the two controlling parameters: the normalized radius ratio and the dimensionless thermo-geometrical parameter is verifiable.

Fluid flow and heat transfer modeling in the event of lost circulation and its application in locating loss zones

Lost circulation is one of the most persistent and costly drilling problems that drilling engineers have been struggling with for decades. The pinpointing of the zones of loss allows the treatments to be applied directly to the points of loss rather than to the entire open hole.This paper presents an approach to predict the location of single loss zone in a vertical well by interpreting the transient mud circulating temperature profiles altered by mud loss. The fluid flow and heat transfer numerical model in estimating the transient mud circulating temperature profiles during a lost circulation event was developed. The temperature profile in both the flow conduits (drillpipe and annulus) were modeled using mass and energy balances. The flow rate of drilling mud decreases in the annulus above the loss zone as part of the fluids lost into the fractures, which in turn alters the heat transmission status between the drillpipe, annulus, and near-wellbore formation. The wellbore is divided into two sections, which accounts for single loss zone. Case studies were performed and numerical solution results were presented and analyzed. According to the results, alterations induced by mud loss include: 1) Declines in both annular mud temperature and drillpipe mud temperature over time, and 2) Discontinuity in the first order derivative of annular mud temperature with respect to depth at the location of loss. By matching the simulated results with the distributed temperature measurements at different time stamps, the depth of the loss zone can be identified.

Analytical approach with Laplace transform to the inverse problem of one‐dimensional heat conduction transfer: Application to second and third boundary conditions

AbstractAn analytical method using Laplace transformation has been developed for one‐dimensional heat conduction. This method succeeded in explicitly deriving the analytical solution by which the surface temperature for the first kind of boundary condition can be well predicted. The analytical solutions for the surface temperature and heat flux are applied to the second and third of the boundary conditions. These solutions are also found to estimate the corresponding surface conditions with a high degree of accuracy when the surface conditions smoothly change. On the other hand, when these conditions erratically change such as the first derivative of temperature with time, the accuracy of the estimation becomes slightly less than that for a smooth condition. This trend in the estimation is similar irrespective of any kind of boundary condition. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 29–41, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10069

Analytical Approach with Laplace Transformation to the Inverse Problem of One Dimensional Heat Conduction. Application to Second and Third BoundaryConditions.

An analytical method using Laplace transformation has been developed for one-dimensional heat conduction. This method succeeded in explicitly deriving the analytical solution by which the surface temperature for the first kind of boundary condition can be predicted well. The analytical solutions for the surface temperature and heat flux are applied to the second and the third of boundary conditions. These solutions are also found to estimate the corresponding surface conditions with a high accuracy when the surface conditions smoothly change. On the other hand, when these conditions sharply change such as the first derivative of temperature with time, the accuracy of the estimation becomes a little less than that for a smooth condition. This trend in the estimation accuracy is similar irrespective of any kind of boundary condition.